Color difference - Wikipedia

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class="mw-page-title-main">Color difference</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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<div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Metric for difference between two colors</div> <p>In <a href="/wiki/Color_science" title="Color science">color science</a>, <b>color difference</b> or <b>color distance</b> is the separation between two <a href="/wiki/Color" title="Color">colors</a>. This <a href="/wiki/Metric_space" title="Metric space">metric</a> allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of great importance to those whose work is color-critical. Common definitions make use of the <a href="/wiki/Euclidean_distance" title="Euclidean distance">Euclidean distance</a> in a <a href="/wiki/Cross-platform_software" title="Cross-platform software">device-independent</a> <a href="/wiki/Color_space" title="Color space">color space</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Euclidean">Euclidean</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=1" title="Edit section: Euclidean"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="sRGB">sRGB</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=2" title="Edit section: sRGB"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As most definitions of color difference are distances within a <a href="/wiki/Color_space" title="Color space">color space</a>, the standard means of determining distances is the Euclidean distance. If one presently has an RGB (red, green, blue) tuple and wishes to find the color difference, computationally one of the easiest is to consider <i>R</i>, <i>G</i>, <i>B</i> linear dimensions defining the color space. </p><p>A very simple example can be given between the two colors with RGB values (0, 64, 0) (<span style="display:inline-block;border:1.62px solid black;vertical-align:text-top;" title="#004000"><span class="mw-no-invert" style="display:block;padding:0;width:1em;height:1em;background:#004000;color:inherit;"> </span></span>) and (255, 64, 0) (<span style="display:inline-block;border:1.62px solid black;vertical-align:text-top;" title="#ff4000"><span class="mw-no-invert" style="display:block;padding:0;width:1em;height:1em;background:#FF4000;color:inherit;"> </span></span>): their distance is 255. Going from there to (255, 64, 128) (<span style="display:inline-block;border:1.62px solid black;vertical-align:text-top;" title="#ff4080"><span class="mw-no-invert" style="display:block;padding:0;width:1em;height:1em;background:#FF4080;color:inherit;"> </span></span>) is a distance of 128. </p><p>When we wish to calculate distance from the first point to the third point (i.e. changing more than one of the color values), we can do this: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{distance}}={\sqrt {(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>distance</mtext> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{distance}}={\sqrt {(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15763fc04b6dbbc90c64db3b39a1442106a394af" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:54.177ex; height:4.843ex;" alt="{\displaystyle {\text{distance}}={\sqrt {(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}}}.}"></span> </p><p>When the result should be computationally simple as well, it is often acceptable to remove the square root and simply use </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{distance}}^{2}=(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>distance</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{distance}}^{2}=(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d43d0de6c828f8e3e85f746ceacb2ee734f2b42" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:52.907ex; height:3.176ex;" alt="{\displaystyle {\text{distance}}^{2}=(R_{2}-R_{1})^{2}+(G_{2}-G_{1})^{2}+(B_{2}-B_{1})^{2}.}"></span> </p><p>This will work in cases when a single color is to be compared to a single color and the need is to simply know whether a distance is greater. If these squared color distances are summed, such a metric effectively becomes the <a href="/wiki/Variance" title="Variance">variance</a> of the color distances. </p><p>There have been many attempts to weigh RGB values to better fit human perception, where the components are commonly weighted (red 30%, green 59%, and blue 11%), however, these are demonstrably<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (March 2022)">citation needed</span></a></i>]</sup> worse at color determinations and are properly the contributions to the brightness of these colors, rather than to the degree to which human vision has less tolerance for these colors. The closer approximations would be more properly (for non-linear <a href="/wiki/SRGB" title="SRGB">sRGB</a>, using a color range of 0–255):<sup id="cite_ref-euc_1-0" class="reference"><a href="#cite_note-euc-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{cases}{\sqrt {2\Delta R^{2}+4\Delta G^{2}+3\Delta B^{2}}},&{\bar {R}}<128,\\{\sqrt {3\Delta R^{2}+4\Delta G^{2}+2\Delta B^{2}}}&{\text{otherwise}},\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>3</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>R</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo><</mo> <mn>128</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>2</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mtext>otherwise</mtext> </mrow> <mo>,</mo> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{cases}{\sqrt {2\Delta R^{2}+4\Delta G^{2}+3\Delta B^{2}}},&{\bar {R}}<128,\\{\sqrt {3\Delta R^{2}+4\Delta G^{2}+2\Delta B^{2}}}&{\text{otherwise}},\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f50986379fe97fcefc2f5f72babe60606b022e1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:41.635ex; height:7.509ex;" alt="{\displaystyle {\begin{cases}{\sqrt {2\Delta R^{2}+4\Delta G^{2}+3\Delta B^{2}}},&{\bar {R}}<128,\\{\sqrt {3\Delta R^{2}+4\Delta G^{2}+2\Delta B^{2}}}&{\text{otherwise}},\end{cases}}}"></span> </p><p>where: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\Delta R&=R_{1}-R_{2},\\\Delta G&=G_{1}-G_{2},\\\Delta B&=B_{1}-B_{2},\\{\bar {R}}&={\frac {1}{2}}(R_{1}+R_{2}).\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>R</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>G</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>B</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>R</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Delta R&=R_{1}-R_{2},\\\Delta G&=G_{1}-G_{2},\\\Delta B&=B_{1}-B_{2},\\{\bar {R}}&={\frac {1}{2}}(R_{1}+R_{2}).\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0b2a7aaeeb8abed8de9644b58586f6882e786a04" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.307ex; margin-bottom: -0.198ex; width:20.544ex; height:14.176ex;" alt="{\displaystyle {\begin{aligned}\Delta R&=R_{1}-R_{2},\\\Delta G&=G_{1}-G_{2},\\\Delta B&=B_{1}-B_{2},\\{\bar {R}}&={\frac {1}{2}}(R_{1}+R_{2}).\end{aligned}}}"></span> </p><p>One of the better low-cost approximations, sometimes called "redmean", combines the two cases smoothly:<sup id="cite_ref-euc_1-1" class="reference"><a href="#cite_note-euc-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}{\bar {r}}&={\frac {1}{2}}(R_{1}+R_{2}),\\\Delta C&={\sqrt {\left(2+{\frac {\bar {r}}{256}}\right)\Delta R^{2}+4\Delta G^{2}+\left(2+{\frac {255-{\bar {r}}}{256}}\right)\Delta B^{2}}}.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <mi>C</mi> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">¯</mo> </mover> </mrow> <mn>256</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>4</mn> <mi mathvariant="normal">Δ</mi> <msup> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>255</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mrow> <mn>256</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>B</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}{\bar {r}}&={\frac {1}{2}}(R_{1}+R_{2}),\\\Delta C&={\sqrt {\left(2+{\frac {\bar {r}}{256}}\right)\Delta R^{2}+4\Delta G^{2}+\left(2+{\frac {255-{\bar {r}}}{256}}\right)\Delta B^{2}}}.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ee06baaa28944c5b1e06876439d1b579cf03c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -6.005ex; width:60.092ex; height:13.176ex;" alt="{\displaystyle {\begin{aligned}{\bar {r}}&={\frac {1}{2}}(R_{1}+R_{2}),\\\Delta C&={\sqrt {\left(2+{\frac {\bar {r}}{256}}\right)\Delta R^{2}+4\Delta G^{2}+\left(2+{\frac {255-{\bar {r}}}{256}}\right)\Delta B^{2}}}.\end{aligned}}}"></span> </p><p>There are a number of color distance formulae that attempt to use color spaces like <a href="/wiki/HSL_and_HSV" title="HSL and HSV">HSV</a> or <a href="/wiki/HSL_and_HSV" title="HSL and HSV">HSL</a> with the hue represented as a circle, placing the various colors within a three-dimensional space of either a cylinder or cone, but most of these are just modifications of RGB; without accounting for differences in human color perception, they will tend to be on par with a simple Euclidean metric.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This seems correct so surely somebody has said it in a book before. (January 2023)">citation needed</span></a></i>]</sup> </p> <div class="mw-heading mw-heading3"><h3 id="Uniform_color_spaces">Uniform color spaces</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=3" title="Edit section: Uniform color spaces"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>CIELAB and CIELUV are relatively perceptually-uniform color spaces and they have been used as spaces for Euclidean measures of color difference. The CIELAB version is known as CIE76. However, the non-uniformity of these spaces were later discovered, leading to the creation of more complex formulae. </p> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="#Tolerance">§ Tolerance</a></div> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p><a href="/wiki/Uniform_color_space" class="mw-redirect" title="Uniform color space">Uniform color space</a>: a color space in which equivalent numerical differences represent equivalent visual differences, regardless of location within the color space. A truly uniform color space has been the goal of color scientists for many years. Most color spaces, though not perfectly uniform, are referred to as uniform color spaces, since they are more nearly uniform when compared to the chromaticity diagram. </p><div class="templatequotecite">— <cite>X-rite glossary<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></cite></div></blockquote> <p>A uniform color space is supposed to make a simple measure of color difference, usually Euclidean, "just work". Color spaces that improve on this issue include <a href="/wiki/CIECAM02#Color_spaces" title="CIECAM02">CAM02-UCS</a>, CAM16-UCS, and J<sub>z</sub>a<sub>z</sub>b<sub>z</sub>.