Layer and framework theories of lightness SORANZO, Alessandro
This document is the author deposited version. You are advised to consult the publisher's version if you wish to cite from it. Published version SORANZO, Alessandro and GILCHRIST, Alan (2019). Layer and framework theories of lightness. Attention, perception, and psychophysics.
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Sheffield Hallam University Research Archive http://shura.shu.ac.uk Attention, Perception, & Psychophysics
Layer and framework theories of lightness
Journal: Attention, Perception, & Psychophysics
Manuscript ID PP-TR-18-005.R2
Manuscript Type: Tutorial Review - Invited
Date Submitted by the Forn/a Review Only Author:
Complete List of Authors: Soranzo, Alessandro; Sheffield Hallam University, Facutly of Development & Society Gilchrist, Alan; Rutgers University, Psychology; Alan Gilchrist, Alan Gilchrist
Color and Light: Lightness/Brightness, Color and Light: Constancy, Color Keywords: and Light: Contrast
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1 2 3 4 Layer and framework theories of lightness 5 6 7 8 9 Alessandro Soranzo* and Alan Gilchrist& 10 11 12 13 14 *Faculty of Development and Society - Sheffield Hallam University, Sheffield, UK. 15 16 &Department of Psychology, Rutgers University, Newark, NJ 07102, USA. 17 18 19 20 21 Corresponding author:For AlessandroReview Soranzo Only 22 23 Faculty of Development and Society 24 25 Sheffield Hallam University (UK) 26 27 Sheffield S10 2BP 28 29 30 31 32 Tel. (+44)(0) 114 225 6532 33 34 Fax (+44)(0) 114 225 2430 35 36 37 38 39 E-mail: [email protected] 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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1 2 3 ABSTRACT 4 5 6 Lightness (the perceived dimension running from black to white) represents a problem 7 8 for vision science because the light coming to the eye from an object totally fails to specify the 9 10 shade of gray of the object, due to the confounding of surface gray and illumination intensity. 11 12 The two leading approaches, decomposition theories and anchoring theories, split the retinal 13 14 15 image into overlapping layers and adjacent frameworks respectively. Because each approach 16 17 has important strengths and some weaknesses, an integration of them would mark an 18 19 important step forward for lightness theory. But the problem remains how this integration can 20 21 For Review Only 22 actually be realized. 23 24 25 26 27 28 29 Keywords: Lightness; Decomposition; Anchoring; Scaling; Transparency; Layers; 30 31 Frameworks; Gamut compression; Articulation 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
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1 2 3 4 Introduction: The genesis of the lightness debate 5 6 7 Lightness is the perceived dimension running from black to white. Surface lightness is a 8 9 basic property of an object, along with size and motion. Yet an understanding of how lightness 10 11 is computed by the brain is far from complete. The problem is that because the light coming to 12 13 14 the eye from an object depends on both the amount of light the surface reflects (reflectance) 15 16 and the intensity of the illumination, it totally fails to specify the shade of gray of the object. 17 18 Nevertheless, surface lightness tends to remain constant even when the illumination changes; 19 20 21 this is referred to as lightnessFor constancy.Review Only 22 23 Modern theories of lightness constancy can be dated to the late nineteenth century, when 24 25 a controversy broke out between, on one hand Hering (1878) who supported a low-level 26 27 explanation of lightness phenomena based on processes sensitive to contrast and, on the other 28 29 30 hand Helmholtz (1925) who favored a high-level explanation based on processes involving 31 32 unconscious inference. Helmholtz argued that, in addition to sensing the luminance of a target 33 34 surface, the visual system unconsciously estimates the illumination level and it is the 35 36 37 relationship between target luminance and estimated illumination that predicts the lightness 38 39 percept. Hering (1878) argued that Helmholtz’s appeal to cognition is unnecessary and that 40 41 low-level processes like adaptation, pupil size, and lateral inhibition can explain the 42 43 44 approximate lightness constancy that exists. 45 46 David Katz (1935) was the first to study lightness constancy and its failures 47 48 systematically. In his most widely emulated method, subjects were asked to adjust the gray 49 50 level of a disk in bright illumination to make it appear equal in lightness to another disk in 51 52 53 shadow. He found both constancy and systematic deviations from constancy. The matched 54 55 level of the two disks was closer to a reflectance match (100% constancy) than to a luminance 56 57 match (0% constancy), although the gray disk in shadow appeared darker than the disk in 58 59 60 brighter illumination.
