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research_areas[0].push(new demo('Brightness contrast: standard','In viewing this stimulus, people invariably perceive the square on the brighter surround (left) to be darker than the square on the darker surround (right). Click on the "Play" button to convince yourself that the squares are equiluminant or click on the "Move mask" button to manually position the mask over the squares.', 'simultaneous-brightness-contrast/', 'SBC1.swf','null','bcs')); research_areas[0].push(new demo('Brightness contrast: gradient','In this example of simultaneous brightness contrast, the brightness of the circle is perceived to increase as it moves to the darker side (right) of the gradient and to decrease as it moves to the left side. Click on the "Move mask" button to position a mask over the gradient and convince yourself that that the luminance of the circle remains constant.','simultaneous-brightness-contrast/','SBCgr.swf')); research_areas[0].push(new demo('Brightness contrast: cube scene','As can be seen by masking out the context, the gray diamonds on the upper and lower front face of the cubes are identical, but look very different in the unmasked scene. When the information in a scene indicates that, on statistical grounds, two targets are differently reflective surfaces under different illuminants, they look differently bright (or light). (Image from: An empirical explanation of brightness. Williams, SM, McCoy AN, Purves D. Proc. Natl. Acad. Sci. 95: 13301-13306 [1998])','simultaneous-brightness-contrast/','SBC0.swf',null,'bcc')); research_areas[0].push(new demo('Brightness contrast: multiple cues','When diverse statistical information about the sources of a visual stimulus is mutually consistent, two equiluminant surfaces can be made to appear dramatically different than they do in standard presentations. In this case, the empirical information indicates a high probability that the two surfaces are differently reflective materials under different levels of illumination, making the same patch in one part of the scene look very dark gray, and in another part of the scene very light gray. (Image by Beau Lotto)','simultaneous-brightness-contrast/','SBC3.swf',null,'bcx')); research_areas[0].push(new demo('Brightness contrast with color: cube','Just as achromatic patches can be made to look differently bright by empirical information, color patches can be dramatically affected by empirical cues about the amount of illumination they are likely to be under. In this example, the effect is primarily on the color brightness of the relevant tiles rather than on sensations of hue or saturation as such. (Image by Beau Lotto)','brightness/brightness.html','BCC.swf',null,'bccc')); research_areas[0].push(new demo('Craik-O\'Brien-Cornsweet effect','In viewing this scene, people invariably perceive the surface of the top block to be darker than the bottom block. Click on the play button to see that these territories are in fact identical. Covering the center section, including the shaded gradients, shows that the source of the difference is this component of the scene. (Image by Beau Lotto)','craik-obrain-cornsweet-effect/','COC2.swf',null,'coc')); research_areas[0].push(new demo('Mach Bands','(Left) Photograph of a real-world cube manifesting a photometric highlight and lowlight (see luminance profile beneath the photo). (Right) A computer- generated image of a similar object, but lacking the highlight and lowlight. Despite the objective absence of these adornments, brightness maxima and minima (Mach bands) are apparent in the positions of their photometric counterparts in A. (Image from: Mach bands as empirically derived associations. Lotto RB, Williams SM, Purves D., Proc. Natl. Acad. Sci. 96: 5245-5250 [1999])','mach-bands-2/','mach.swf')); research_areas[0].push(new demo('Chubb Illusion (variant)','When the dark and light segments of both the inner and outer disks are not aligned, the gray portions of the inner disk look different (more contrast) than when they are aligned (press the rotate button to shift from the unaligned to aligned configuration to see this effect). The original version of this illusion appears in Chubb, C, Sperling, G and Solomon, JA (1989) Texture interactions determine perceived contrast. PNAS 86:9631-9635.','chubb-illusion/','Chubb.swf')); research_areas[0].push(new demo('Emmert\'s effect','This fascinating demonstration clearly indicates the ambiguity of retinal images. By staring at the first stimulus, a retinal after-image is created that occupies a fixed retinal area. Nonetheless, the form and size of the after-image changes according to the surface on which it is seen, as will be apparent by looking at the after-image on a nearby sheet of white paper or a more distant, light colored wall.',null,'Emmt.swf')); research_areas[0].push(new demo('Test 1: Brightness Contrast: Standard','Directions for taking the test: Using the adjustment buttons below at right, adjust the brightness of the target square on the darker background to match the brightness of the target on the