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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">Identification of something to locations in physical space</div> <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">Not to be confused with <a href="/wiki/Rubbersheeting" title="Rubbersheeting">Rubbersheeting</a>.</div> <p><b>Georeferencing</b> or <b>georegistration</b> is a type of <a href="/wiki/Coordinate_transformation" class="mw-redirect" title="Coordinate transformation">coordinate transformation</a> that binds a digital raster image or vector database that represents a geographic space (usually a scanned map or <a href="/wiki/Aerial_photograph" class="mw-redirect" title="Aerial photograph">aerial photograph</a>) to a <a href="/wiki/Spatial_reference_system" title="Spatial reference system">spatial reference system</a>, thus locating the digital data in the real world.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><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> It is thus the geographic form of <a href="/wiki/Image_registration" title="Image registration">image registration</a> or <a href="/wiki/Image_rectification" title="Image rectification">image rectification</a>. The term can refer to the mathematical formulas used to perform the transformation, the <a href="/wiki/Geospatial_metadata" title="Geospatial metadata">metadata</a> stored <a href="/wiki/Sidecar_file" title="Sidecar file">alongside</a> or within the image file to specify the transformation, or the process of manually or automatically aligning the image to the real world to create such metadata. The most common result is that the image can be visually and analytically integrated with other geographic data in <a href="/wiki/Geographic_information_systems" class="mw-redirect" title="Geographic information systems">geographic information systems</a> and <a href="/wiki/Remote_sensing" title="Remote sensing">remote sensing</a> software. </p><p>A number of mathematical methods are available, but the process typically involves identifying a sample of several <b>ground control points</b> (<b>GCPs</b>) with known locations on the image and the ground, then using <a href="/wiki/Curve_fitting" title="Curve fitting">curve fitting</a> techniques to generate a parametric (or piecewise parametric) formula to transform the rest of the image.<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> Once the parameters of the formula are stored, the image may be transformed dynamically at drawing time, or resampled to generate a georeferenced <a href="/wiki/GIS_file_format#raster" title="GIS file format">raster GIS file</a> or <a href="/wiki/Orthophoto" title="Orthophoto">orthophoto</a>. </p><p>The term georeferencing has also been used to refer to other types of transformation from general expressions of geographic location (<i><a href="/wiki/Geocode" title="Geocode">geocodes</a></i>) to coordinate measurements,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> but most of these other methods are more commonly called <a href="/wiki/Geocoding" class="mw-redirect" title="Geocoding">geocoding</a>. Because of this ambiguity, <i>Georegistration</i> is preferred by some to refer to the image transformation.<sup id="cite_ref-longley2011_5-0" class="reference"><a href="#cite_note-longley2011-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 141–143">: 141–143 </span></sup> Occasionally, this process has been called <i><a href="/wiki/Rubbersheeting" title="Rubbersheeting">rubbersheeting</a></i>, but that term is more commonly applied to a very similar process applied to <a href="/wiki/Data_model_(GIS)#vector" title="Data model (GIS)">vector GIS</a> data.<sup id="cite_ref-longley2011_5-1" class="reference"><a href="#cite_note-longley2011-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 240">: 240 </span></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Motivation">Motivation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Georeferencing&action=edit&section=1" title="Edit section: Motivation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Georeferencing is crucial to make <a href="/wiki/Aerial_imagery" class="mw-redirect" title="Aerial imagery">aerial</a> and <a href="/wiki/Satellite_imagery" title="Satellite imagery">satellite imagery</a>, usually raster images, useful for mapping as it explains how other data, such as the above <a href="/wiki/GPS" class="mw-redirect" title="GPS">GPS</a> points, relate to the imagery.</li> <li>Very essential information may be contained in data or images that were produced at a different point of time. It may be desired either to combine or compare this data with that currently available. The latter can be used to analyze the changes in the features under study over a period of time.</li> <li>Different maps may use different projection systems. Georeferencing tools contain methods to combine and overlay these maps with minimum distortion.