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1 2 3 During the 1920s and 1930s the Gestalt Theorists turned their attention to lightness 4 5 6 perception, making a series of important contributions. They emphasized the importance of 7 8 relative luminance, anticipating Wallach’s (1948) later finding that two disks of different 9 10 luminance appear equal in lightness when they have the same disk/background luminance 11 12 ratio. They rejected both Hering’s low-level account and Helmholtz’s high-level theory, 13 14 15 arguing that Hering and Helmholtz shared the same two-stage approach featuring a primary 16 17 stage of raw sensations followed by a second stage in which those sensations were interpreted 18 19 based on experience, and suggesting that such a theory is not falsifiable. 20 21 For Review Only 22 According to Gelb (1929, excerpted in Ellis, 1938, p. 206): “The essentially problematic 23 24 aspect of the phenomenon has invariably been taken to be the discrepancy between the 25 26 "stimulus" and "colour" reaction. Assuming that retinal stimuli and colour-vision stood in a 27 28 29 more or less direct correspondence with one another, any departure from this primitive and 30 31 self-evident relationship - i.e. any "discrepancy" - was explained on empiristic grounds. Thus, 32 33 if the discrepancy would not be rendered comprehensible by reference to "physiological" 34 35 (peripheral) factors alone, "psychological" factors would also be invoked. In this way the 36 37 38 phenomena of colour constancy were classified as the product of central processes operating 39 40 upon and reorganizing genetically simpler colour-processes." 41 42 The Gestaltists put forward the first mid-level theory. Köhler (1947, p. 103) wrote, “Our 43 44 45 view will be that, instead of reacting to local stimuli by local and mutually independent events, 46 47 the organism responds to the pattern of stimuli to which it is exposed; and that this answer is a 48 49 unitary process, a functional whole which gives, in experience, a sensory scene rather than a 50 51 52 mosaic of local sensations. Only from this point of view can we explain the fact that, with a 53 54 constant local stimulus, local experience is found to vary when the surrounding stimulation is 55 56 changed.” 57 58 59 60
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1 2 3 The Gestaltists were well ahead of their time, anticipating concepts that would come to 4 5 6 be seen as important only after the computer revolution. Katona (1929), Gelb (1932), Wolff 7 8 (1933), and Kardos (1934) demonstrated the critical role of depth perception in lightness. The 9 10 later enthusiasm for explanations based on lateral inhibition at the retina would be possible 11 12 only by neglecting this work (Soranzo, 2015). 13 14 15 Koffka (1935) and Kardos (1934) proposed that fields of illumination are treated as 16 17 frames of reference for computing lightness, providing more concreteness to Helmholtz’s 18 19 notion of estimating illumination level. Koffka (1935, p. 245) emphasized the crucial role of 20 21 For Review Only 22 relative luminance at edges (gradients), writing “Our theory of whiteness constancy, will be 23 24 based on this characteristic of colours, which we found confirmed in so many passages, that 25 26 perceived qualities depend upon stimulus gradients.” And Koffka made a distinction between 27 28 29 luminance gradients that represent reflectance borders and that represent illumination borders. 30 31 Koffka also spoke of a complementary relationship between lightness and perceived 32 33 illumination. 34 35 36 37 38 Gestalt theory abandoned 39 40 At the end of World War II, the center of scientific work shifted from Europe to the 41 42 United States, and the Gestalt contributions were pushed aside. A low-level explanation was 43 44 45 particularly in vogue during the 1960’s mainly because of the physiological discovery of the 46 47 lateral inhibition process in the limulus (horseshoe crab) retina (Hartline, Wagner, & Ratliff, 48 49 1956). Later, however, during the so-called cognitive revolution, the low-level approach was 50 51 52 challenged by a series of newfound visual phenomena directly contradicting a retinal 53 54 interaction explanation. Experiments showed that a change in perceived depth could shift the 55 56 lightness of a target surface virtually from black to white, with no change in the retinal image 57 58 (Gilchrist, 1977; 1980; Adelson, 1993), or that a dramatic change in the lightness of a target 59 60
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1 2 3 could be produced merely by causing a (spatially remote) reflectance boundary to appear as an 4 5 6 illumination boundary (Gilchrist et al. 1983). 7 8 The discovery of these visual phenomena led to the emergence of several inverse-optics, 9 10 or decomposition, theories (Land & McCann, 1971; Bergström, 1977; Gilchrist, 1977;1979; 11 12 Barrow & Tenenbaum, 1978; Marr, 1982; Gilchrist et al. 1983; Adelson, 1993; Arend, 1994; 13 14 15 Adelson and Pentland, 1996), which sought to decompose the retinal image into components 16 17 of perceived surface lightness and illumination that mirror the physical variables of reflectance 18 19 and illumination that had combined to produce the retinal image in the first place. These are 20 21 For Review Only 22 informally called layer theories. 23 24 Later, as the failure of the decomposition theories to explain lightness illusions (Agostini 25 26 & Galmonte, 2002; Agostini & Proffitt, 1993; Economou et al. 2007; Bressan & Actis-Grosso, 27 28 29 2001; Soranzo & Agostini, 2006a,b) and failures of lightness constancy (Gilchrist, 1988) 30 31 became clear, some theorists abandoned the inverse optics approach and proposed new, mid- 32 33 level, so-called framework theories (Gilchrist et al. 1999; Adelson, 2000) that featured 34 35 illumination frames of reference. 