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Rec._ITU-R_BT.2124_or_ΔEITP"><span id="Rec._ITU-R_BT.2124_or_.CE.94EITP"></span>Rec. ITU-R BT.2124 or Δ<i>E</i><sub>ITP</sub></h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=4" title="Edit section: Rec. ITU-R BT.2124 or ΔEITP"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 2019 a new standard for <a href="/wiki/Wide_Color_Gamut" class="mw-redirect" title="Wide Color Gamut">WCG</a> and <a href="/wiki/High-dynamic-range_video" class="mw-redirect" title="High-dynamic-range video">HDR</a> was introduced, since CIEDE2000 was not adequate for it: CIEDE2000 is not reliable below 1 cd/m<sup>2</sup> and has not been verified above 100 cd/m<sup>2</sup>; in addition, even in BT.709 blue primary CIEDE2000 is underpredicting the error.<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Δ<i>E</i><sub>ITP</sub> is scaled so that a value of 1 indicates the potential of a just noticeable color difference. The Δ<i>E</i><sub>ITP</sub> color difference metric is derived from display referenced <a href="/wiki/ICtCp" title="ICtCp">IC<sub>T</sub>C<sub>P</sub></a>, but XYZ is also available in the standard. The formula is a simply scaled Euclidean distance:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{\text{ITP}}=720{\sqrt {(I_{1}-I_{2})^{2}+(T_{1}-T_{2})^{2}+(P_{1}-P_{2})^{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>ITP</mtext> </mrow> </msub> <mo>=</mo> <mn>720</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{\text{ITP}}=720{\sqrt {(I_{1}-I_{2})^{2}+(T_{1}-T_{2})^{2}+(P_{1}-P_{2})^{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8d781f03bd08160527147ee227dfea354b01c90" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:53.203ex; height:4.843ex;" alt="{\displaystyle \Delta E_{\text{ITP}}=720{\sqrt {(I_{1}-I_{2})^{2}+(T_{1}-T_{2})^{2}+(P_{1}-P_{2})^{2}}},}"></span> </p><p>where the components of this "ITP" is given by </p> <dl><dd><i>I</i> = <i>I</i>,</dd> <dd><i>T</i> = 0.5 <i>C</i><sub><i>T</i></sub>,</dd> <dd><i>P</i> = <i>C</i><sub><i>P</i></sub>.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Other_geometric_constructions">Other geometric constructions</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=5" title="Edit section: Other geometric constructions"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Euclidean measure is known to work poorly on large color distances (i.e. more than 10 units in most systems). A hybrid approach where a <a href="/wiki/Taxicab_distance" class="mw-redirect" title="Taxicab distance">taxicab distance</a> is used between the lightness and the chroma plane, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Delta E_{\text{HyAB}}={\sqrt {(a_{2}-a_{1})^{2}+(b_{2}-b_{1})^{2}}}+\left|L_{2}-L_{1}\right|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>HyAB</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>+</mo> <mrow> <mo>|</mo> <mrow> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Delta E_{\text{HyAB}}={\sqrt {(a_{2}-a_{1})^{2}+(b_{2}-b_{1})^{2}}}+\left|L_{2}-L_{1}\right|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a499033c59313b2f0b5028a455236a4fc789af89" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:48.971ex; height:3.343ex;" alt="{\textstyle \Delta E_{\text{HyAB}}={\sqrt {(a_{2}-a_{1})^{2}+(b_{2}-b_{1})^{2}}}+\left|L_{2}-L_{1}\right|}"></span>, is shown to work better on CIELAB.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="CIELAB_ΔE*"><span id="CIELAB_.CE.94E.2A"></span>CIELAB ΔE*</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=6" title="Edit section: CIELAB ΔE*"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Missing_information plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/44px-Wiki_letter_w.svg.png" decoding="async" width="44" height="44" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/66px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/6c/Wiki_letter_w.svg/88px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This section <b>is missing information</b> about acceptability difference values in industry.<span class="hide-when-compact"> Please expand the section to include this information. Further details may exist on the <a href="/wiki/Talk:Color_difference" title="Talk:Color difference">talk page</a>.</span> <span class="date-container"><i>(<span class="date">July 2021</span>)</i></span></div></td></tr></tbody></table> <p>The <a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">International Commission on Illumination</a> (CIE) calls their distance metric <span class="texhtml">Δ<i>E*</i></span> (also inaccurately called <span class="texhtml"><i>dE</i>*</span>, <span class="texhtml mvar" style="font-style:italic;">dE</span>, or "Delta E") where <a href="/wiki/Delta_(letter)" title="Delta (letter)">delta</a> is a <a href="/wiki/Greek_letter" class="mw-redirect" title="Greek letter">Greek letter</a> often used to denote difference, and <b>E</b> stands for <i>Empfindung</i>; German for "sensation". Use of this term can be traced back to <a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a> and <a href="/wiki/Ewald_Hering" title="Ewald Hering">Ewald Hering</a>.<sup id="cite_ref-google_7-0" class="reference"><a href="#cite_note-google-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-google2_8-0" class="reference"><a href="#cite_note-google2-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Perceptual non-uniformities in the underlying <a href="/wiki/CIELAB" class="mw-redirect" title="CIELAB">CIELAB</a> color space have led to the CIE refining their definition over the years, leading to the superior (as recommended by the CIE) 1994 and 2000 formulas.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> These non-uniformities are important because <a href="/wiki/Color_vision#Physiology_of_color_perception" title="Color vision">the human eye is more sensitive to certain colors than others</a>. CIELAB metric is used to define color tolerance of CMYK solids. A good metric should take this into account in order for the notion of a "<a href="/wiki/Just_noticeable_difference" class="mw-redirect" title="Just noticeable difference">just noticeable difference</a>" (JND) to have meaning. Otherwise, a certain <span class="texhtml">Δ<i>E</i></span> may be insignificant between two colors in one part of the color space while being significant in some other part.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>All <span class="texhtml">Δ<i>E*</i></span> formulae are originally designed to have the difference of 1.0 stand for a JND. This convention is generally followed by other perceptual distance functions such as the aforementioned <span class="texhtml">Δ<i>E</i><sub>ITP</sub></span>.<sup id="cite_ref-colorwiki_11-0" class="reference"><a href="#cite_note-colorwiki-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> However, further experimentation may invalidate this design assumption, the revision of CIE76 <span class="texhtml">Δ<i>E</i><sup>*</sup><sub><i>ab</i></sub></span> JND to 2.3 being an example.<sup id="cite_ref-CIE76_JND_12-0" class="reference"><a href="#cite_note-CIE76_JND-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="CIE76">CIE76</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=7" title="Edit section: CIE76"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The CIE 1976 color difference formula is the first formula that related a measured color difference to a known set of CIELAB coordinates. This formula has been succeeded by the 1994 and 2000 formulas because the CIELAB space turned out to be not as perceptually uniform as intended, especially in the saturated regions. This means that this formula rates these colors too highly as opposed to other colors. </p><p>Given two colors in <a href="/wiki/CIELAB_color_space" title="CIELAB color space">CIELAB color space</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle ({L_{1}^{*}},{a_{1}^{*}},{b_{1}^{*}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle ({L_{1}^{*}},{a_{1}^{*}},{b_{1}^{*}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3c31512c8a10009ee057ac5305390c007175d07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.85ex; height:3.009ex;" alt="{\textstyle ({L_{1}^{*}},{a_{1}^{*}},{b_{1}^{*}})}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle ({L_{2}^{*}},{a_{2}^{*}},{b_{2}^{*}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle ({L_{2}^{*}},{a_{2}^{*}},{b_{2}^{*}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f966a84292db1ae9f04bb933c3210625fba139b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.85ex; height:3.009ex;" alt="{\textstyle ({L_{2}^{*}},{a_{2}^{*}},{b_{2}^{*}})}"></span>, the CIE76 color difference formula is defined as: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{ab}^{*}={\sqrt {(L_{2}^{*}-L_{1}^{*})^{2}+(a_{2}^{*}-a_{1}^{*})^{2}+(b_{2}^{*}-b_{1}^{*})^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo stretchy="false">(</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{ab}^{*}={\sqrt {(L_{2}^{*}-L_{1}^{*})^{2}+(a_{2}^{*}-a_{1}^{*})^{2}+(b_{2}^{*}-b_{1}^{*})^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d30890885ec8cfc97e205208245f64d92c6688f0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:48.266ex; height:4.843ex;" alt="{\displaystyle \Delta E_{ab}^{*}={\sqrt {(L_{2}^{*}-L_{1}^{*})^{2}+(a_{2}^{*}-a_{1}^{*})^{2}+(b_{2}^{*}-b_{1}^{*})^{2}}}.}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Delta E_{ab}^{*}\approx 2.3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>≈</mo> <mn>2.3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Delta E_{ab}^{*}\approx 2.3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51ba040957b8768b4e053e9c8548667929241f2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.529ex; height:2.843ex;" alt="{\textstyle \Delta E_{ab}^{*}\approx 2.3}"></span> corresponds to a <a href="/wiki/Just-noticeable_difference" title="Just-noticeable difference">JND</a> (just noticeable difference).