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Mathematics">Mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Georeferencing&action=edit&section=2" title="Edit section: Mathematics"><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">Main article: <a href="/wiki/Geometric_transformation" title="Geometric transformation">Geometric transformation</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:WorldFileParametersSchemas.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/4/41/WorldFileParametersSchemas.gif/220px-WorldFileParametersSchemas.gif" decoding="async" width="220" height="556" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/41/WorldFileParametersSchemas.gif/330px-WorldFileParametersSchemas.gif 1.5x, //upload.wikimedia.org/wikipedia/en/4/41/WorldFileParametersSchemas.gif 2x" data-file-width="395" data-file-height="998" /></a><figcaption>Graphical view of the affine transformation.</figcaption></figure> <p>The registration of an image to a geographic space is essentially the transformation from an input coordinate system (the inherent coordinates of pixels in the images based on row and column number) to an output coordinate system, a <a href="/wiki/Spatial_reference_system" title="Spatial reference system">spatial reference system</a> of the user's choice, such as the <a href="/wiki/Geographic_coordinate_system" title="Geographic coordinate system">geographic coordinate system</a> or a particular <a href="/wiki/Universal_Transverse_Mercator" class="mw-redirect" title="Universal Transverse Mercator">Universal Transverse Mercator</a> zone. It is thus the extension of the typical task of <a href="/wiki/Curve_fitting" title="Curve fitting">curve fitting</a> a relationship between two variables to four dimensions. The goal is to have a pair of functions of the form: </p> <dl><dd><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 x_{out}=F(x_{in},y_{in})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>F</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{out}=F(x_{in},y_{in})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0deca260de88d0e2e4fe60a82b65a698a81f6015" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.616ex; height:2.843ex;" alt="{\displaystyle x_{out}=F(x_{in},y_{in})}"></span></dd> <dd><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 y_{out}=G(x_{in},y_{in})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>G</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{out}=G(x_{in},y_{in})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bf012b3db3bb76f8e9b9f4f7733e9b9413b4148" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.512ex; height:2.843ex;" alt="{\displaystyle y_{out}=G(x_{in},y_{in})}"></span></dd></dl> <p>Such that for every pixel in the image (<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 x_{in},y_{in}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{in},y_{in}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be82937a1617987c70179a7d8b9b489744c24cb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.075ex; height:2.009ex;" alt="{\displaystyle x_{in},y_{in}}"></span> being its column and row number, respectively), a corresponding real-world coordinate can be calculated. </p><p>Several types of functions are available in most GIS and remote sensing software for georeferencing.<sup id="cite_ref-esri_6-0" class="reference"><a href="#cite_note-esri-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> As the simplest type of two-dimensional curve is a straight line, so the simplest form of coordinate transformation is a linear transformation, the most common type being the <a href="/wiki/Affine_transformation" title="Affine transformation">affine transformation</a>:<sup id="cite_ref-bolstad_7-0" class="reference"><a href="#cite_note-bolstad-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 171">: 171 </span></sup> </p> <dl><dd><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 x_{out}=Ax_{in}+By_{in}+C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>A</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>B</mi> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{out}=Ax_{in}+By_{in}+C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6386a22ddab23219e34fcd32d83da34df54d9032" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.987ex; height:2.509ex;" alt="{\displaystyle x_{out}=Ax_{in}+By_{in}+C}"></span></dd> <dd><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 y_{out}=Dx_{in}+Ey_{in}+F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>D</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>E</mi> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{out}=Dx_{in}+Ey_{in}+F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd9247d8600c67ab977a873f960bfcff6b0a8aeb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:23.963ex; height:2.509ex;" alt="{\displaystyle y_{out}=Dx_{in}+Ey_{in}+F}"></span></dd></dl> <p>Where A-F are constant coefficients set for the entire image. These formulas allow an image to be <i>moved</i> (the C and F coefficients specify the desired location of the top left corner of the image), <i>scaled</i> (without rotation, the A and E coefficients specify the size of each cell or <a href="/wiki/Spatial_resolution" title="Spatial resolution">spatial resolution</a>), and <i>rotated</i>.