36 37 38 Meanwhile low-level approaches based on lateral inhibition became more sophisticated 39 40 as they morphed into, for example, the neural/computational models proposed by Grossberg & 41 42 Mingolla, 1987; Grossberg & Todorovic, 1988; Pessoa, Mingolla, & Neumann, 1995; or the 43 44 45 spatial filtering models proposed by Blakeslee & McCourt, 2001; Kingdom & Moulden, 1992; 46 47 Watt & Morgan, 1985). But these, strictly speaking, are models of brightness (perceived 48 49 luminance) not lightness (perceived reflectance). The important problem is how we perceive 50 51 52 the properties of objects (like reflectance), not how we perceive the properties of the light 53 54 entering the eye. 55 56 57 58 59 60
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1 2 3 Both layer and framework theories attempt to explain surface lightness, and both assume 4 5 6 that the retinal image is parsed into components. But they propose different components. The 7 8 debate between these layer and framework theories is the focus of the present paper. 9 10 11 12 13 Decomposition Theories 14 15 16 The theories of lightness that arose in the 1970s with the cognitive revolution generally 17 18 sought to explain veridicality, not error, using an inverse optics approach to decompose the 19 20 21 image into its reflectanceFor and Reviewilluminance layers Only(Land & McCann, 1971; Bergström, 1977; 22 23 Gilchrist, 1977; Barrow & Tenenbaum, 1978; Gilchrist, 1979; Marr, 1982; Gilchrist, et al, 24 25 1983; Adelson, 1993; Arend, 1994; Adelson and Pentland, 1996). Unlike the earlier low-level 26 27 explanations that took absolute luminance as the input, these theories generally assumed that 28 29 30 only luminance ratios at edges are encoded at the retina. Gilchrist (1979; Gilchrist & Jacobsen, 31 32 1983; Gilchrist, et al., 1983) and Arend (1994) suggested that luminance ratios at edges are 33 34 extracted from the retinal image and classified as either changes in reflectance or illumination. 35 36 37 All the reflectance edges are then integrated to form a map of surface reflectance across the 38 39 visual field and the illumination edges are integrated to form an additional map of the 40 41 overlying pattern of illumination on the scene (Gilchrist, 1979; Gilchrist et al, 1983). Barrow 42 43 44 & Tenenbaum (1978) called these layers intrinsic images. 45 46 Figure 1a represents how the visual system decomposes luminance in a bipartite field of 47 48 illumination according to the decomposition approaches. 49 50 51 52 53 54 55 56 57 58 59 60
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Figure 1a (left): Layer Fortheories split Review the retinal image into aOnly layer of perceived illumination projected onto a layer of 22 surface reflectance. Figure 1b (right) Framework theories parse the retinal image into frameworks of illumination bounded by corners, occlusion boundaries, and penumbrae. 23 24 25 26 If the layers are parsed successfully, perception is completely veridical and no errors are 27 28 predicted. But in that case the decomposition approach could not explain either failures of 29 30 constancy or illusions, such as simultaneous lightness contrast (gray patch on a white 31 32 background appears darker than identical patch on black background). Seeking to 33 34 35 accommodate these so-called errors, several authors (Gilchrist, 1988; Ross & Pessoa, 2000; 36 37 Soranzo & Agostini, 2004; Soranzo et al. 2009; Soranzo, Lugrin & Wilson, 2013; Spehar et al. 38 39 2002) proposed the idea of partial classification of luminance edges. Lightness constancy 40 41 42 errors are explained by assuming that the illumination edges are not fully excluded from the 43 44 integration, but partially encoded as reflectance changes. Ironically, these attempts have been 45 46 only partially successful. 47 48 49 50 51 Other decomposition theories 52 53 54 Other theories have much in common with intrinsic image theories even if they don’t 55 56 speak in terms of overlapping layers. Bergström (1977) proposed that by means of an analysis 57 58 59 into common and relative components, the light composing the retinal image is decomposed 60
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1 2 3 into changes of reflectance, illumination, and 3D form. Musatti (1953) had earlier proposed a 4 5 6 very similar idea using the now-confusing terms assimilation and contrast. Adelson & 7 8 Pentland (1996) offered a vivid metaphor in which a workshop constructs a theatre set using 9 10 workers who paint surfaces, configure lighting, and bend metal, mirroring Bergström’s three 11 12 components. Brainard & Maloney (2011) have proposed an equivalent illumination model, 13 14 15 suggesting that constancy fails when the illumination is misperceived. 16 17 Although strictly speaking, these theories are not layer theories, they imply that the 18 19 retinal image is experienced as a layer of illumination projected onto a layer of surface 20 21 For Review Only 22 reflectance. More importantly, they share with the intrinsic image theories the crucial idea of 23 24 complementarity between perceived illumination and perceived reflectance, whether or not 25 26 there is an error in the attribution of the luminance to the different components. When a 27 28 29 paleontologist cracks open a layer of rock to reveal a fossil, the two resulting layers of rock 30 31 are exactly complementary to each other, even if the split does not fall exactly along the 32 33 surface of the fossil. Likewise, when the visual system splits the luminance, the two resulting 34 35 layers of lightness and perceived illumination are complementary to each other, even if the 36 37 38 split does not correspond exactly to the actual proportions of reflectance and illumination. 