<sup id="cite_ref-CIE76_JND_12-1" class="reference"><a href="#cite_note-CIE76_JND-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="CMC_l:c_(1984)"><span id="CMC_l:c_.281984.29"></span>CMC l:c (1984)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=8" title="Edit section: CMC l:c (1984)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1984, the Colour Measurement Committee of the <a href="/wiki/Society_of_Dyers_and_Colourists" title="Society of Dyers and Colourists">Society of Dyers and Colourists</a> defined a difference measure based on the <a href="/wiki/CIELAB_color_space#Cylindrical_model" title="CIELAB color space">CIE L*C*h</a> color model, an alternative representation of <a href="/wiki/CIELAB_color_space" title="CIELAB color space">L*a*b* coordinates</a>. Named after the developing committee, their metric is called <b>CMC l:c</b>. The <a href="/wiki/Quasimetric" class="mw-redirect" title="Quasimetric">quasimetric</a> (i.e. it violates symmetry: parameter T is based on the hue of the reference <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14e8880a2e4243a2fe5157e574a0547ef3d5d373" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.393ex; height:2.509ex;" alt="{\displaystyle h_{1}}"></span> alone) has two parameters: lightness (l) and chroma (c), allowing the users to weight the difference based on the ratio of l:c that is deemed appropriate for the application. Commonly used values are 2:1<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> for acceptability and 1:1 for the threshold of imperceptibility. </p><p>The distance of a color <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle (L_{2}^{*},C_{2}^{*},h_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle (L_{2}^{*},C_{2}^{*},h_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea62b9842967cd97a5046f8548b05c4a1a2c2c39" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.76ex; height:3.009ex;" alt="{\textstyle (L_{2}^{*},C_{2}^{*},h_{2})}"></span> to a reference <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle (L_{1}^{*},C_{1}^{*},h_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle (L_{1}^{*},C_{1}^{*},h_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7000431e430dbf1983342ae17bd666a66d65fa84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.76ex; height:3.009ex;" alt="{\textstyle (L_{1}^{*},C_{1}^{*},h_{1})}"></span> is:<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{CMC}^{*}={\sqrt {\left({\frac {L_{2}^{*}-L_{1}^{*}}{l\times S_{L}}}\right)^{2}+\left({\frac {C_{2}^{*}-C_{1}^{*}}{c\times S_{C}}}\right)^{2}+\left({\frac {\Delta H_{ab}^{*}}{S_{H}}}\right)^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> <mi>M</mi> <mi>C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow> <mi>l</mi> <mo>×</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow> <mi>c</mi> <mo>×</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{CMC}^{*}={\sqrt {\left({\frac {L_{2}^{*}-L_{1}^{*}}{l\times S_{L}}}\right)^{2}+\left({\frac {C_{2}^{*}-C_{1}^{*}}{c\times S_{C}}}\right)^{2}+\left({\frac {\Delta H_{ab}^{*}}{S_{H}}}\right)^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae763b66d2a262845957129445bc0da3a82fd356" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:57.479ex; height:7.676ex;" alt="{\displaystyle \Delta E_{CMC}^{*}={\sqrt {\left({\frac {L_{2}^{*}-L_{1}^{*}}{l\times S_{L}}}\right)^{2}+\left({\frac {C_{2}^{*}-C_{1}^{*}}{c\times S_{C}}}\right)^{2}+\left({\frac {\Delta H_{ab}^{*}}{S_{H}}}\right)^{2}}}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{L}={\begin{cases}0.511&L_{1}^{*}<16\\{\frac {0.040975L_{1}^{*}}{1+0.01765L_{1}^{*}}}&L_{1}^{*}\geq 16\end{cases}}\quad S_{C}={\frac {0.0638C_{1}^{*}}{1+0.0131C_{1}^{*}}}+0.638\quad S_{H}=S_{C}(FT+1-F)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>0.511</mn> </mtd> <mtd> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo><</mo> <mn>16</mn> </mtd> </mtr> <mtr> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.040975</mn> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.01765</mn> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> </mfrac> </mrow> </mtd> <mtd> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>≥</mo> <mn>16</mn> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.0638</mn> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mn>0.0131</mn> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> </mfrac> </mrow> <mo>+</mo> <mn>0.638</mn> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>F</mi> <mi>T</mi> <mo>+</mo> <mn>1</mn> <mo>−</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{L}={\begin{cases}0.511&L_{1}^{*}<16\\{\frac {0.040975L_{1}^{*}}{1+0.01765L_{1}^{*}}}&L_{1}^{*}\geq 16\end{cases}}\quad S_{C}={\frac {0.0638C_{1}^{*}}{1+0.0131C_{1}^{*}}}+0.638\quad S_{H}=S_{C}(FT+1-F)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c34ea9724f4947acb5ed0fe7969a15745f34291" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:84.988ex; height:7.843ex;" alt="{\displaystyle S_{L}={\begin{cases}0.511&L_{1}^{*}<16\\{\frac {0.040975L_{1}^{*}}{1+0.01765L_{1}^{*}}}&L_{1}^{*}\geq 16\end{cases}}\quad S_{C}={\frac {0.0638C_{1}^{*}}{1+0.0131C_{1}^{*}}}+0.638\quad S_{H}=S_{C}(FT+1-F)}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\sqrt {\frac {C_{1}^{*^{4}}}{C_{1}^{*^{4}}+1900}}}\quad T={\begin{cases}0.56+|0.2\cos(h_{1}+168^{\circ })|&164^{\circ }\leq h_{1}\leq 345^{\circ }\\0.36+|0.4\cos(h_{1}+35^{\circ })|&{\mbox{otherwise}}\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </msubsup> <mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mrow> </msubsup> <mo>+</mo> <mn>1900</mn> </mrow> </mfrac> </msqrt> </mrow> <mspace width="1em" /> <mi>T</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mn>0.56</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>0.2</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msup> <mn>168</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mtd> <mtd> <msup> <mn>164</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>≤</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>≤</mo> <msup> <mn>345</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mn>0.36</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mn>0.4</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msup> <mn>35</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mtd> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>otherwise</mtext> </mstyle> </mrow> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\sqrt {\frac {C_{1}^{*^{4}}}{C_{1}^{*^{4}}+1900}}}\quad T={\begin{cases}0.56+|0.2\cos(h_{1}+168^{\circ })|&164^{\circ }\leq h_{1}\leq 345^{\circ }\\0.36+|0.4\cos(h_{1}+35^{\circ })|&{\mbox{otherwise}}\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9423ee2b6f1ecadf2b31272ef4962ff575c24f9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:75.174ex; height:8.176ex;" alt="{\displaystyle F={\sqrt {\frac {C_{1}^{*^{4}}}{C_{1}^{*^{4}}+1900}}}\quad T={\begin{cases}0.56+|0.2\cos(h_{1}+168^{\circ })|&164^{\circ }\leq h_{1}\leq 345^{\circ }\\0.36+|0.4\cos(h_{1}+35^{\circ })|&{\mbox{otherwise}}\end{cases}}}"></span> </p><p>CMC l:c is designed to be used with <a href="/wiki/CIE_Standard_Illuminant_D65" class="mw-redirect" title="CIE Standard Illuminant D65">D65</a> and the <a href="/wiki/CIE_1931_color_space#CIE_standard_observer" title="CIE 1931 color space">CIE Supplementary Observer</a>.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="CIE94">CIE94</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=9" title="Edit section: CIE94"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The CIE 1976 color difference definition was extended to address perceptual non-uniformities, while retaining the CIELAB color space, by the introduction of application-specific parametric weighting factors <i>k<sub>L</sub></i>, <i>k<sub>C</sub></i> and <i>k<sub>H</sub></i>, and functions <i>S<sub>L</sub></i>, <i>S<sub>C</sub></i>, and <i>S<sub>H</sub></i> derived from an automotive paint test's tolerance data.<sup id="cite_ref-colorwiki_11-1" class="reference"><a href="#cite_note-colorwiki-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p><p>As with the CMC I:c, Δ<i>E</i> (1994) is defined in the L*C*h* color space and likewise violates symmetry, therefore defining a quasimetric. Given a reference color<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (L_{1}^{*},a_{1}^{*},b_{1}^{*})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (L_{1}^{*},a_{1}^{*},b_{1}^{*})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6689cd5c8d17cb1f3e0236708bdb9dc6a65ee263" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.85ex; height:3.009ex;" alt="{\displaystyle (L_{1}^{*},a_{1}^{*},b_{1}^{*})}"></span> and another color <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (L_{2}^{*},a_{2}^{*},b_{2}^{*})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (L_{2}^{*},a_{2}^{*},b_{2}^{*})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e92994bd240914a791e628511da7ff346377996d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.85ex; height:3.009ex;" alt="{\displaystyle (L_{2}^{*},a_{2}^{*},b_{2}^{*})}"></span>, the difference is<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{94}^{*}={\sqrt {\left({\frac {\Delta L^{*}}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C^{*}}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H^{*}}{k_{H}S_{H}}}\right)^{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>94</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{94}^{*}={\sqrt {\left({\frac {\Delta L^{*}}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C^{*}}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H^{*}}{k_{H}S_{H}}}\right)^{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f68b26725248d6e550a66482ba9a71cb2bfa107" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:50.169ex; height:7.676ex;" alt="{\displaystyle \Delta E_{94}^{*}={\sqrt {\left({\frac {\Delta L^{*}}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C^{*}}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H^{*}}{k_{H}S_{H}}}\right)^{2}}},}"></span> </p><p>where </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\Delta L^{*}&=L_{1}^{*}-L_{2}^{*},\\C_{1}^{*}&={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\\C_{2}^{*}&={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\\\Delta C^{*}&=C_{1}^{*}-C_{2}^{*},\\\Delta H^{*}&={\sqrt {{\Delta E_{ab}^{*}}^{2}-{\Delta L^{*}}^{2}-{\Delta C^{*}}^{2}}}={\sqrt {{\Delta a^{*}}^{2}+{\Delta b^{*}}^{2}-{\Delta C^{*}}^{2}}},\\\Delta a^{*}&=a_{1}^{*}-a_{2}^{*},\\\Delta b^{*}&=b_{1}^{*}-b_{2}^{*},\\S_{L}&=1,\\S_{C}&=1+K_{1}C_{1}^{*},\\S_{H}&=1+K_{2}C_{1}^{*},\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <mi mathvariant="normal">Δ</mi> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Delta L^{*}&=L_{1}^{*}-L_{2}^{*},\\C_{1}^{*}&={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\\C_{2}^{*}&={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\\\Delta C^{*}&=C_{1}^{*}-C_{2}^{*},\\\Delta H^{*}&={\sqrt {{\Delta E_{ab}^{*}}^{2}-{\Delta L^{*}}^{2}-{\Delta C^{*}}^{2}}}={\sqrt {{\Delta a^{*}}^{2}+{\Delta b^{*}}^{2}-{\Delta C^{*}}^{2}}},\\\Delta a^{*}&=a_{1}^{*}-a_{2}^{*},\\\Delta b^{*}&=b_{1}^{*}-b_{2}^{*},\\S_{L}&=1,\\S_{C}&=1+K_{1}C_{1}^{*},\\S_{H}&=1+K_{2}C_{1}^{*},\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6fd6fee8c753cc683f386bf018ad08a76e51d7e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -18.069ex; margin-bottom: -0.269ex; width:62.838ex; height:37.843ex;" alt="{\displaystyle {\begin{aligned}\Delta L^{*}&=L_{1}^{*}-L_{2}^{*},\\C_{1}^{*}&={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\\C_{2}^{*}&={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\\\Delta C^{*}&=C_{1}^{*}-C_{2}^{*},\\\Delta H^{*}&={\sqrt {{\Delta E_{ab}^{*}}^{2}-{\Delta L^{*}}^{2}-{\Delta C^{*}}^{2}}}={\sqrt {{\Delta a^{*}}^{2}+{\Delta b^{*}}^{2}-{\Delta C^{*}}^{2}}},\\\Delta a^{*}&=a_{1}^{*}-a_{2}^{*},\\\Delta b^{*}&=b_{1}^{*}-b_{2}^{*},\\S_{L}&=1,\\S_{C}&=1+K_{1}C_{1}^{*},\\S_{H}&=1+K_{2}C_{1}^{*},\\\end{aligned}}}"></span> </p><p>and where <i>k<sub>C</sub></i> and <i>k<sub>H</sub></i> are usually both set to unity, and the parametric weighting factors <i>k<sub>L</sub></i>, <i>K</i><sub>1</sub> and <i>K</i><sub>2</sub> depend on the application: </p> <dl><dd><table class="wikitable" border="1"> <tbody><tr> <th> </th> <th>graphic arts </th> <th>textiles </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29637b9b588fc987792392455e792730f5dfc7f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.563ex; height:2.509ex;" alt="{\displaystyle k_{L}}"></span> </td> <td>1 </td> <td>2 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8520077dbcf03c2aabefd98d41a2269ed41a54fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.509ex;" alt="{\displaystyle K_{1}}"></span> </td> <td>0.045 </td> <td>0.048 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/57e1b324cf5b68f2729a8634ff76e396b634b75d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.509ex;" alt="{\displaystyle K_{2}}"></span> </td> <td>0.015 </td> <td>0.014 </td></tr></tbody></table></dd></dl> <p>Geometrically, the quantity <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta H_{ab}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mi>b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H_{ab}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b149a49f1c0ea419b79ac966b1138ca5b4440f9c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.674ex; height:2.843ex;" alt="{\displaystyle \Delta H_{ab}^{*}}"></span> corresponds to the arithmetic mean of the chord lengths of the equal chroma circles of the two colors.