<sup id="cite_ref-chang2014_8-0" class="reference"><a href="#cite_note-chang2014-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 115">: 115 </span></sup> In the last case, if the cell size is <i>r</i> in both the x and y directions, and the image is to be rotated <i>α</i> degrees counter-clockwise, then <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 A=E=r\cos(\alpha ),B=D=r\sin(\alpha )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mi>E</mi> <mo>=</mo> <mi>r</mi> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mi>B</mi> <mo>=</mo> <mi>D</mi> <mo>=</mo> <mi>r</mi> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=E=r\cos(\alpha ),B=D=r\sin(\alpha )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c08a53e7c0c23e97e967662393814c6ef58cb1ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.067ex; height:2.843ex;" alt="{\displaystyle A=E=r\cos(\alpha ),B=D=r\sin(\alpha )}"></span>. The <a href="/wiki/World_file" title="World file">world file</a> developed by Esri is a commonly used <a href="/wiki/Sidecar_file" title="Sidecar file">sidecar file</a> that specifies these six coefficients for image georeferencing. </p><p>Higher order polynomial transformations are also commonly used. For example, a Second-order polynomial transformation would be: </p> <dl><dd><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 x_{out}=Ax_{in}+By_{in}+Cx_{in}^{2}+Dy_{in}^{2}+Ex_{in}y_{in}+F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>A</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>B</mi> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>C</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>D</mi> <msubsup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>E</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{out}=Ax_{in}+By_{in}+Cx_{in}^{2}+Dy_{in}^{2}+Ex_{in}y_{in}+F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bb12d98f74babc7827eb153e4bc28dfeac9c4ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:50.03ex; height:3.176ex;" alt="{\displaystyle x_{out}=Ax_{in}+By_{in}+Cx_{in}^{2}+Dy_{in}^{2}+Ex_{in}y_{in}+F}"></span></dd> <dd><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 y_{out}=Gx_{in}+Hy_{in}+Ix_{in}^{2}+Jy_{in}^{2}+Kx_{in}y_{in}+L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mi>G</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>H</mi> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>I</mi> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>J</mi> <msubsup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mi>K</mi> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{out}=Gx_{in}+Hy_{in}+Ix_{in}^{2}+Jy_{in}^{2}+Kx_{in}y_{in}+L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1e05a51b2ac7cb111ba17e8fd835dd6fd6205037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:49.308ex; height:3.176ex;" alt="{\displaystyle y_{out}=Gx_{in}+Hy_{in}+Ix_{in}^{2}+Jy_{in}^{2}+Kx_{in}y_{in}+L}"></span></dd></dl> <p>The second-order terms (and third-order terms in a third-order polynomial) allow for the variable warping of the image, which is especially useful for removing the inherent <a href="/wiki/Distortion_(optics)" title="Distortion (optics)">distortion</a> in aerial photographs. </p><p>In addition to global parametric formulas, piecewise formulas can also be used, which transform different parts of the image in different ways. A common example is a <a href="/wiki/Thin_plate_spline" title="Thin plate spline">Thin plate spline</a> transformation.<sup id="cite_ref-qgis_9-0" class="reference"><a href="#cite_note-qgis-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="The_GCP_method">The GCP method</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Georeferencing&action=edit&section=3" title="Edit section: The GCP method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is very rare that a user would specify the parameters for the transformation directly. Instead, most <a href="/wiki/Geographic_information_system" title="Geographic information system">GIS</a> and <a href="/wiki/Remote_sensing" title="Remote sensing">remote sensing</a> software provides an interactive environment for visually aligning the image to the destination coordinate system. The most common method for doing this is to create a series of <i>ground control points</i> (GCP).<sup id="cite_ref-bolstad_7-1" class="reference"><a href="#cite_note-bolstad-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 170">: 170 </span></sup> A ground control point is a location that can be identified on both the image and the ground, so that it has precise coordinates in both the image coordinate system (<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 x_{in}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{in}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8c792be9821fb9c617b3a0963e52fa0d9244975" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.116ex; height:2.009ex;" alt="{\displaystyle x_{in}}"></span> = pixel column, <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 y_{in}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{in}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8524dd32682861d31a0d433d0d8db5ec56962305" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.925ex; height:2.009ex;" alt="{\displaystyle