39 40 This implies that when a higher amount of luminance is attributed to lightness a 41 42 complementary smaller amount of luminance is attributed to illumination. This idea of 43 44 45 complementarity can be found in Koffka (1935; page 244) who suggested "the possibility that 46 47 a combination of whiteness and [perceived illumination], possibly their product, is an 48 49 invariant for a given local stimulation under a definite set of total conditions. If two equal 50 51 52 proximal stimulations produce two surfaces of different whiteness, then these surfaces will 53 54 also have different [perceived illuminations], the whiter one will be less, the blacker one more 55 56 [brightly illuminated]." (For clarity we have substituted the term “perceived illumination” for 57 58 59 60
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1 2 3 Koffka’s term “brightness”, which meant perceived illumination then, but currently means 4 5 6 perceived luminance.) 7 8 Framework approach 9 10 11 Attempting to account for both lightness constancy and its failures, several theorists 12 13 14 have moved away from the inverse optics logic of the decomposition approach toward theories 15 16 that feature frames of reference but are also more rough and ready. Gilchrist abandoned his 17 18 inverse optics approach and proposed a new anchoring theory (Gilchrist et al. 1999; Gilchrist, 19 20 21 2006). Commenting thatFor “the HelmholtzianReview approach Only is overkill” Adelson (2000, p. 344) also 22 23 shifted towards a frameworks approach. Similarly, Anderson abandoned Metelli's (1974) 24 25 inverse optics approach in favor of a mid-level theory of transparency (see, for example, 26 27 Anderson & Khang, 2010). 28 29 30 Anchoring theory 31 32 33 Helmholtz (1925) suggested that in order to compute lightness, the illumination level 34 35 must be taken into account. However, according to anchoring theory (Gilchrist, 2006; 36 37 38 Gilchrist et al., 1999) the visual system doesn’t need to know the actual level of illumination – 39 40 it only needs to know which surfaces are getting the same amount of illumination. This 41 42 translates the problem into one of perceptual grouping. Multiple surfaces perceived as equally 43 44 45 illuminated can be called illumination groups, and these are products of both grouping and 46 47 segmentation processes. For example, in Gilchrist’s work on depth and lightness, these groups 48 49 coincide with perceived planes. Coplanar surfaces can be said to be grouped by coplanarity or, 50 51 52 alternatively, segregated by depth boundaries. Such groups of equi-illuminated surfaces 53 54 function as frames of reference (Dunker, 1938; Koffka, 1935). 55 56 The lightness of a given surface is computed relative to its frame of reference, but not 57 58 exclusively! Lightness is a weighted average of the lightness computed for a target strictly 59 60
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1 2 3 within its local framework (such as the region within a shadow) and its lightness computed in 4 5 6 relation to the entire (global) visual field (Gilchrist et al., 1999). This scheme is roughly 7 8 equivalent to an earlier proposal by Kardos (1934) called co-determination, in which lightness 9 10 is seen partly in relation to its relevant framework and partly to the foreign framework. The 11 12 weighting of local and global values depends primarily on the number of elements, or 13 14 15 articulation level (Katz, 1935), of the local framework. Within each framework, lightness is 16 17 anchored by assigning white to the highest luminance and evaluating every other shade 18 19 relative to that, using the formula: 20 21 For Review Only 22 23 24 Perceived reflectance = target luminance/highest luminance X 90%. 25 26 27 28 29 Bressan (2006) has proposed an alternative version of anchoring theory called double- 30 31 anchoring theory that includes a surround-as-white rule of anchoring. 32 33 Adelson’s (2000) newer approach is based on the concepts of atmospheres and adaptive 34 35 windows. An atmosphere is a region of the visual field sharing the same illumination or glare 36 37 38 or fog. Each adaptive window has its own atmosphere and lightness estimates are computed 39 40 based on the statistics within the window. The window is adaptive because its size changes as 41 42 a function of the number of surfaces in a given area of the image. The window needs to be 43 44 45 large enough so that it includes a sufficient number of samples. But if the window is too large 46 47 it will include samples from different atmospheres. This theory is similar to anchoring theory 48 49 and it gives a great importance to the number samples in each adaptive window: the window 50 51 52 grows when there are too few samples and shrinks when there are more than enough. In 53 54 Gilchrist’s theory, a local framework coincides with illumination boundaries while in 55 56 Adelson’s theory the adaptive window has a soft boundary that doesn’t necessarily coincide 57 58 with illumination boundaries. 59 60