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="CIEDE2000">CIEDE2000</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=10" title="Edit section: CIEDE2000"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since the 1994 definition did not adequately resolve the <a href="/wiki/Perceptual_uniformity" class="mw-redirect" title="Perceptual uniformity">perceptual uniformity</a> issue, the CIE refined their definition with the CIEDE2000 formula published in 2001, adding five corrections:<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <ul><li>A hue rotation term (R<sub>T</sub>), to deal with the problematic blue region (hue angles in the neighborhood of 275°):<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>Compensation for neutral colors (the primed values in the L*C*h differences)</li> <li>Compensation for lightness (S<sub>L</sub>)</li> <li>Compensation for chroma (S<sub>C</sub>)</li> <li>Compensation for hue (S<sub>H</sub>)</li></ul> <p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta E_{00}^{*}={\sqrt {\left({\frac {\Delta L'}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C'}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H'}{k_{H}S_{H}}}\right)^{2}+R_{T}{\frac {\Delta C'}{k_{C}S_{C}}}{\frac {\Delta H'}{k_{H}S_{H}}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msubsup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>00</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>L</mi> <mo>′</mo> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mo>′</mo> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mo>′</mo> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>C</mi> <mo>′</mo> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mo>′</mo> </msup> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> </mrow> </mfrac> </mrow> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta E_{00}^{*}={\sqrt {\left({\frac {\Delta L'}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C'}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H'}{k_{H}S_{H}}}\right)^{2}+R_{T}{\frac {\Delta C'}{k_{C}S_{C}}}{\frac {\Delta H'}{k_{H}S_{H}}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aec5cdd29cf9fdbd7352935eaee1524d5718340e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:68.805ex; height:7.676ex;" alt="{\displaystyle \Delta E_{00}^{*}={\sqrt {\left({\frac {\Delta L'}{k_{L}S_{L}}}\right)^{2}+\left({\frac {\Delta C'}{k_{C}S_{C}}}\right)^{2}+\left({\frac {\Delta H'}{k_{H}S_{H}}}\right)^{2}+R_{T}{\frac {\Delta C'}{k_{C}S_{C}}}{\frac {\Delta H'}{k_{H}S_{H}}}}}}"></span> </p><p>The formulae below should use degrees rather than radians; the issue is significant for <i>R<sub>T</sub></i>. </p><p>The parametric weighting factors <i>k<sub>L</sub></i>, <i>k<sub>C</sub></i>, and <i>k<sub>H</sub></i> are usually set to unity. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta L^{\prime }=L_{2}^{*}-L_{1}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta L^{\prime }=L_{2}^{*}-L_{1}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/37ccaf1193cfa9e708e800d27cc899a62c4d16c8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:15.416ex; height:3.176ex;" alt="{\displaystyle \Delta L^{\prime }=L_{2}^{*}-L_{1}^{*}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {L}}={\frac {L_{1}^{*}+L_{2}^{*}}{2}}\quad {\bar {C}}={\frac {C_{1}^{*}+C_{2}^{*}}{2}}\quad {\mbox{where }}C_{1}^{*}={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\quad C_{2}^{*}={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mn>2</mn> </mfrac> </mrow> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mn>2</mn> </mfrac> </mrow> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>where </mtext> </mstyle> </mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> <mspace width="1em" /> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mrow> <mo>,</mo> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {L}}={\frac {L_{1}^{*}+L_{2}^{*}}{2}}\quad {\bar {C}}={\frac {C_{1}^{*}+C_{2}^{*}}{2}}\quad {\mbox{where }}C_{1}^{*}={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\quad C_{2}^{*}={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb6569c46531f0184eae201c5eed2b872a13ddab" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:80.494ex; height:5.676ex;" alt="{\displaystyle {\bar {L}}={\frac {L_{1}^{*}+L_{2}^{*}}{2}}\quad {\bar {C}}={\frac {C_{1}^{*}+C_{2}^{*}}{2}}\quad {\mbox{where }}C_{1}^{*}={\sqrt {{a_{1}^{*}}^{2}+{b_{1}^{*}}^{2}}},\quad C_{2}^{*}={\sqrt {{a_{2}^{*}}^{2}+{b_{2}^{*}}^{2}}},\quad }"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{1}^{\prime }=a_{1}^{*}+{\frac {a_{1}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)\quad a_{2}^{\prime }=a_{2}^{*}+{\frac {a_{2}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> <mspace width="1em" /> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mn>2</mn> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> <mo>+</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}^{\prime }=a_{1}^{*}+{\frac {a_{1}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)\quad a_{2}^{\prime }=a_{2}^{*}+{\frac {a_{2}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba63ff38a1ca84ff7c3352b03173c12b2728f657" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.838ex; width:71.538ex; height:8.843ex;" alt="{\displaystyle a_{1}^{\prime }=a_{1}^{*}+{\frac {a_{1}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)\quad a_{2}^{\prime }=a_{2}^{*}+{\frac {a_{2}^{*}}{2}}\left(1-{\sqrt {\frac {{\bar {C}}^{7}}{{\bar {C}}^{7}+25^{7}}}}\right)}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {C}}^{\prime }={\frac {C_{1}^{\prime }+C_{2}^{\prime }}{2}}{\mbox{ and }}\Delta {C'}=C'_{2}-C'_{1}\quad {\mbox{where }}C_{1}^{\prime }={\sqrt {a_{1}^{'^{2}}+b_{1}^{*^{2}}}}\quad C_{2}^{\prime }={\sqrt {a_{2}^{'^{2}}+b_{2}^{*^{2}}}}\quad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext> and </mtext> </mstyle> </mrow> <mi mathvariant="normal">Δ</mi> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi>C</mi> <mo>′</mo> </msup> </mrow> <mo>=</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mo>′</mo> </msubsup> <mo>−</mo> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mo>′</mo> </msubsup> <mspace width="1em" /> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>where </mtext> </mstyle> </mrow> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msubsup> </msqrt> </mrow> <mspace width="1em" /> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi></mi> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msup> <mo>∗</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </msubsup> </msqrt> </mrow> <mspace width="1em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {C}}^{\prime }={\frac {C_{1}^{\prime }+C_{2}^{\prime }}{2}}{\mbox{ and }}\Delta {C'}=C'_{2}-C'_{1}\quad {\mbox{where }}C_{1}^{\prime }={\sqrt {a_{1}^{'^{2}}+b_{1}^{*^{2}}}}\quad C_{2}^{\prime }={\sqrt {a_{2}^{'^{2}}+b_{2}^{*^{2}}}}\quad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c114873cd58b5678349ac6bf838e16a501f73e4b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:81.898ex; height:5.676ex;" alt="{\displaystyle {\bar {C}}^{\prime }={\frac {C_{1}^{\prime }+C_{2}^{\prime }}{2}}{\mbox{ and }}\Delta {C'}=C'_{2}-C'_{1}\quad {\mbox{where }}C_{1}^{\prime }={\sqrt {a_{1}^{'^{2}}+b_{1}^{*^{2}}}}\quad C_{2}^{\prime }={\sqrt {a_{2}^{'^{2}}+b_{2}^{*^{2}}}}\quad }"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h_{1}^{\prime }={\text{atan2}}(b_{1}^{*},a_{1}^{\prime })\mod 360^{\circ },\quad h_{2}^{\prime }={\text{atan2}}(b_{2}^{*},a_{2}^{\prime })\mod 360^{\circ }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>atan2</mtext> </mrow> <mo stretchy="false">(</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi>mod</mi> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <mspace width="1em" /> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>atan2</mtext> </mrow> <mo stretchy="false">(</mo> <msubsup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> <mspace width="1em" /> <mi>mod</mi> <mspace width="thinmathspace" /> <mspace width="thinmathspace" /> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h_{1}^{\prime }={\text{atan2}}(b_{1}^{*},a_{1}^{\prime })\mod 360^{\circ },\quad h_{2}^{\prime }={\text{atan2}}(b_{2}^{*},a_{2}^{\prime })\mod 360^{\circ }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/89a1520e804efcc5658d90d4d5afb5450e52b398" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:65.674ex; height:3.009ex;" alt="{\displaystyle h_{1}^{\prime }={\text{atan2}}(b_{1}^{*},a_{1}^{\prime })\mod 360^{\circ },\quad h_{2}^{\prime }={\text{atan2}}(b_{2}^{*},a_{2}^{\prime })\mod 360^{\circ }}"></span> </p><p>The inverse tangent (tan<sup>−1</sup>) can be computed using a common library routine <code>atan2(b, a<span class="nowrap" style="padding-left:0em;">′</span>)</code> which usually has a range from −π to π radians; color specifications are given in 0 to 360 degrees, so some adjustment is needed. The inverse tangent is indeterminate if both <i>a<span class="nowrap" style="padding-left:0em;">′</span></i> and <i>b</i> are zero (which also means that the corresponding <i>C<span class="nowrap" style="padding-left:0.05em;">′</span></i> is zero); in that case, set the hue angle to zero. See <a href="#CITEREFSharma2005">Sharma 2005</a>, eqn. 7. </p><p>The example above expects the parameter order of atan2 to be <code>atan2(y, x)</code>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta h'={\begin{cases}h_{2}^{\prime }-h_{1}^{\prime }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\h_{2}^{\prime }-h_{1}^{\prime }+360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }\leq h_{1}^{\prime }\\h_{2}^{\prime }-h_{1}^{\prime }-360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }>h_{1}^{\prime }\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>≤</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>></mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>≤</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>></mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>></mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta h'={\begin{cases}h_{2}^{\prime }-h_{1}^{\prime }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\h_{2}^{\prime }-h_{1}^{\prime }+360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }\leq h_{1}^{\prime }\\h_{2}^{\prime }-h_{1}^{\prime }-360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }>h_{1}^{\prime }\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/825da182e2bed96aac9fdca6ed700c0a9c548d9e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:52.686ex; height:9.176ex;" alt="{\displaystyle \Delta h'={\begin{cases}h_{2}^{\prime }-h_{1}^{\prime }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\h_{2}^{\prime }-h_{1}^{\prime }+360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }\leq h_{1}^{\prime }\\h_{2}^{\prime }-h_{1}^{\prime }-360^{\circ }&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{2}^{\prime }>h_{1}^{\prime }\end{cases}}}"></span> </p><p>When either <i>C<span class="nowrap" style="padding-left:0.05em;">′</span></i><sub>1</sub> or <i>C<span class="nowrap" style="padding-left:0.05em;">′</span></i><sub>2</sub> is zero, then Δh<span class="nowrap" style="padding-left:0em;">′</span> is irrelevant and may be set to zero. See <a href="#CITEREFSharma2005">Sharma 2005</a>, eqn. 10. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta H^{\prime }=2{\sqrt {C_{1}^{\prime }C_{2}^{\prime }}}\sin(\Delta h^{\prime }/2),\quad {\bar {H}}^{\prime }={\begin{cases}(h_{1}^{\prime }+h_{2}^{\prime })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }+360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }<360^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }-360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }\geq 360^{\circ }\end{cases}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </msqrt> </mrow> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">Δ</mi> <msup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> <mo stretchy="false">)</mo> <mo>,</mo> <mspace width="1em" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>{</mo> <mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false"> <mtr> <mtd> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>≤</mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>></mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo><</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mtd> <mtd> <mrow> <mo>|</mo> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>−</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mrow> <mo>|</mo> </mrow> <mo>></mo> <msup> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>,</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo>≥</mo> <msup> <mn>360</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mtd> </mtr> </mtable> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta H^{\prime }=2{\sqrt {C_{1}^{\prime }C_{2}^{\prime }}}\sin(\Delta h^{\prime }/2),\quad {\bar {H}}^{\prime }={\begin{cases}(h_{1}^{\prime }+h_{2}^{\prime })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }+360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }<360^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }-360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }\geq 360^{\circ }\end{cases}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2e53389e2e34937516faa45958d3d5d11b526fc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.005ex; width:94.425ex; height:9.176ex;" alt="{\displaystyle \Delta H^{\prime }=2{\sqrt {C_{1}^{\prime }C_{2}^{\prime }}}\sin(\Delta h^{\prime }/2),\quad {\bar {H}}^{\prime }={\begin{cases}(h_{1}^{\prime }+h_{2}^{\prime })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|\leq 180^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }+360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }<360^{\circ }\\(h_{1}^{\prime }+h_{2}^{\prime }-360^{\circ })/2&\left|h_{1}^{\prime }-h_{2}^{\prime }\right|>180^{\circ },h_{1}^{\prime }+h_{2}^{\prime }\geq 360^{\circ }\end{cases}}}"></span> </p><p>When either <i>C<span class="nowrap" style="padding-left:0.05em;">′</span></i><sub>1</sub> or <i>C<span class="nowrap" style="padding-left:0.05em;">′</span></i><sub>2</sub> is zero, then <span style="text-decoration:overline;">H</span><span class="nowrap" style="padding-left:0.15em;">′</span> is <i>h<span class="nowrap" style="padding-left:0em;">′</span></i><sub>1</sub>+<i>h<span class="nowrap" style="padding-left:0em;">′</span></i><sub>2</sub> (no divide by 2; essentially, if one angle is indeterminate, then use the other angle as the average; relies on indeterminate angle being set to zero). See <a href="#CITEREFSharma2005">Sharma 2005</a>, eqn. 7 and p. 23 stating most implementations on the Internet at the time had "an error in the computation of average hue". </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T=1-0.17\cos({\bar {H}}^{\prime }-30^{\circ })+0.24\cos(2{\bar {H}}^{\prime })+0.32\cos(3{\bar {H}}^{\prime }+6^{\circ })-0.20\cos(4{\bar {H}}^{\prime }-63^{\circ })}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mn>0.17</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>−</mo> <msup> <mn>30</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mn>0.24</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mn>0.32</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>3</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>+</mo> <msup> <mn>6</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>−</mo> <mn>0.20</mn> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>4</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>−</mo> <msup> <mn>63</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T=1-0.17\cos({\bar {H}}^{\prime }-30^{\circ })+0.24\cos(2{\bar {H}}^{\prime })+0.32\cos(3{\bar {H}}^{\prime }+6^{\circ })-0.20\cos(4{\bar {H}}^{\prime }-63^{\circ })}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf90387d4e41884cb0aa9b46cb9d1bbf355ae788" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:87.003ex; height:3.343ex;" alt="{\displaystyle T=1-0.17\cos({\bar {H}}^{\prime }-30^{\circ })+0.24\cos(2{\bar {H}}^{\prime })+0.32\cos(3{\bar {H}}^{\prime }+6^{\circ })-0.20\cos(4{\bar {H}}^{\prime }-63^{\circ })}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{L}=1+{\frac {0.015\left({\bar {L}}-50\right)^{2}}{\sqrt {20+{\left({\bar {L}}-50\right)}^{2}}}}\quad S_{C}=1+0.045{\bar {C}}^{\prime }\quad S_{H}=1+0.015{\bar {C}}^{\prime }T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>0.015</mn> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>−</mo> <mn>50</mn> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msqrt> <mn>20</mn> <mo>+</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>L</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>−</mo> <mn>50</mn> </mrow> <mo>)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </msqrt> </mfrac> </mrow> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mn>0.045</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mspace width="1em" /> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>H</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>+</mo> <mn>0.015</mn> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{L}=1+{\frac {0.015\left({\bar {L}}-50\right)^{2}}{\sqrt {20+{\left({\bar {L}}-50\right)}^{2}}}}\quad S_{C}=1+0.045{\bar {C}}^{\prime }\quad S_{H}=1+0.015{\bar {C}}^{\prime }T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d0b046552a0e79aeecc1405c82880e7dcbeec33e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.671ex; width:70.137ex; height:9.343ex;" alt="{\displaystyle S_{L}=1+{\frac {0.015\left({\bar {L}}-50\right)^{2}}{\sqrt {20+{\left({\bar {L}}-50\right)}^{2}}}}\quad S_{C}=1+0.045{\bar {C}}^{\prime }\quad S_{H}=1+0.015{\bar {C}}^{\prime }T}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{T}=-2{\sqrt {\frac {{\bar {C}}'^{7}}{{\bar {C}}'^{7}+25^{7}}}}\sin \left[60^{\circ }\cdot \exp \left(-\left[{\frac {{\bar {H}}'-275^{\circ }}{25^{\circ }}}\right]^{2}\right)\right]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>C</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mrow> <mo class="MJX-variant">′</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>7</mn> </mrow> </msup> </mrow> </mfrac> </msqrt> </mrow> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <msup> <mn>60</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>⋅</mo> <mi>exp</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mo>−</mo> <msup> <mrow> <mo>[</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>H</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>′</mo> </msup> <mo>−</mo> <msup> <mn>275</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mrow> <msup> <mn>25</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> </mfrac> </mrow> <mo>]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mo>]</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{T}=-2{\sqrt {\frac {{\bar {C}}'^{7}}{{\bar {C}}'^{7}+25^{7}}}}\sin \left[60^{\circ }\cdot \exp \left(-\left[{\frac {{\bar {H}}'-275^{\circ }}{25^{\circ }}}\right]^{2}\right)\right]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dfac3639cdbaea983a37bbaa81a914d904b22d6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.671ex; width:57.565ex; height:8.676ex;" alt="{\displaystyle R_{T}=-2{\sqrt {\frac {{\bar {C}}'^{7}}{{\bar {C}}'^{7}+25^{7}}}}\sin \left[60^{\circ }\cdot \exp \left(-\left[{\frac {{\bar {H}}'-275^{\circ }}{25^{\circ }}}\right]^{2}\right)\right]}"></span> </p><p>CIEDE 2000 is not mathematically continuous. The discontinuity stems from calculating the mean hue <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Delta H^{\prime }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Delta H^{\prime }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/183f0d3b8e346d9f5539245f25d6b6e801dd480d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.724ex; height:2.343ex;" alt="{\textstyle \Delta H^{\prime }}"></span> and the hue difference <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Delta h'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msup> <mi>h</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Delta h'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cee8f11753fb8670fac47c2df8f8202b623787ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.96ex; height:2.343ex;" alt="{\textstyle \Delta h'}"></span>. The maximum discontinuity happens when the hues of two sample colors are about 180° apart, and is usually small relative to ΔE (less than 4%).<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> There is also a negligible amount of discontinuity from hue rollover.<sup id="cite_ref-Sharma05_26-0" class="reference"><a href="#cite_note-Sharma05-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p><p>Sharma, Wu, and Dalal has provided some additional notes on the mathematics and implementation of the formula.<sup id="cite_ref-Sharma05_26-1" class="reference"><a href="#cite_note-Sharma05-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Tolerance">Tolerance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=11" title="Edit section: Tolerance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Uniform_color_space" class="mw-redirect" title="Uniform color space">Uniform color space</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:CIExy1931_MacAdam.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/CIExy1931_MacAdam.png/250px-CIExy1931_MacAdam.png" decoding="async" width="250" height="276" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/CIExy1931_MacAdam.png/375px-CIExy1931_MacAdam.