lighter background. The + button increases target brightness, the – button decreases brightness. When the targets appear to be equally bright, click the "DONE" button. A second image will appear. Again, adjust the brightness of the target square on the darker background to match the brightness of the target on the lighter background. After selecting the "DONE" button, a graph of your results and a brief explanation will be displayed.','simultaneous-brightness-contrast/','Brightness1.swf','Explanation of results: In both of the test images, the two target squares appear unequally bright but are in fact identical. The graph (right) illustrates this brightness misperception. The blue bar in the graph indicates the initial grayscale value of both squares. The yellow bar indicates the value of the target on the dark surround after your adjustments. For most people, the degree of misperception is greater for the image indicated by the icon on the right. See the Research section of the website for the biological explanation of this effect.')); research_areas[0].push(new demo('Test 2: Brightness Contrast: Cube Scene','Directions for taking the test: Using the adjustment buttons below at right, adjust the brightness of the target diamond on the darker background (top face of the cube in the foreground) to match the brightness of the target on the lighter background (left face of the cube in the foreground). The + button increases target brightness, the – button decreases brightness. When the targets appear to be equally bright, click the "DONE" button. A second image will appear. Again, adjust the brightness of the target on the darker background (this time the left face of the cube in the foreground) to match the brightness of the target on the lighter background (top face of the cube in the foreground). After selecting the "DONE" button, a graph of your results and a brief explanation will be displayed.','simultaneous-brightness-contrast/','Brightness2.swf','Explanation of results: In both of the test images, the two targets (diamonds) appear unequally bright but are in fact identical. The graph (right) illustrates this brightness misperception. The blue bar in the graph indicates the initial grayscale value of both diamonds. The yellow bar indicates the value of the diamond on the dark surround after your adjustments. For most people, the degree of misperception is greater for the image indicated by the icon on the right in which the dark surround appears to be in shadow, that is when the left face of the cube is darker. See the Research section of the website for the biological explanation of this effect.')); research_areas[0].push(new demo('Test 3: Brightness Contrast: Rotated Cube','Directions for taking the test: Using the adjustment buttons below at right, adjust the brightness of the target diamond on the darker background (top face of the cube) to match the brightness of the target on the lighter background (bottom face). The + button increases target brightness, the – button decreases brightness. When the targets appear to be equally bright, click the "DONE" button. A second image will appear. Again, adjust the brightness of the target (diamond) on the darker background (this time, the bottom face) to match the brightness of the target on the lighter background (top face). After selecting the "DONE" button, a graph of your results and a brief explanation will be displayed.','simultaneous-brightness-contrast/','Brightness3.swf','Explanation of results: In both of the test images, the two targets (diamonds) appear unequally bright but are in fact, identical. The graph (right) illustrates this brightness misperception. The blue bar in the graph indicates the initial grayscale value of both diamonds. The yellow bar indicates the value of the diamond on the dark surround after your adjustments. For most people, the degree of misperception is greater for the image (scene) indicated by the icon on the right in which the dark surround appears to be in shadow, that is when the bottom face of the cube is darker. It should be noted that in this test the two cube images are identical except that the second image is rotated 180 degrees. See the Research section of the website for the biological explanation of this effect.')); research_areas[1].push(new demo('Color contrast: standard','It has been known for more than 150 years that spectrally identical patches can look differently colored when placed in spectrally different surrounds. The two central targets here are identical, as can be seen by masking out the surround.','color-contrast-and-constancy-2/','Color2.swf',null,'ccs')); research_areas[1].push(new demo('Color contrast: multiple cues','Moving the mask makes it apparent that statistical information about probable sources strongly affects color, as well as lightness and/or brightness. Here, two spectrally identical patches (indicated with a dot) appear gray-green when viewed in isolation, but look reddish and bluish, respectively, when viewed in the context of empirical information that makes different surfaces under different chromatic