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1 2 3 4 5 6 Comparison between the two theories 7 8 9 Layer and framework approaches parse the retinal image in different ways. While layer 10 11 theories split the retinal into two overlapping layer-images, framework theories parse the 12 13 14 image into adjacent regions of differing illumination level. At first glance, these two ways of 15 16 decomposing the image appear incommensurate, even orthogonal. But each theory seems to 17 18 offer important insights and this suggests that reconciliation might be possible. 19 20 21 Figure 1b representsFor how Review the visual system Only parses the scene into two fields of 22 23 illumination according to anchoring theories. As one can see by comparing Figure 1a and 1b, 24 25 the components into which the image is decomposed are quite different for layer and 26 27 framework theories. In anchoring theories, the image is segmented into frameworks using 28 29 30 illumination boundaries (cast edges, occlusion edges, and corners) to parse the image into 31 32 "contiguous regions of illumination or shadow, like states on a map" (Gilchrist, 2006; page 33 34 331) whereas in the intrinsic image approach, the image is split into complementary 35 36 37 overlapping layers, one composed by integrating all the illumination edges, the other 38 39 composed of all the reflectance edges. 40 41 Consider some crucial strengths and weaknesses of each approach. 42 43 44 The anchoring problem: Both layer and framework theories emphasize that lightness is 45 46 associated with relative luminance. But the problem of how relative luminance values in the 47 48 image are transformed into specific lightness values has been dealt with explicitly only by 49 50 framework theories. According to empirical work the highest luminance is automatically 51 52 53 anchored to white (Li and Gilchrist, 1999). In general, decomposition theories have not 54 55 offered a satisfying solution to the anchoring problem. In support of a decomposition 56 57 approach, Kingdom (2011) and Rudd (2013; 2014) proposed that the highest value in the 58 59 60 reflectance layer, that is the highest lightness, is anchored to white. Rudd (2014) proposed an
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1 2 3 alternative anchoring rule, the highest reflectance anchoring specifying that the “highest 4 5 6 reflectance in the scene always appears white, but the highest reflectance may not always be 7 8 the same as the highest luminance” (p. 8). The author underlined that it is the largest 9 10 reflectance in the neural representation, rather than the largest reflectance in the world, that 11 12 appears white. However, Gilchrist et al (1999) reported a test, shown in Figure 2, pitting 13 14 15 highest luminance against highest lightness, with results clearly supporting highest luminance. 16 17 Due to the presence of the spotlight, the dark gray target on the left had the highest luminance 18 19 in the display and it appeared fully white. The white target, although it had the highest value in 20 21 For Review Only 22 the reflectance layer, appeared only light gray. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Figure 2. In this display (Gilchrist et al. 1999; p. 828) the dark gray target is the highest luminance in the display, and it 41 appears lighter than the white target, which would be the highest value in the reflectance layer. 42 43 Zavagno et al (2004) has noted that the phenomenon of self-luminosity directly 44 45 contradicts the claim that the highest luminance appears white. This apparent contradiction has 46 47 48 been resolved by evidence that, in addition to relative luminance, lightness is anchored by 49 50 relative area, with a tendency for the largest area to appear white (Li & Gilchrist, 1999; 51 52 Bonato & Gilchrist 1999; Gilchrist 2006). Gilchrist (2006) has introduced a distinction 53 54 55 between upward and downward induction. When the luminance difference between a target 56 57 surface and its surround increases, and the higher luminance occupies a much larger area than 58 59 the lower luminance, the change is expressed as a darkening of the darker region, with little 60
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1 2 3 change in the lighter region. When the darker region occupies a much larger area, then an 4 5 6 increase in luminance difference is expressed mainly as a trend towards self-luminosity. 7 8 2) The scaling problem. While the anchoring problem concerns which value of relative 9 10 luminance is tied to which point on the lightness dimension, the scaling problem deals with 11 12 how distances along the luminance scale are mapped onto distances along the lightness 13 14 15 dimension. Decomposition theories have generally assumed that log luminance differences 16 17 map directly onto log lightness differences (i.e.: log matched reflectance differences) in 1:1 18 19 fashion. But lightness differences can be either compressed or expanded relative to luminance 20 21 For Review Only 22 differences. Testing a high dynamic range Mondrian, Radonjic et al (2011) found a dramatic 23 24 compression of the range; a 2,500:1 luminance range was perceived as spanning only a 30:1 25 26 reflectance range. Other work has shown a robust expansion; Ivory et al. (2011) found that a 27 28 29 5:1 luminance range Mondrian was perceived as spanning almost a 30:1 reflectance range. 30 31 This is attributed by anchoring theory to scale normalization, a tendency to perceive the 32 33 canonical range from white to black (30:1) within a framework. Expansion and compression 34 35 of the gamut has not been addressed, and is not easily accommodated, by decomposition 36 37 38 theories. 39 40 In 1995, Cataliotti & Gilchrist reported a dramatic new illusion dubbed the staircase 41 42 Gelb effect. A row of 5 squares ranging from black to white was suspended in mid-air and 43 44 45 illuminated by a bright spotlight. Not only did this arrangement produce a huge failure of 46 47 constancy, with the black square appearing light grey, but more importantly, it introduced a 48 49 strong compression of perceived reflectances relative to actual (see figure 3). In this case the 50 51 52 compression cannot be attributed to scale normalization because it goes in the opposite 53 54 direction. 55 56 57 58 59 60