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/CIExy1931_MacAdam.png/500px-CIExy1931_MacAdam.png 2x" data-file-width="1140" data-file-height="1260" /></a><figcaption>A MacAdam diagram in the <a href="/wiki/CIE_1931_color_space" title="CIE 1931 color space">CIE 1931 color space</a>. The ellipses are shown ten times their actual size.</figcaption></figure> <p><b>Tolerancing</b> concerns the question "What is a set of colors that are imperceptibly/acceptably close to a given reference?" If the distance measure is <i><b>perceptually uniform</b></i>, then the answer is simply "the set of points whose distance to the reference is less than the just-noticeable-difference (JND) threshold". This requires a perceptually uniform metric in order for the threshold to be constant throughout the <a href="/wiki/Gamut" title="Gamut">gamut</a> (range of colors). Otherwise, the threshold will be a function of the reference color—cumbersome as a practical guide. </p><p>In the <a href="/wiki/CIE_1931_color_space" title="CIE 1931 color space">CIE 1931 color space</a>, for example, the tolerance contours are defined by the <a href="/wiki/MacAdam_ellipse" title="MacAdam ellipse">MacAdam ellipse</a>, which holds L* (lightness) fixed. As can be observed on the adjacent diagram, the <a href="/wiki/Ellipse" title="Ellipse">ellipses</a> denoting the tolerance contours vary in size. It is partly this non-uniformity that led to the creation of <a href="/wiki/CIELUV" title="CIELUV">CIELUV</a> and <a href="/wiki/CIELAB" class="mw-redirect" title="CIELAB">CIELAB</a>. </p><p>More generally, if the lightness is allowed to vary, then we find the tolerance set to be <a href="/wiki/Ellipsoid" title="Ellipsoid">ellipsoidal</a>. Increasing the weighting factor in the aforementioned distance expressions has the effect of increasing the size of the ellipsoid along the respective axis.<sup id="cite_ref-xrite_27-0" class="reference"><a href="#cite_note-xrite-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>The definition of "acceptably close" also depends on the industrial requirements and practicality. In the automotive industry the <span class="texhtml">Δ<i>E*</i><sub>CMC</sub></span> in the automotive industry is rather stringent, often less than 0.5 under D65/10. In printing, the typical limit is 2.0 under D50, though some processes require up to 5.0.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/CIELAB_color_space" title="CIELAB color space">CIELAB</a></li> <li><a href="/wiki/Color_coding_in_data_visualization" class="mw-redirect" title="Color coding in data visualization">Color coding in data visualization</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Footnotes">Footnotes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=13" title="Edit section: Footnotes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Notes">Notes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=14" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Called such because the operator is not <a href="/wiki/Commutative" class="mw-redirect" title="Commutative">commutative</a>. This makes it a <a href="/wiki/Quasimetric" class="mw-redirect" title="Quasimetric">quasimetric</a>. Specifically, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S_{\{C,H\}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo fence="false" stretchy="false">{</mo> <mi>C</mi> <mo>,</mo> <mi>H</mi> <mo fence="false" stretchy="false">}</mo> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S_{\{C,H\}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/80148da6324832154c6e60a8fda3187febbe4177" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.467ex; height:3.009ex;" alt="{\displaystyle S_{\{C,H\}}}"></span> both depend on <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{1}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{1}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4bbf361be926883a6e065eef4eb40574c19c971a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.852ex; height:2.843ex;" alt="{\displaystyle C_{1}^{*}}"></span> only.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="References">References</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=15" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-euc-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-euc_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-euc_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.compuphase.com/cmetric.htm">"Colour metric"</a>. <i>Compu Phase</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Compu+Phase&rft.atitle=Colour+metric&rft_id=http%3A%2F%2Fwww.compuphase.com%2Fcmetric.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.xrite.com/learning-color-education/other-resources/glossary#U">"Color Glossary"</a>. <i>X-Rite</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=X-Rite&rft.atitle=Color+Glossary&rft_id=https%3A%2F%2Fwww.xrite.com%2Flearning-color-education%2Fother-resources%2Fglossary%23U&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiLiWangXu2017" class="citation journal cs1">Li, Changjun; 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Brucelindbloom.com<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-04-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Delta+E+%28CMC%29&rft.pub=Brucelindbloom.com&rft.aulast=Lindbloom&rft.aufirst=Bruce+Justin&rft_id=http%3A%2F%2Fwww.brucelindbloom.com%2FEqn_DeltaE_CMC.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20060312161957/http://www.hunterlab.com/appnotes/an10_96ar.pdf">"CMC"</a> <span class="cs1-format">(PDF)</span>. <i>Insight on Color</i>. <b>8</b> (13). 1–15 October 1996. Archived from <a rel="nofollow" class="external text" href="http://www.hunterlab.com/appnotes/an10_96ar.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 2006-03-12.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Insight+on+Color&rft.atitle=CMC&rft.volume=8&rft.issue=13&rft.date=1996-10-01%2F1996-10-15&rft_id=http%3A%2F%2Fwww.hunterlab.com%2Fappnotes%2Fan10_96ar.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindbloom" class="citation web cs1">Lindbloom, Bruce Justin. <a rel="nofollow" class="external text" href="http://www.brucelindbloom.com/Eqn_DeltaE_CIE94.html">"Delta E (CIE 1994)"</a>. Brucelindbloom.com<span class="reference-accessdate">. Retrieved <span class="nowrap">2011-03-23</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Delta+E+%28CIE+1994%29&rft.pub=Brucelindbloom.com&rft.aulast=Lindbloom&rft.aufirst=Bruce+Justin&rft_id=http%3A%2F%2Fwww.brucelindbloom.com%2FEqn_DeltaE_CIE94.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.colorpro.com/info/software/heggie.html">"Colour Difference Software by David Heggie"</a>. Colorpro.com. 1995-12-19<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-04-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Colour+Difference+Software+by+David+Heggie&rft.pub=Colorpro.com&rft.date=1995-12-19&rft_id=http%3A%2F%2Fwww.colorpro.com%2Finfo%2Fsoftware%2Fheggie.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation report cs1">Colorimetry - Part 4: CIE 1976 L*a*b* Colour Space (Report). Draft Standard. CIE. 2007. CIE DS 014-4.3/E:2007.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Colorimetry+-+Part+4%3A+CIE+1976+L%2Aa%2Ab%2A+Colour+Space&rft.series=Draft+Standard&rft.pub=CIE&rft.date=2007&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKlein2010" class="citation book cs1">Klein, Georg A. (2010-05-18). <span class="id-lock-limited" title="Free access subject to limited trial, subscription normally required"><a rel="nofollow" class="external text" href="https://archive.org/details/industrialcolorp00klei_495"><i>Industrial Color Physics</i></a></span>. Springer. p. <a rel="nofollow" class="external text" href="https://archive.org/details/industrialcolorp00klei_495/page/n158">147</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4419-1196-4" title="Special:BookSources/978-1-4419-1196-4"><bdi>978-1-4419-1196-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Industrial+Color+Physics&rft.pages=147&rft.pub=Springer&rft.date=2010-05-18&rft.isbn=978-1-4419-1196-4&rft.aulast=Klein&rft.aufirst=Georg+A.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Findustrialcolorp00klei_495&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSharma2005" class="citation journal cs1">Sharma, Gaurav; Wu, Wencheng; Dalal, Edul N. (2005). <a rel="nofollow" class="external text" href="http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf">"The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations"</a> <span class="cs1-format">(PDF)</span>. <i>Color Research & Application</i>. <b>30</b> (1). <a href="/wiki/Wiley_Interscience" class="mw-redirect" title="Wiley Interscience">Wiley Interscience</a>: 21–30. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcol.20070">10.1002/col.20070</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+Research+%26+Application&rft.atitle=The+CIEDE2000+color-difference+formula%3A+Implementation+notes%2C+supplementary+test+data%2C+and+mathematical+observations&rft.volume=30&rft.issue=1&rft.pages=21-30&rft.date=2005&rft_id=info%3Adoi%2F10.1002%2Fcol.20070&rft.aulast=Sharma&rft.aufirst=Gaurav&rft.au=Wu%2C+Wencheng&rft.au=Dalal%2C+Edul+N.&rft_id=http%3A%2F%2Fwww.ece.rochester.edu%2F~gsharma%2Fciede2000%2Fciede2000noteCRNA.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLindbloom" class="citation web cs1">Lindbloom, Bruce Justin. <a rel="nofollow" class="external text" href="http://www.brucelindbloom.com/Eqn_DeltaE_CIE2000.html">"Delta E (CIE 2000)"</a>. Brucelindbloom.com<span class="reference-accessdate">. Retrieved <span class="nowrap">2009-04-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Delta+E+%28CIE+2000%29&rft.pub=Brucelindbloom.com&rft.aulast=Lindbloom&rft.aufirst=Bruce+Justin&rft_id=http%3A%2F%2Fwww.brucelindbloom.com%2FEqn_DeltaE_CIE2000.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.brucelindbloom.com/MunsellCalcHelp.html#BluePurple">The "Blue Turns Purple" Problem</a>, Bruce Lindbloom</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">See implementation in <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSharma" class="citation web cs1">Sharma, Gaurav. <a rel="nofollow" class="external text" href="https://hajim.rochester.edu/ece/sites/gsharma/ciede2000/">"The CIEDE2000 Color-Difference Formula"</a>. "Excel spreadsheet" hyperlink<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-24</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+CIEDE2000+Color-Difference+Formula&rft.pages=%22Excel+spreadsheet%22+hyperlink&rft.aulast=Sharma&rft.aufirst=Gaurav&rft_id=https%3A%2F%2Fhajim.rochester.edu%2Fece%2Fsites%2Fgsharma%2Fciede2000%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSharmaWuDalalCelik2004" class="citation journal cs1">Sharma, Gaurav; Wu, Wencheng; Dalal, Edul N.; Celik, Mehmet U. (1 January 2004). <a rel="nofollow" class="external text" href="https://doi.org/10.2352%2FCIC.2004.12.1.art00058">"Mathematical Discontinuities in CIEDE2000 Color Difference Computations"</a>. <i>Color and Imaging Conference</i>. <b>12</b> (1): 334–339. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.2352%2FCIC.2004.12.1.art00058">10.2352/CIC.2004.12.1.art00058</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+and+Imaging+Conference&rft.atitle=Mathematical+Discontinuities+in+CIEDE2000+Color+Difference+Computations&rft.volume=12&rft.issue=1&rft.pages=334-339&rft.date=2004-01-01&rft_id=info%3Adoi%2F10.2352%2FCIC.2004.12.1.art00058&rft.aulast=Sharma&rft.aufirst=Gaurav&rft.au=Wu%2C+Wencheng&rft.au=Dalal%2C+Edul+N.&rft.au=Celik%2C+Mehmet+U.&rft_id=https%3A%2F%2Fdoi.org%2F10.2352%252FCIC.2004.12.1.art00058&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-Sharma05-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-Sharma05_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Sharma05_26-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSharmaWuDalal2005" class="citation journal cs1">Sharma, Gaurav; Wu, Wencheng; Dalal, Edul N. (February 2005). "The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations". <i>Color Research & Application</i>. <b>30</b> (1): 21–30. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcol.20070">10.1002/col.20070</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+Research+%26+Application&rft.atitle=The+CIEDE2000+color-difference+formula%3A+Implementation+notes%2C+supplementary+test+data%2C+and+mathematical+observations&rft.volume=30&rft.issue=1&rft.pages=21-30&rft.date=2005-02&rft_id=info%3Adoi%2F10.1002%2Fcol.20070&rft.aulast=Sharma&rft.aufirst=Gaurav&rft.au=Wu%2C+Wencheng&rft.au=Dalal%2C+Edul+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-xrite-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-xrite_27-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSusan_Hughes1998" class="citation web cs1">Susan Hughes (14 January 1998). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151010064956/http://www.xrite.com/documents/literature/en/L10-024_Color_Tolerance_en.pdf">"A guide to Understanding Color Tolerancing"</a> <span class="cs1-format">(PDF)</span>. Archived from <a rel="nofollow" class="external text" href="http://www.xrite.com/documents/literature/en/L10-024_Color_Tolerance_en.pdf">the original</a> <span class="cs1-format">(PDF)</span> on 10 October 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">2014-12-02</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=A+guide+to+Understanding+Color+Tolerancing&rft.date=1998-01-14&rft.au=Susan+Hughes&rft_id=http%3A%2F%2Fwww.xrite.com%2Fdocuments%2Fliterature%2Fen%2FL10-024_Color_Tolerance_en.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHuda" class="citation web cs1">Huda, Mike. <a rel="nofollow" class="external text" href="https://www.xrite.com/blog/tips-to-define-tolerances">"Tips for Defining a Realistic Pass/Fail Tolerance"</a>. <i>X-Rite</i><span class="reference-accessdate">. Retrieved <span class="nowrap">13 September</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=X-Rite&rft.atitle=Tips+for+Defining+a+Realistic+Pass%2FFail+Tolerance&rft.aulast=Huda&rft.aufirst=Mike&rft_id=https%3A%2F%2Fwww.xrite.com%2Fblog%2Ftips-to-define-tolerances&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239549316">.mw-parser-output .refbegin{margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}@media screen{.mw-parser-output .refbegin{font-size:90%}}</style><div class="refbegin" style=""> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRobertson1990" class="citation journal cs1">Robertson, Alan R. (1990). <a rel="nofollow" class="external text" href="http://www3.interscience.wiley.com/cgi-bin/fulltext/114184816/PDFSTART">"Historical development of CIE recommended color difference equations"</a>. <i>Color Research & Application</i>. <b>15</b> (3): 167–170. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fcol.5080150308">10.1002/col.5080150308</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Color+Research+%26+Application&rft.atitle=Historical+development+of+CIE+recommended+color+difference+equations&rft.volume=15&rft.issue=3&rft.pages=167-170&rft.date=1990&rft_id=info%3Adoi%2F10.1002%2Fcol.5080150308&rft.aulast=Robertson&rft.aufirst=Alan+R.&rft_id=http%3A%2F%2Fwww3.interscience.wiley.com%2Fcgi-bin%2Ffulltext%2F114184816%2FPDFSTART&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span><sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Link_rot" title="Wikipedia:Link rot"><span title=" Dead link tagged May 2020">dead link</span></a></i><span style="visibility:hidden; color:transparent; padding-left:2px">‍</span>]</span></sup></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMelgosaQuesadaHita1994" class="citation journal cs1">Melgosa, M.; Quesada, J. J.; Hita, E. (December 1994). "Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset". <i><a href="/wiki/Applied_Optics" title="Applied Optics">Applied Optics</a></i>. <b>33</b> (34): 8069–77. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1994ApOpt..33.8069M">1994ApOpt..33.8069M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1364%2FAO.33.008069">10.1364/AO.33.008069</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/20963027">20963027</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Applied+Optics&rft.atitle=Uniformity+of+some+recent+color+metrics+tested+with+an+accurate+color-difference+tolerance+dataset&rft.volume=33&rft.issue=34&rft.pages=8069-77&rft.date=1994-12&rft_id=info%3Apmid%2F20963027&rft_id=info%3Adoi%2F10.1364%2FAO.33.008069&rft_id=info%3Abibcode%2F1994ApOpt..33.8069M&rft.aulast=Melgosa&rft.aufirst=M.&rft.au=Quesada%2C+J.+J.&rft.au=Hita%2C+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcDonald1997" class="citation book cs1">McDonald, Roderick, ed. (1997). <i>Colour Physics for Industry</i> (2nd ed.). <a href="/wiki/Society_of_Dyers_and_Colourists" title="Society of Dyers and Colourists">Society of Dyers and Colourists</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-901956-70-8" title="Special:BookSources/0-901956-70-8"><bdi>0-901956-70-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Colour+Physics+for+Industry&rft.edition=2nd&rft.pub=Society+of+Dyers+and+Colourists&rft.date=1997&rft.isbn=0-901956-70-8&rfr_id=info%3Asid%2Fen.wikipedia.org%3AColor+difference" class="Z3988"></span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Color_difference&action=edit&section=17" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.brucelindbloom.com/ColorDifferenceCalc.html">Bruce Lindbloom's color difference calculator</a>. Uses all CIELAB metrics defined herein.</li> <li><a rel="nofollow" class="external text" href="http://www.ece.rochester.edu/~gsharma/ciede2000/">The CIEDE2000 Color-Difference Formula</a>, by Gaurav Sharma. Implementations in MATLAB and Excel.</li> <li><a rel="nofollow" class="external text" href="https://hexcolor.co/colors-between">Explore the Spectrum with Colors in Between</a>, by Bettie M. Cobb.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Color_topics" title="Template:Color topics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Color_topics" title="Template talk:Color topics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Color_topics" title="Special:EditPage/Template:Color topics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Color_topics" style="font-size:114%;margin:0 4em"><a href="/wiki/Color" title="Color">Color</a> topics</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_science" title="Color science">Color science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Color physics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Electromagnetic_spectrum" title="Electromagnetic spectrum">Electromagnetic spectrum</a> <ul><li><a href="/wiki/Light" title="Light">Light</a></li> <li><a href="/wiki/Rainbow" title="Rainbow">Rainbow</a></li> <li><a href="/wiki/Visible_spectrum" title="Visible spectrum">Visible</a></li></ul></li> <li><a href="/wiki/Spectral_color" title="Spectral color">Spectral colors</a></li> <li><a href="/wiki/Chromophore" title="Chromophore">Chromophore</a> <ul><li><a href="/wiki/Structural_coloration" title="Structural coloration">Structural coloration</a></li> <li><a href="/wiki/Animal_coloration" title="Animal coloration">Animal coloration</a></li></ul></li> <li><a href="/wiki/Color_of_chemicals" title="Color of chemicals">Color of chemicals</a> <ul><li><a href="/wiki/Color_of_water" title="Color of water">Water</a></li></ul></li> <li><a href="/wiki/Spectral_power_distribution" title="Spectral power distribution">Spectral power distribution</a></li> <li><a href="/wiki/Colorimetry" title="Colorimetry">Colorimetry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_vision" title="Color vision">Color perception</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chromesthesia" title="Chromesthesia">Chromesthesia</a> <ul><li><a href="/wiki/Sonochromatism" title="Sonochromatism">Sonochromatism</a></li></ul></li> <li><a href="/wiki/Color_blindness" title="Color blindness">Color blindness</a> <ul><li><a href="/wiki/Achromatopsia" title="Achromatopsia">Achromatopsia</a></li> <li><a href="/wiki/Dichromacy" title="Dichromacy">Dichromacy</a></li></ul></li> <li><a href="/wiki/Color_calibration" title="Color calibration">Color calibration</a></li> <li><a href="/wiki/Color_constancy" title="Color constancy">Color constancy</a></li> <li><a href="/wiki/Color_task" title="Color task">Color task</a> <ul><li><a href="/wiki/Color_code" title="Color code">Color code</a></li></ul></li> <li><a href="/wiki/Color_temperature" title="Color temperature">Color temperature</a></li> <li><a href="/wiki/Color_vision_test" title="Color vision test">Color vision test</a></li> <li><a href="/wiki/Evolution_of_color_vision" title="Evolution of color vision">Evolution of color vision</a></li> <li><a href="/wiki/Impossible_color" title="Impossible color">Impossible colors</a></li> <li><a href="/wiki/Metamerism_(color)" title="Metamerism (color)">Metamerism</a></li> <li><a href="/wiki/Opponent_process" title="Opponent process">Opponent process</a> <ul><li><a href="/wiki/Afterimage" title="Afterimage">Afterimage</a></li> <li><a href="/wiki/Unique_hues" title="Unique hues">Unique hues</a></li></ul></li> <li><a href="/wiki/Tetrachromacy" title="Tetrachromacy">Tetrachromacy</a></li> <li><i><a href="/wiki/The_dress" title="The dress">The dress</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_psychology" title="Color psychology">Color psychology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Color_symbolism" title="Color symbolism">Color symbolism</a></li> <li><a href="/wiki/Color_preferences" title="Color preferences">Color preferences</a></li> <li><a href="/wiki/L%C3%BCscher_color_test" title="Lüscher color test">Lüscher color test</a></li> <li><a href="/wiki/Kruithof_curve" title="Kruithof curve">Kruithof curve</a></li> <li><a href="/wiki/Political_colour" title="Political colour">Political color</a></li> <li><a href="/wiki/National_colours" title="National colours">National colors</a></li> <li><a href="/wiki/Chromophobia" title="Chromophobia">Chromophobia</a></li> <li><a href="/wiki/Chromotherapy" title="Chromotherapy">Chromotherapy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_reproduction" title="Color reproduction">Color reproduction</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Color_photography" title="Color photography">Color photography</a> <ul><li><a href="/wiki/Color_balance" title="Color balance">Color balance</a></li> <li><a href="/wiki/Colour_cast" title="Colour cast">Color cast</a></li></ul></li> <li><a href="/wiki/Digital_image_processing" title="Digital image processing">Digital image processing</a></li> <li><a href="/wiki/Color_management" title="Color management">Color management</a></li> <li><a href="/wiki/Color_printing" title="Color printing">Color printing</a> <ul><li><a href="/wiki/Multi-primary_color_display" title="Multi-primary color display">Multi-primary color display</a></li> <li><a href="/wiki/Quattron" title="Quattron">Quattron</a></li></ul></li> <li><a href="/wiki/Color_model" title="Color model">Color model</a> <ul><li><a href="/wiki/Additive_color" title="Additive color">additive</a> <ul><li><a href="/wiki/RGB" class="mw-redirect" title="RGB">RGB</a></li></ul></li> <li><a href="/wiki/Subtractive_color" title="Subtractive color">subtractive</a> <ul><li><a href="/wiki/CMYK" class="mw-redirect" title="CMYK">CMYK</a></li></ul></li></ul></li> <li><a href="/wiki/Color_space" title="Color space">Color space</a></li> <li><a href="/wiki/Color_mapping" class="mw-redirect" title="Color mapping">Color mapping</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:RGB_color_wheel.