illuminants a highly likely source of the stimulus. (Image by Beau Lotto)','color-contrast-and-constancy-2/','Color1.swf',null,'ccx')); research_areas[1].push(new demo('Color contrast: cube','In this remarkable demonstration, physically identical patches that appear neutral gray when viewed in isolation can be made to look either yellow or blue, depending on the context in which they appear. Although quite unbelievable at first glance, the reality of the demonstration can be confirmed by masking out the context. (Image by Beau Lotto)','color-contrast-and-constancy-2/','Cntrst_cube.swf',null,'ccc')); research_areas[1].push(new demo('Color constancy: cube','In this equally remarkable example, differently colored patches can be made to look more or less the same color (red in this case) by empirical information, which changes the probable spectral sources of the differently colored tiles. These demonstrations show that color contrast and constancy are both manifestations of the same empirically determined visual strategy for seeing color. (Image by Beau Lotto)','color-contrast-and-constancy-2/','Cnstcy_cube.swf',null,'ccc2')); research_areas[1].push(new demo('Chromatic adaptation','The effects of chromatic adaptation can be experienced by focusing on the central white dot in for 20-30 seconds (press the Play button to set timer), and then refocusing on the corresponding dot in the subsequently displayed image. The colors elicited by the two physically identical scenes but seen by components of the visual system "adapted" to red and green, respectively, look appreciably different.','color-contrast-and-constancy-2/','Chromat.swf')); research_areas[2].push(new demo('Perception of angles','A wide range of empirical factors influences the perception of angles. In this scene, the subtenses of the four angular objects in the retinal stimulus are identical, each measuring approximately 90°. As a result of this variety of depicted cues about the attributes of the possible real-world sources (see text), the subtenses of the four identical angles look quite different. Press the "Play" button to convince yourself. (Image by Beau Lotto)','angles-4/','angles.swf',null,'line')); research_areas[2].push(new demo('Poggendorff','Drag the red line on the right until it appears continuous (colinear) with the red line on the left. When you are done, click the highlighted button below the image to remove the mask.',null,'pg.swf',null,'line')); research_areas[2].push(new demo('Line length','Which line is longer? Use the plus or minus buttons to adjust the length of the horizontal (bottom) line until it appears to match the length of the vertical (top) line. Click the done button to see how your adjusted line compares to the actual line length.',null,'ll.swf',null,'line')); research_areas[2].push(new demo('Müller-Lyer','Drag the red arrowhead until the line between the arrowheads appears to be the same length as the line between the inverted arrowheads above. When you are done, click the highlighted button below the image to see how your adjusted line compares to the actual line length.',null,'ml.swf',null,'line')); // no depth demos research_areas[4].push(new demo('Objective and perceived motion','This demonstration indicates the profound ambiguity of the image sequences that generate perceptions of motion. The stimulus is always a line translating from left to right. The apparent direction and speed of the line, however, are markedly changed by the context, as can be seen by clicking on the appropriate buttons. (Images after: A wholly empirical explanation of perceived motion. Yang, Z, Shimpi, A., Purves, D., Proc. Natl. Acad. Sci. 9:5252-5257 [2001])','objective-and-perceived-motion-2/','Motion2.swf')); research_areas[4].push(new demo('Motion perception from simple sequential stimuli','When two or more stimuli are presented in temporal succession and at different spatial locations, the perception of motion can be elicited. In this example, two frames are alternated at a constant interval (~100 ms): the first frame contains diagonally opposed stimuli in the upper left and lower right locations of an imaginary rectangle; the second frame contains diagonally opposed stimuli in the upper right and lower left locations of the same imaginary rectangle. As the spatial separation between stimuli increases along the vertical axis, the perception of motion between horizontal and vertical sequential stimuli changes. This change suggest that the visual system generates motion percepts on an empirical basis, according to the stimulus patterns that sources have most often projected on the retinal image plane.',null,'4point.swf',null,null)); // no geo forms demos research_areas[6].push(new demo('Tonal preferences','This demonstration provides an opportunity to evaluate the pleasantness of different tone combinations. Each slider represents one of 13 musical intervals (an interval is defined by two tones played together). You can listen to each interval by clicking on the button below it. Use the sliders above each icon to rank the intervals in terms of how pleasant