y_{in}}"></span> = pixel row) and the ground coordinate system (<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 x_{out},y_{out}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{out},y_{out}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0110939ac3fb4ef7f77ef84f8617392724cf2f4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.63ex; height:2.009ex;" alt="{\displaystyle x_{out},y_{out}}"></span>). Easily visible locations that be precisely located are preferred as GCP's, such as a road intersection or the corner of a building. When very high accuracy registration is required, it is common to place or paint high-contrast markers on the ground at survey control monuments before the photography is taken, and use GNSS-measured coordinates for the output. In most software, these are entered by pointing at the location on the image, then pointing at the same location on a vector base map or <a href="/wiki/Orthophoto" title="Orthophoto">orthophoto</a> that is already in the desired coordinate system. This can then be moved and adjusted to improve accuracy. </p><p>With a minimal set of GCPs, the known coordinates can be entered into the mathematical equations for the desired type of transformation, which can then be solved using <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> to determine the coefficients and derive the formulas to use for the entire grid.<sup id="cite_ref-chang2014_8-1" class="reference"><a href="#cite_note-chang2014-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 116">: 116 </span></sup> For example, the linear affine transformation above has six unknown coefficients, so six equations with known <<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 x_{in},y_{in},x_{out},y_{out}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{in},y_{in},x_{out},y_{out}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6359552efa11ca90ba2b56bf26d8ed6ebcf5120f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.738ex; height:2.009ex;" alt="{\displaystyle x_{in},y_{in},x_{out},y_{out}}"></span>> are needed to derive them, which will require three ground control points.<sup id="cite_ref-bolstad_7-2" class="reference"><a href="#cite_note-bolstad-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 171">: 171 </span></sup> The second-order polynomial requires a minimum of six ground control points, and so on. </p><p>The entered GCPs are rarely perfectly located and are even more rarely perfectly representative of the distortion in the rest of the image, but the algebraic solution, which appears to be a perfect match, masks any error. To avoid this, it is common to create many more than the minimal required set (creating an <a href="/wiki/Overdetermined_system" title="Overdetermined system">overdetermined system</a>), and use <a href="/wiki/Least_squares" title="Least squares">least squares</a> regression to derive a set of function parameters that most closely matches the points.<sup id="cite_ref-chang2014_8-2" class="reference"><a href="#cite_note-chang2014-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 116">: 116 </span></sup> This is almost never a perfect match, so the variance between each GCP location and the location predicted by the functions can be measured and summarized as a <a href="/wiki/Root-mean-square_deviation" class="mw-redirect" title="Root-mean-square deviation">Root-mean-square error</a> (RMSE). A lower RMSE thus means that the transformation formulas closely match the GCPs. </p><p>Once the function parameters are determined, the transformation functions can be used to transform every pixel of the image to its real-world location. Two options are usually available for making this transformation permanent. One option is to save the parameters themselves as a form of <a href="/wiki/Geospatial_metadata" title="Geospatial metadata">metadata</a>, either in the header of the image file itself (e.g., <a href="/wiki/GeoTIFF" title="GeoTIFF">GeoTIFF</a>), or in a sidecar file stored alongside the image file (e.g., a <a href="/wiki/World_file" title="World file">world file</a>). With this metadata, the software can perform the transformation dynamically as it displays the image, so that it appears to align with other data in the desired coordinate system. The alternative method is <a href="/wiki/Image_rectification" title="Image rectification">rectification</a>, in which the image is <a href="/wiki/Image_scaling" title="Image scaling">resampled</a> to create a new raster grid that is natively tied to the coordinate system. Rectification was traditionally the only option, until the computing power became available for the intense calculations of dynamic coordinate transformations; even now, drawing and analysis performance is better with a rectified image. </p> <div class="mw-heading mw-heading2"><h2 id="Software_implementations">Software implementations</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Georeferencing&action=edit&section=4" title="Edit section: Software implementations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Esri" title="Esri">Esri</a> GIS software has had this capability for many years, including the Georeferencing tool in ArcGIS Pro.