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/RGB_color_wheel.svg/100px-RGB_color_wheel.svg.png" decoding="async" width="100" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/56/RGB_color_wheel.svg/150px-RGB_color_wheel.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/56/RGB_color_wheel.svg/200px-RGB_color_wheel.svg.png 2x" data-file-width="600" data-file-height="500" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Philosophy_of_color" title="Philosophy of color">Color<br />philosophy</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_scheme" title="Color scheme">Color scheme</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Color_picker" title="Color picker">Color tool</a> <ul><li><a href="/wiki/Monochromatic_colors" class="mw-redirect" title="Monochromatic colors">Monochromatic colors</a> <ul><li><a href="/wiki/Black-and-white" title="Black-and-white">black-and-white</a></li></ul></li> <li><a href="/wiki/Complementary_colors" title="Complementary colors">Complementary colors</a></li> <li><a href="/wiki/Analogous_colors" title="Analogous colors">Analogous colors</a></li> <li><a href="/wiki/Grey" title="Grey">Achromatic colors (Neutral)</a></li> <li><a href="/wiki/Polychrome" title="Polychrome">Polychromatic colors</a></li></ul></li> <li><a href="/wiki/Light-on-dark_color_scheme" title="Light-on-dark color scheme">Light-on-dark</a></li> <li><a href="/wiki/Web_colors" title="Web colors">Web colors</a></li> <li><a href="/wiki/Tincture_(heraldry)" title="Tincture (heraldry)">Tinctures in heraldry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_theory" title="Color theory">Color theory</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Color_mixing" title="Color mixing">Color mixing</a> <ul><li><a href="/wiki/Primary_color" title="Primary color">Primary color</a></li> <li><a href="/wiki/Secondary_color" title="Secondary color">Secondary color</a></li></ul></li> <li><a href="/wiki/Chromaticity" title="Chromaticity">Chromaticity</a></li> <li><a href="/wiki/Color_solid" title="Color solid">Color solid</a></li> <li><a href="/wiki/Color_wheel" title="Color wheel">Color wheel</a></li> <li><a href="/wiki/Color_triangle" title="Color triangle">Color triangle</a></li> <li><a href="/wiki/Color_analysis" title="Color analysis">Color analysis</a> (fashion)</li> <li><a href="/wiki/Color_realism_(art_style)" title="Color realism (art style)">Color realism (art style)</a></li> <li><i><a href="/wiki/On_Vision_and_Colours" title="On Vision and Colours">On Vision and Colours</a></i> (Schopenhauer)</li> <li><i><a href="/wiki/Theory_of_Colours" title="Theory of Colours">Theory of Colours</a></i> (Goethe)</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_term" title="Color term">Color terms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Color_term#Basic_color_terms" title="Color term">Basic terms</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Blue" title="Blue">Blue</a></li> <li><a href="/wiki/Green" title="Green">Green</a></li> <li><a href="/wiki/Red" title="Red">Red</a></li> <li><a href="/wiki/Yellow" title="Yellow">Yellow</a></li> <li><a href="/wiki/Pink" title="Pink">Pink</a></li> <li><a href="/wiki/Purple" title="Purple">Purple</a></li> <li><a href="/wiki/Orange_(colour)" title="Orange (colour)">Orange</a></li> <li><a href="/wiki/Black" title="Black">Black</a></li> <li><a href="/wiki/Grey" title="Grey">Gray</a></li> <li><a href="/wiki/White" title="White">White</a></li> <li><a href="/wiki/Brown" title="Brown">Brown</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Color_in_culture" title="Category:Color in culture">Cultural differences</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Linguistic_relativity_and_the_color_naming_debate" title="Linguistic relativity and the color naming debate">Linguistic relativity and the color naming debate</a> <ul><li><a href="/wiki/Blue%E2%80%93green_distinction_in_language" title="Blue–green distinction in language">Blue–green distinction in language</a></li></ul></li> <li>Color history <ul><li><a href="/wiki/Black-and-white_dualism" title="Black-and-white dualism">Black-and-white dualism</a></li> <li><a href="/wiki/Blue_in_culture" title="Blue in culture">Blue in culture</a></li> <li><a href="/wiki/Color_in_Chinese_culture" title="Color in Chinese culture">Color in Chinese culture</a></li> <li><a href="/wiki/Traditional_colors_of_Japan" title="Traditional colors of Japan">Traditional colors of Japan</a></li> <li><a href="/wiki/Human_skin_color" title="Human skin color">Human skin color</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Color dimensions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Hue" title="Hue">Hue</a> <ul><li><a href="/wiki/Dichromatism" title="Dichromatism">Dichromatism</a></li></ul></li> <li><a href="/wiki/Colorfulness" title="Colorfulness">Colorfulness</a> <ul><li><a href="/wiki/Pastel_(color)" title="Pastel (color)">Pastel colors</a></li></ul></li> <li><a href="/wiki/Luminance" title="Luminance">Luminance</a> <ul><li><a href="/wiki/Lightness" title="Lightness">Lightness</a></li> <li><a href="/wiki/Darkness" title="Darkness">Darkness</a></li> <li><a href="/wiki/Brightness" title="Brightness">Brightness</a></li> <li><a href="/wiki/Iridescence" title="Iridescence">Iridescence</a></li> <li><a href="/wiki/Fluorescence" title="Fluorescence">Fluorescence</a></li></ul></li> <li><a href="/wiki/Grayscale" title="Grayscale">Grayscale</a></li> <li><a href="/wiki/Tint,_shade_and_tone" title="Tint, shade and tone">Tint, shade and tone</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Color<br />organizations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pantone" title="Pantone">Pantone</a></li> <li><a href="/wiki/Color_Marketing_Group" title="Color Marketing Group">Color Marketing Group</a></li> <li><a href="/wiki/Color_Association_of_the_United_States" title="Color Association of the United States">Color Association of the United States</a></li> <li><a href="/wiki/International_Colour_Authority" title="International Colour Authority">International Colour Authority</a></li> <li><a href="/wiki/International_Commission_on_Illumination" title="International Commission on Illumination">International Commission on Illumination</a> (CIE)</li> <li><a href="/wiki/International_Color_Consortium" title="International Color Consortium">International Color Consortium</a></li> <li><a href="/wiki/International_Colour_Association" title="International Colour Association">International Colour Association</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Names</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Lists_of_colors" title="Lists of colors">Lists</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_colors:_A%E2%80%93F" title="List of colors: A–F">List of colors: A–F</a></li> <li><a href="/wiki/List_of_colors:_G%E2%80%93M" title="List of colors: G–M">List of colors: G–M</a></li> <li><a href="/wiki/List_of_colors:_N%E2%80%93Z" title="List of colors: N–Z">List of colors: N–Z</a></li> <li><a href="/wiki/List_of_colors_(compact)" class="mw-redirect" title="List of colors (compact)">List of colors (compact)</a></li> <li><a href="/wiki/List_of_colors_by_shade" title="List of colors by shade">List of colors by shade</a></li> <li><a href="/wiki/List_of_color_palettes" title="List of color palettes">List of color palettes</a></li> <li><a href="/wiki/List_of_color_spaces_and_their_uses" title="List of color spaces and their uses">List of color spaces</a></li> <li><a href="/wiki/List_of_Crayola_crayon_colors" title="List of Crayola crayon colors">List of Crayola crayon colors</a> <ul><li><a href="/wiki/History_of_Crayola_crayons" title="History of Crayola crayons">history</a></li></ul></li> <li><a href="/wiki/Color_chart" title="Color chart">Color chart</a></li> <li><a href="/wiki/List_of_RAL_colors" class="mw-redirect" title="List of RAL colors">List of RAL colors</a></li> <li><a href="/wiki/Web_colors" title="Web colors">List of web colors</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_colors_by_shade" title="List of colors by shade">Shades of:</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Shades_of_red" title="Shades of red">Red</a></li> <li><a href="/wiki/Shades_of_orange" title="Shades of orange">Orange</a></li> <li><a href="/wiki/Shades_of_yellow" title="Shades of yellow">Yellow</a></li> <li><a href="/wiki/Shades_of_green" title="Shades of green">Green</a></li> <li><a href="/wiki/Shades_of_cyan" title="Shades of cyan">Cyan</a></li> <li><a href="/wiki/Shades_of_blue" title="Shades of blue">Blue</a></li> <li><a href="/wiki/Shades_of_violet" title="Shades of violet">Violet</a></li> <li><a href="/wiki/Shades_of_purple" title="Shades of purple">Purple</a></li> <li><a href="/wiki/Shades_of_magenta" title="Shades of magenta">Magenta</a></li> <li><a href="/wiki/Shades_of_pink" title="Shades of pink">Pink</a></li> <li><a href="/wiki/Shades_of_brown" title="Shades of brown">Brown</a></li> <li><a href="/wiki/Shades_of_white" title="Shades of white">White</a></li> <li><a href="/wiki/Shades_of_gray" title="Shades of gray">Gray</a></li> <li><a href="/wiki/Shades_of_black" title="Shades of black">Black</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Index_of_color-related_articles" title="Index of color-related articles">Related</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Visual_perception" title="Visual perception">Vision</a> <ul><li><a href="/wiki/Contrast_(vision)" title="Contrast (vision)">Contrast</a></li></ul></li> <li><a href="/wiki/Qualia" title="Qualia">Qualia</a></li> <li><a href="/wiki/Lighting" title="Lighting">Lighting</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Color" title="Category:Color">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="List-Class article"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/d/db/Symbol_list_class.svg/16px-Symbol_list_class.svg.png" 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Color difference - Wikipedia