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Figure 3. Staircase Gelb illusion. When a series of squares, ranging from black to white, is suspended in mid-air 18 and illuminated by a spotlight, the perceived shades of gray are dramatically compressed relative to their actual shades. 19 20 For Review Only 21 Gamut compression in the staircase Gelb illusion poses a challenge to layer theories 22 23 24 because the lightness of each square is shifted upward by a different amount. An error in 25 26 decomposition, for example, if a portion of an illumination edge were erroneously classified as 27 28 a reflectance change or if some portion of the common component were erroneously attributed 29 30 31 to surface reflectance, would produce an offset in lightness values, rather than compression. In 32 33 the spotlight, all reflectances should appear to be lightened by the same amount, but not 34 35 compressed. Gamut compression is associated with the juxtaposition of two fields with 36 37 38 differing levels of illumination, especially when one of the field is smaller in area and/or is 39 40 surrounded by the other. An analogous sort of gamut compression is found in a shadowed 41 42 area, except that the compression is downward: high reflectances in shadow deviate from 43 44 constancy more than low reflectances (Ivory & Gilchrist, 2010). 45 46 47 According to anchoring theory the compression stems from what Kardos (1934) called 48 49 co-determination; the lightness of a surface is not determined exclusively within its own 50 51 framework of illumination but is partially anchored relative to the adjacent or surrounding 52 53 54 field of illumination. Gilchrist and colleagues (Gilchrist et al, 1999) have argued that, although 55 56 each of the five shades is computed veridically within the spotlight, they are all computed to 57 58 59 60
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1 2 3 be white relative to the surrounding dimmer illumination. The compression is held to result 4 5 6 from the averaging of these equal lightness values together with their veridical values. 7 8 However, recent data from the Gilchrist lab has contradicted a prediction based on this 9 10 account. When spotlight intensity is increased beyond 30 times the room level, no further 11 12 compression should occur. With all shades computed as white relative to the global anchor, 13 14 15 the source of compression is maxed out. However, experiments have shown (Gilchrist & 16 17 Ivory, 2013) that the compression continues to increase as the spotlight intensity is increased 18 19 beyond 30 times the room level, but that the degree of gamut compression is predicted by the 20 21 For Review Only 22 luminance ratio between the highest luminance in the spotlight and the highest luminance in 23 24 the surrounding field of illumination. This finding supports the general idea of co- 25 26 determination while rejecting the particular mechanism proposed in the original version of 27 28 29 anchoring theory (Gilchrist et al, 1999). 30 31 It has been argued (Bloj et al., 2004; Allred & Brainard, 2013) that gamut compression 32 33 can be accommodated within the decomposition approach by assuming the perception of a 34 35 different level of illumination on each patch within the shadow. But this construction defies 36 37 38 the intuitive concept of illumination as dispersed across multiple surfaces. 39 40 3) Role of articulation. One of the most powerful factors in lightness is articulation, 41 42 which refers to the number of distinct patches within a field of illumination. In their early 43 44 45 work, Katz (1935) and Burzlaff (1931) found poor constancy when subjects matched a disk in 46 47 bright illumination to a disk in an adjacent field in shadow. But they found almost perfect 48 49 constancy when each field contained a tableau of 48 patches. Although this fact was forgotten 50 51 52 during much of the prior century, many experiments in recent decades have confirmed it 53 54 (Agostini & Galmonte, 1999; Schirillo & Arend, 1995; Arend & Goldstein, 1987; Cataliotti & 55 56 Gilchrist, 1995). This is easily accommodated by anchoring theory, with articulation level 57 58 determining the weight of each competing framework in the co-determination process. But it 59 60
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1 2 3 is difficult to see how the role of articulation can be accommodated by a layer approach. In 4 5 6 Gilchrist’s intrinsic image theory, for example, the degree of constancy found between 7 8 adjacent fields of illumination should depend simply on how veridically the illumination edge 9 10 between them is encoded and classified. The number of distinct patches within each field 11 12 should play no role. 13 14 15 4) Area effects. Katz (1935) also found that the degree of constancy is influenced by the 16 17 size of the field of illumination; hence his laws of field size. Such effects make sense within a 18 19 framework approach because the area of a field influences the weight of that field in the co- 20 21 For Review Only 22 determination process. But, just as with articulation effects, area effects do not seem 23 24 commensurate with layer theories. 25 26 Layer theories are associated with the idea of inverse optics. So, for example, when a 27 28 29 shadow falling across a scene introduces a luminance step into the image, that step is 30 31 classified as a change of illumination, and excluded from the reflectance map. In other words, 32 33 the confounding of illumination and reflectance in the formation of the image is inverted by 34 35 edge classification. But effects of articulation and area have no counterpart in image 36 37 38 formation. They do not function to invert or disentangle confounded variables. For example, if 39 40 surfaces in the real world reflected more light as they become larger in area, then the effect of 41 42 area on lightness would be consistent with a decomposition approach. But that is not the way 43 44 45 the world works. 