<sup id="cite_ref-esri_6-1" class="reference"><a href="#cite_note-esri-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/QGIS" title="QGIS">QGIS</a> has a Georeferencer tool, originally developed as an add-on but now integrated into the software.<sup id="cite_ref-qgis_9-1" class="reference"><a href="#cite_note-qgis-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup></li> <li><a rel="nofollow" class="external text" href="https://doc.hexagongeospatial.com/r/pWMRSd2zrKmOxN_x64q27A/sM_oWidtfoLKKZW6BtgQ2A">Image Georeferencing and Rectification</a> in <a href="/wiki/ERDAS_Imagine" class="mw-redirect" title="ERDAS Imagine">ERDAS Imagine</a></li> <li><a rel="nofollow" class="external text" href="https://www.nv5geospatialsoftware.com/docs/registrationimagetomap.html">Image to Map Registration</a> in <a href="/wiki/ENVI_(software)" class="mw-redirect" title="ENVI (software)">ENVI</a></li> <li><a rel="nofollow" class="external text" href="https://allmaps.org/">Allmaps</a> supports various transformation algorithms (including the Thin Plate Spline transformation), and the computation of distortions, through its <a rel="nofollow" class="external text" href="https://www.npmjs.com/package/@allmaps/transform">@allmaps/transform</a> package.</li></ul> <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=Georeferencing&action=edit&section=5" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Altimetry" class="mw-redirect" title="Altimetry">Altimetry</a></li> <li><a href="/wiki/Cadaster" class="mw-redirect" title="Cadaster">Cadaster</a></li> <li><a href="/wiki/Geocoding" class="mw-redirect" title="Geocoding">Geocoding</a></li> <li><a href="/wiki/Geomessaging" title="Geomessaging">Geomessaging</a></li> <li><a href="/wiki/Geoportal" title="Geoportal">Geoportal</a></li> <li><a href="/wiki/Geopositioning" title="Geopositioning">Geopositioning</a></li> <li><a href="/wiki/GeoReader" title="GeoReader">GeoReader</a></li> <li><a href="/wiki/Geotagging" title="Geotagging">Geotagging</a></li> <li><a href="/wiki/Hydrography" title="Hydrography">Hydrography</a></li> <li><a href="/wiki/Image_registration" title="Image registration">Image registration</a></li> <li><a href="/wiki/Linear_referencing" title="Linear referencing">Linear referencing</a></li> <li><a href="/wiki/Reverse_geocoding" title="Reverse geocoding">Reverse geocoding</a></li> <li><a href="/wiki/Rubbersheeting" title="Rubbersheeting">Rubbersheeting</a></li> <li><a href="/wiki/Reference_ellipsoid" class="mw-redirect" title="Reference ellipsoid">Reference ellipsoid</a></li> <li><a href="/wiki/Spatial_reference_system" title="Spatial reference system">Spatial reference system</a></li> <li><a href="/wiki/Toponym_resolution" title="Toponym resolution">Toponym resolution</a></li> <li><a href="/wiki/Transport_infrastructure" class="mw-redirect" title="Transport infrastructure">Transport infrastructure</a></li> <li><a href="/wiki/World_Geodetic_System" title="World Geodetic System">World Geodetic System</a></li></ul></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Georeferencing&action=edit&section=6" title="Edit section: References"><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"> <div class="mw-references-wrap"><ol class="references"> <li 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"Georeferencing: From Texts to Maps". <i><a href="/w/index.php?title=International_Encyclopedia_of_Geography:_People,_the_Earth,_Environment_and_Technology&action=edit&redlink=1" class="new" title="International Encyclopedia of Geography: People, the Earth, Environment and Technology (page does not exist)">International Encyclopedia of Geography: People, the Earth, Environment and Technology</a></i>. <b>vi</b>: 2897–2907. <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%2F9781118786352.wbieg0160">10.1002/9781118786352.wbieg0160</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780470659632" title="Special:BookSources/9780470659632"><bdi>9780470659632</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Encyclopedia+of+Geography%3A+People%2C+the+Earth%2C+Environment+and+Technology&rft.atitle=Georeferencing%3A+From+Texts+to+Maps.&rft.volume=vi&rft.pages=2897-2907&rft.date=2017&rft_id=info%3Adoi%2F10.1002%2F9781118786352.wbieg0160&rft.isbn=9780470659632&rft.au=Leidner%2C+J.L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> <li id="cite_note-longley2011-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-longley2011_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-longley2011_5-1"><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="CITEREFLongleyGoodchildMaguireRhind2011" class="citation book cs1">Longley, Paul A.; Goodchild, Michael F.; Maguire, David J.; Rhind, David W. (2011). <i>Geographic Information Systems & Science</i> (3rd ed.). Wiley.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geographic+Information+Systems+%26+Science&rft.edition=3rd&rft.pub=Wiley&rft.date=2011&rft.aulast=Longley&rft.aufirst=Paul+A.&rft.au=Goodchild%2C+Michael+F.&rft.au=Maguire%2C+David+J.