each one sounds. For example, decide which interval sounds best and move its slider up to the #1 position. Then choose the next best sounding interval and move its slider to the #2 position. Continue playing the sounds and adjusting the sliders until you have ranked all the intervals and are satisfied with the preference order you have produced (preview by pressing "Play by Ranking"). When you are finished, press the "Done" button to see how your ranking compares to the median preference order derived from studies in the literature.','sound-2/','sound_consonance.swf','Although individuals differ in their preference orders, listeners generally agree about which intervals sound pleasing and which do not. Your choices are indicated by the yellow line; the blue line indicates the median preference order derived from studies in the literature (from Malmberg, 1918). The fact that listeners hear musical intervals in more or less the same way suggests that the perception of musical tones is based on some fundamental aspect of human hearing. We have proposed that tone perception is determined by experience with the natural sources of tonal stimuli for human listeners, namely speech.')); research_areas[6].push(new demo('Missing fundamental','In this segment you will be able to vary the number of harmonics in a complex tone. The point is to demonstrate the surprising fact that the pitch one hears always corresponds to the fundamental frequency of the harmonic series even when there is no energy at that frequency. This phenomenon is referred to as "hearing the missing fundamental", the fundamental being mathematically defined as the common divisor of a harmonics series. The harmonics are integer multiples of the fundamental frequency, and arise from the physics of naturally vibrating objects such as a guitar string (or the vocal cords in the human larynx). You can elicit the effect by subtracting the fundamental, leaving only the overtones. When the fundamental is missing the pitch remains that of the fundamental, even though the overall sound has a different quality (called "timbre").','sound-2/','sound_fundamental.swf','[explanation for missing fundamental]')); var active_demo = null; function demo(name, desc, link, swf, expl, dl) { this.title = name; this.description = desc; this.link = link; this.swf = swf; this.explanation = expl; this.download = dl; } function do_demo(j, k) // research area, demo # { if(active_demo == research_areas[j][k]) return; active_demo = research_areas[j][k]; document.getElementById('demo_title').innerHTML = active_demo.title; do_setText('description'); window.frames.player.location = '/player.html?' + active_demo.swf; } function do_setText(fld) { var o = active_demo; var desc = document.getElementById('demo_desc'); if(fld == 'description') { var s = o.description; if(o.link != null) { s += '<div style="padding-top: 6px;"><a href="https://purveslab.net/' + o.link + '">» Read the empirical 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id="menu-lightnessbrightness" class="menu"><li id="menu-item-1787" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1787"><a href="https://purveslab.net/lightnessbrightness-2/">Overview</a></li> <li id="menu-item-1786" class="menu-item menu-item-type-post_type menu-item-object-page current-menu-item page_item page-item-1783 current_page_item menu-item-1786"><a href="https://purveslab.net/simultaneous-brightness-contrast/" aria-current="page">Simultaneous brightness contrast</a></li> <li id="menu-item-1802" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1802"><a href="https://purveslab.net/mach-bands-2/">Mach Bands</a></li> <li id="menu-item-1811" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1811"><a href="https://purveslab.net/chubb-illusion/">Chubb Illusion</a></li> <li id="menu-item-1827" class="menu-item menu-item-type-post_type menu-item-object-page menu-item-1827"><a 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A) A target (the diamond) on a less luminant background (left) is perceived as being brighter than the same target on a more luminant background (right), even though the two targets are physical identical, and appear so if both are presented on the same background (as shown above). B) Diagram of the usual explanation of this phenomenon, based on the center-surround receptive field properties of retinal ganglion cells. the center-surround receptive field organization of input level neurons will, as illustrated here, cause less lateral inibition, and therefore more signal passed centrally from high contrast boundaries than from lower ones. </span></div> </aside><aside id="execphp-_x_system-1430317798" class="widget widget_execphp"> <div class="execphpwidget"><span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_21.gif" data-mfp-type="image"> <img src="https://purveslab.net/wp-content/uploads/brightness_2_th1.jpg" style="cursor:pointer !important; margin-top:20px; margin-bottom:15px;"> <br> <b> Figure 2 </b> / Evidence that distorted neuronal responses to local contrast (Figure 1B) cannot explain simultaneous brightness contrast. A) In the