46 47 5) Transparency and veiling luminance. Obviously, perception of opaque surfaces seen 48 49 through a transparent layer favors a layer decomposition approach because the scene contains 50 51 52 spatially separated layers. Indeed Metelli’s (1975) work on transparency was an early and 53 54 explicit inverse optics approach, with perceptual color scission the inverse of color fusion. The 55 56 transparent surfaces he studied include both a filter and a veil component. But a veiling 57 58 luminance can occur without a filter component, as when looking through a sheet of light 59 60
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1 2 3 reflected in a window. Glare also constitutes a veiling luminance in the eye. When a veiling 4 5 6 luminance is superimposed on a scene, both luminance values and luminance ratios are 7 8 altered. Nevertheless, empirical results show an impressively high degree of lightness 9 10 constancy through a veiling luminance (Gilchrist & Jacobsen, 1983). Both layer and 11 12 framework theories work well for the filter component, like the shadow it mimics (Metelli, 13 14 15 1974; 1975), but the veil component is better handled by a layer theory. 16 17 6) Black rooms and white rooms. Gilchrist and Jacobsen (1984) obtained lightness 18 19 matches for two miniature rooms filled with abstract 3D objects. One was painted entirely 20 21 For Review Only 22 black, including the contents, and the other was painted entirely white. The white room was 23 24 perceived as completely white while the black room was perceived as a middle gray, a result 25 26 that is more consistent with a layer theory than a framework theory. Because all of the 27 28 29 luminance edges were either gradual or, when sharp, coincidental with a change of planarity, 30 31 they were perceptually attributed to the illumination. Presumably the removal of these edges 32 33 from the image leaves only a homogeneous reflectance layer. But the specific lightness value 34 35 of that layer is not specified. The same challenge applies to shape-from-shading. Algorithms 36 37 38 exist that transform the luminance variations across the image of a sculpture into a specific 39 40 three-dimensional shape with homogeneous lightness (Horn, 1975, 1977; Pentland, 1989). But 41 42 they do not specify that lightness value. 43 44 45 Perception in a three-dimensional world of one reflectance poses a challenge for a 46 47 framework theory as there are no obvious frameworks. One could treat each plane as a 48 49 framework but such a framework would have the minimum articulation level of one. 50 51 52 Gilchrist and Jacobsen (1983) showed that the luminance variations across the white 53 54 room and the black room were qualitatively the same, but with much greater amplitude (i.e., 55 56 high contrast) in the black room. Recent work by Gilchrist and Ivory (2011) further isolated 57 58 59 60
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1 2 3 this factor. They found that reducing the variation amplitude by covering a black room with a 4 5 6 veiling luminance makes it appear as a white room. 7 8 But why does the black room (without the veil) appear middle gray rather than black? 9 10 Could this appearance be the result of a compromise between the highest luminance rule of 11 12 anchoring (indicating a white room) and the high-contrast luminance variations (indicating a 13 14 15 black room)? This would be consistent with the spirit of compromise in the anchoring theory, 16 17 but without the competing frameworks. 18 19 Adelson (2000, p. 346) has observed that X-junctions that emerge where the edge of a 20 21 For Review Only 22 veiling luminance intersects a more distant reflectance edge creates the impression of a haze 23 24 or veil. Although Anderson and his co-authors (Anderson, Singh, & Meng, 2006; Anderson & 25 26 Winawer, 2005; 2008; Anderson, 1999, 2003) are leading proponents of layer theories, they 27 28 29 have proposed a Transmittance Anchoring Principle (TAP), for discovering what part of a 30 31 scene is covered by a veiling luminance. TAP states that the “visual system treats the highest 32 33 contrast image regions as regions in plain view and only infers the presence of transparent 34 35 surfaces if there are spatial or spatio-temporal perturbations in the contrast magnitude along 36 37 38 contours, surfaces, or textures” (Anderson & Winawer, 2008; page 5). 39 40 41 42 What are the possibilities for integrating layer and framework approaches? 43 44 45 Phenomenology offers important guidance but does not seem to resolve our dilemma. 46 47 We do seem to perceive a layer of illumination projected onto a layer of surface reflectance. 48 49 But we also experience frameworks of illumination. This suggests that an integration of the 50 51 52 two kinds of theory is possible. 53 54 There is no contradiction between layers and frameworks, but rather between layer 55 56 theories and framework theories. It can be said that layer and framework theories parse the 57 58 retinal image into different components, i.e., layers and frameworks. But this is a bit 59 60