&rft.au=Rhind%2C+David+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> <li id="cite_note-esri-6"><span class="mw-cite-backlink">^ <a href="#cite_ref-esri_6-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-esri_6-1"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://pro.arcgis.com/en/pro-app/latest/help/data/imagery/overview-of-georeferencing.htm">"Overview of georeferencing"</a>. <i>ArcGIS Pro Documentation</i>. Esri<span class="reference-accessdate">. Retrieved <span class="nowrap">8 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ArcGIS+Pro+Documentation&rft.atitle=Overview+of+georeferencing&rft_id=https%3A%2F%2Fpro.arcgis.com%2Fen%2Fpro-app%2Flatest%2Fhelp%2Fdata%2Fimagery%2Foverview-of-georeferencing.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> <li id="cite_note-bolstad-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-bolstad_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-bolstad_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-bolstad_7-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBolstad2019" class="citation book cs1">Bolstad, Paul (2019). <i>GIS Fundamentals: A First Text on Geographic Information Systems</i>. Ann Arbor, MI: XanEdu. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-59399-552-2" title="Special:BookSources/978-1-59399-552-2"><bdi>978-1-59399-552-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=GIS+Fundamentals%3A+A+First+Text+on+Geographic+Information+Systems&rft.place=Ann+Arbor%2C+MI&rft.pub=XanEdu&rft.date=2019&rft.isbn=978-1-59399-552-2&rft.aulast=Bolstad&rft.aufirst=Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> <li id="cite_note-chang2014-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-chang2014_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-chang2014_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-chang2014_8-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFChang2014" class="citation book cs1">Chang, Kang-tsung (2014). <i>Introduction to Geographic Information Systems</i> (7th ed.). McGraw-Hill. pp. 50–57. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-07-352290-6" title="Special:BookSources/978-0-07-352290-6"><bdi>978-0-07-352290-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Geographic+Information+Systems&rft.pages=50-57&rft.edition=7th&rft.pub=McGraw-Hill&rft.date=2014&rft.isbn=978-0-07-352290-6&rft.aulast=Chang&rft.aufirst=Kang-tsung&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> <li id="cite_note-qgis-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-qgis_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-qgis_9-1"><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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://docs.qgis.org/3.22/en/docs/user_manual/working_with_raster/georeferencer.html">"16.3 Georeferencer"</a>. <i>QGIS 3.22 documentation</i>. OSGEO<span class="reference-accessdate">. Retrieved <span class="nowrap">8 January</span> 2023</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=QGIS+3.22+documentation&rft.atitle=16.3+Georeferencer&rft_id=https%3A%2F%2Fdocs.qgis.org%2F3.22%2Fen%2Fdocs%2Fuser_manual%2Fworking_with_raster%2Fgeoreferencer.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></span> </li> </ol></div></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=Georeferencing&action=edit&section=7" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHill2006" class="citation book cs1">Hill, Linda L. (2006). <i>Georeferencing</i>. <a href="/wiki/The_MIT_Press" class="mw-redirect" title="The MIT Press">The MIT Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0262083546" title="Special:BookSources/978-0262083546"><bdi>978-0262083546</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Georeferencing&rft.pub=The+MIT+Press&rft.date=2006&rft.isbn=978-0262083546&rft.aulast=Hill&rft.aufirst=Linda+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeoreferencing" class="Z3988"></span></li></ul> <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=Georeferencing&action=edit&section=8" 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.geoinfo.info/geoinfo2008/papers/p13.pdf">Discovering Location Indicators of Toponyms from News to Improve Gazetteer-Based Geo-Referencing</a> - paper presented at Geoinfo 2008</li> <li><a rel="nofollow" class="external text" href="http://www.restore.ac.uk/geo-refer/">Geographical referencing resources for social scientists</a> online tutorial material from the University of Southampton, UK</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Georeferencing&oldid=1259046895">https://en.wikipedia.org/w/index.php?title=Georeferencing&oldid=1259046895</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Category</a>: <ul><li><a href="/wiki/Category:Geographic_data_and_information" title="Category:Geographic data and information">Geographic data and information</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_matches_Wikidata" title="Category:Short description matches Wikidata">Short description matches Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 23 November 2024, at 02:12<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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