Wertheimer-Benary stimulus, two equiluminant targets (the gray triangles) elicit different sensations of brightness despite having the same local contrast relationships (for most observers the upper triangle looks slightly brighter/lighter than the lower one). B) White's illusion is particularly interesting because it generates a perception of relative brightness that is similar to the sensations elicited in Figure 1A, despite the fact that the local contrast of the patches (set inset left) is more or less opposite the standard brightness contrast stimulus shown in Figure 1A. Thus, the targets that appear brighter (the patches on the left) are mainly surrounded by areas of higher luminance, whereas the targets that appear darker are surrounded mainly by areas of lower luminance. C) Differences in lightness/brightness of equiluminant targets in the absence of any differences at all in local luminance contrast. Top panel - Light and dark surrounds with equiluminant test diamonds on the adjacent faces of a cube. Middle panel - The same cube rotated 180°. Bottom panel - Graph showing the average adjustment made by observers to equalize the brightness of the two test targets in the upper and middle panels. </span> </div> </aside><aside id="execphp-_x_system-1430317808" class="widget widget_execphp"> <div class="execphpwidget"><span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_31.jpg" data-mfp-type="image"> <img src="https://purveslab.net/wp-content/uploads/brightness_3_th1.jpg" style="cursor:pointer !important; margin-top:20px; margin-bottom:15px;"> <br> <b> Figure 3 </b> / A probabilistic explanation of simultaneous brightness contrast effects. A) A standard simultaneous brightness contrast stimulus. B and C) Cartoons illustrating the two major categorical sources of the stimulus in (A). The different lightness/brightness of the two identical targets in (A) is seen because the response to the stimulus incorporates all its possible sources in proportion to their past frequency of occurrence, which differs in natural scenes.</span> </div> </aside> </div> </div> <div class="spanlevelone col-md-9"> <div class="widgetdevn content sidebardevn sysdevn2" id="sidebar-content"> <aside id="contents-3" class="widget widget_contents-component"> <article id="post-1783" class="post-1783 page type-page status-publish hentry"> <div class="entry-content blog_postcontent"> <h3 style="font-size:27px !important;">An Empirical Explanation: Simultaneous Brightness Contrast</h3> <blockquote><p>Insofar as a stimulus is consistent with the experience of the visual system with differently reflective objects in different levels of illumination, targets and their contexts will tend to appear differently light or bright.</p></blockquote> <p> <br /> It has long been apparent that the perceived brightness of objects does not correspond in any simple way to their luminance (i.e., to the measured intensity of light corrected for the spectral sensitivity of the human visual system) (<span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_11.jpg" data-mfp-type="image"><a href="#">Figure 1A</a></span>). In particular, two surfaces returning the same amount of light to the eye can look differently bright if the surfaces are observed in different contexts, a phenomenon called simultaneous lightness or brightness contrast (most psychologists refer to ‘lightness’ contrast to distinguish the appearance of surfaces that reflect light from the appearance of endogenous sources of light; for present purposes, this distinction is not critical).<br /> <br /> The explanation of this remarkable effect found in many textbooks is predicated on lateral interactions among retinal ganglion cells or other lower order visual neurons, which demonstrably cause distorted rates of neuronal firing at contrast boundaries, presumably to enhance the detection of edges (<span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_11.jpg" data-mfp-type="image"><a href="#">Figure 1B</a></span>). This interpretation implies that the relative intensities perceived in response to such stimuli are, in effect, ‘readouts’ of the relative firing rate of neurons at the input stages of the visual system. On this basis, any target predominantly surrounded by an area of higher luminance should look darker than the same target predominantly surrounded by an area of lower luminance.<br /> <br /> Despite the apparent concordance of perception and retinal physiology in this instance, a number of observations indicate that identical targets embedded in scenes that have exactly the same local contrast relationships with their surrounds can nonetheless look differently bright (<span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_21.gif" data-mfp-type="image"><a href="#">Figure 2</a></span>). Indeed it is even possible to construct stimuli in which a target in a predominantly higher luminance surround looks brighter than an identical target in a predominantly lower luminance surround (<span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_21.gif" data-mfp-type="image"><a href="#">Figure 2B</a></span>). How, then, can these seeming contradictions in the relationship of luminance and brightness be explained?<br /> <br /> In terms of a wholly empirical strategy of vision, the explanation of the difference in perceived brightness of the two equiluminant targets in <span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_11.jpg" data-mfp-type="image"><a href="#">Figure 1A</a></span> and in this <a href="https://purveslab.net/see-for-yourself/">Demonstration</a> is summarized in <span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_31.jpg" data-mfp-type="image"><a href="#">Figure 3</a></span> (Williams et al, 1998a and b; see also Lotto and Purves, 1999). Since the amount of light returned to the eye from any portion of a scene depends on the illumination and reflectance of the relevant surfaces (among other factors), the equiluminant returns from the targets are inherently ambiguous. Such stimuli will often have been generated by similarly reflective surfaces on differently reflective surrounds under the same illuminant; the same luminance profiles, however, will often have signified differently reflective target surfaces under different amounts of illumination.<br /> <br /> Since dealing successfully with this or any stimulus depends on responding appropriately to the sources of the retinal stimulus rather than the stimulus as such, the visual system can only solve this problem on the basis of past experience. If this idea is correct, then to the extent that the stimulus is consistent with similarly reflective target surfaces under the same illuminant, the targets will tend to appear similarly bright. However, in so far as the stimulus is consistent with the past experience of the visual system with differently reflective objects in different levels of illumination, the targets will tend to appear differently light or bright. Because the standard simultaneous brightness contrast stimulus is consistent with either of these possible sources, the pattern of neural activity elicited – that is, the percept experienced when looking at the stimulus in Figure 1A or <span class="devn-lightbox" data-mfp-src="https://purveslab.net/wp-content/uploads/brightness_31.jpg" data-mfp-type="image"><a href="#">Figure 3A</a></span> (or the related demonstrations) – is a manifestation of both possibilities (and indeed all of the many other possibilities not illustrated) in proportion to their relative frequency of occurrence in past experience with stimuli of this general sort.<br /> <br /> In support of this explanation, crafting the stimulus in this <a href="https://purveslab.net/see-for-yourself/">Demonstration</a> to be more consistent with differently reflective surfaces in different illuminants increases the ‘illusion’ of simultaneous brightness contrast (see <a href="https://purveslab.net/see-for-yourself/">Demonstration</a>, for example), whereas making the stimulus less consistent with this possibility, and more consistent with the source being similar reflective objects under similar illuminants causes the targets to appear more similar, even if all the luminance relationships in the scene are preserved. Other more complex examples that support this interpretation of how lightness/brightness percepts are generated are found in this <a href="https://purveslab.net/see-for-yourself/">Demonstration</a>. </p> <p> </p> <h3>References</h3> <p>Purves D, Lotto B (2011) Why We See What We Do Redux: A Wholly Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.</p> <p>Purves, D., Wojtach, W.T., & Lotto, R.B. (2011) Understanding vision in wholly empirical terms. Proc Natl Acad Sci (doi:10.1073/pnas.1012178108, March 7).</p> <p>Howe CQ, Lotto RB, Purves D (2006). Comparison of Bayesian and empirical ranking approaches to visual perception. J Theoretical Biol 241: 866-875.</p> <p>Yang Z, Purves D (2004) The statistical structure of natural light patterns determines perceived light intensity. Proc Natl Acad Sci 101: 8745-8750.</p> <p>Purves D, Williams SM, Nundy S, Lotto RB (2004) Perceiving the intensity of light. Psychological Rev. Vol 111: 142-158.</p> <p>Purves D, Lotto RB, Williams SM, Nundy S, and Yang, Z (2001) Why we see things the way we do: Evidence for a wholly empirical strategy of vision. Philos. Trans. Roy. Soc., 356:285-297.</p> <p>Purves D, Lotto RB (2003) Why We See What We Do: An Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.</p> <p>Lotto RB, Purves D (1999) The effects of color on brightness. Nat Neurosc 2: 1010-1014.</p> <p>Williams SM, McCoy AN, Purves D (1998b) An empirical explanation of brightness. Proc Natl Acad Sci USA 95:13301-13306.</p> <p>Williams SM, McCoy AN, Purves D (1998a) The influence of depicted illumination on perceived brightness. Proc Natl Acad Sci USA 95:13296-13300.</p> <p>Purves Purves D, Monson BB, Sundararajan J, Wojtach WT (2014). How biological vision succeeds in the physical world. In: Proceedings of the National Academy of Sciences 111: 4750-4755</p> <p>Purves D, Wojtach WT, Lotto RB (2011) Understanding vision in wholly empirical terms. 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