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1 2 3 misleading. For framework theories, the process begins with segregation of the image into 4 5 6 frameworks. But for layer theories, the reflectance and illuminance layers represent the end of 7 8 the process, not the beginning. Layer theories begin with edge encoding and edge 9 10 classification (Gilchrist et al, 1983). Of course, edge classification and framework segregation 11 12 are very closely related. If you know where the illumination edges are, you know where the 13 14 15 frameworks are. 16 17 Both layer and framework approaches have a gestalt flavor. Both accept relative 18 19 luminance as an input. Neither approach is structure-blind. Both find support in Koffka (1935, 20 21 For Review Only 22 see also Gilchrist, 2006, pp. 371-373). The concept of frames of reference was central to 23 24 Koffka’s thinking, which is most clearly revealed in his analysis of motion perception. But he 25 26 also treated different regions of illumination as frameworks. Like Kardos (1934), Koffka did 27 28 29 not consider the lightness value of a target to be exclusively computed within its own 30 31 framework, but recognized that values within one framework are distorted by the presence of 32 33 adjacent or surrounding frameworks. This can be seen in his remark that, "a field part x is 34 35 determined in its appearance by its "appurtenance" to other field parts. The more x belongs to 36 37 38 the field part y, the more will its whiteness be determined by the gradient xy, and the less it 39 40 belongs to the part z, the less will its whiteness depend on the gradient xz" (page 246). 41 42 This graded account of belongingness is consistent with the idea of co-determination 43 44 45 (Kardos Gilchrist), whereas layer theories seem to require more of an all-or-none kind of 46 47 belongingness in which a target belongs exclusively to one framework or another. At the same 48 49 time, Koffka’s lightness/perceived illumination invariance theorem, according to which a 50 51 52 combination of lightness and perceived illumination is invariant for a surface of constant 53 54 luminance, seems equivalent to the complementarity implicit in the decomposition approach. 55 56 Empirical results have shown that both lightness (Li & Gilchrist, 1999) and perceived 57 58 illumination (Kozaki 1965;1973; Oyama, 1968; Gilchrist & Soranzo, under review) are 59 60
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1 2 3 anchored by highest luminance. Although this work was done primarily in the context of 4 5 6 framework theories, these results imply the complementarity layer theories and Koffka’s 7 8 theorem. Consider a group of patches, such as a Mondrian array. When a higher maximum 9 10 luminance is added to the array, two things happen. First, the lightness of a given patch in the 11 12 Mondrian goes down. Second, the perceived illumination on the Mondrian goes up. And as 13 14 15 long as the Mondrian is well articulated, these upward and downward shifts are equal in 16 17 magnitude. However, in the staircase Gelb illusion, with its relatively weak articulation, errors 18 19 in lightness and perceived illumination are not equal and opposite. Gamut compression 20 21 For Review Only 22 implies that the lightness error is different for each square in the staircase. Thus, any error in 23 24 perceived illumination could be equal and opposite to, at most, the lightness error for a single 25 26 square. 27 28 29 30 31 Conclusions 32 33 From what we outlined above, it seems clear that both the decomposition and framework 34 35 approaches to lightness perception have their pro and cons. 36 37 38 Layer theories do not have an adequate account of the anchoring problem. They cannot 39 40 account for scaling effects, such as gamut expansion when viewing a low dynamic range 41 42 Mondrian, gamut compression when viewing a high dynamic range Mondrian, or gamut 43 44 45 compression in the staircase Gelb illusion. And they fail to capture lightness changes that 46 47 occur due to an increase or decrease in the number of visible patches within a field of 48 49 illumination. Framework theories have been quite successful in accounting for these effects. 50 51 52 On the other hand, framework theories cannot account for lightness constancy through 53 54 a veiling luminance, although intuition suggests that this is a version of the scaling problem. 55 56 Layer theories easily accommodate the experience of seeing a veil layer in front of an opaque 57 58 surface layer, but they do not specify how the presence of the veil is detected and how the 59 60
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1 2 3 intensity of the veil is computed. Framework theories have so far said very little about 4 5 6 perception of the illumination level, beyond the important finding that perceived illumination 7 8 level is signaled by highest luminance (Kozaki 1965;1973; Oyama, 1968). One concept 9 10 central to both layer and framework theories is that of illumination edges. In layer theories, 11 12 illumination edges are separated from reflectance edges while in framework theories, 13 14 15 illumination edges form the boundaries of frameworks. 16 17 It seems that a new, more comprehensive theory is needed which is capable of 18 19 integrating the two approaches. However, because the units into which the retinal image is 20 21 For Review Only 22 split, layers vs frameworks, are so different, it is difficult to see how the two approaches can 23 24 be integrated. 25 26 27 28 29 References 30 Adelson, E. H. (1993). Perceptual organization and the judgment of brightness. Science, 31 32 262(5142), 2042–2044. 33 34 Adelson, E. H. (2000). Lightness Perception and Lightness Illusions. The New Cognitive 35 36 37 Neurosciences, 3, 339–351. 38 39 Adelson, E. H., & Pentland, A. P. (1996). The perception of shading and reflectance. (W. 40 41 Knill, D & Richards, Ed.) Perception as Bayesian Inference (Vol. 1). New York: 42 43 44 Cambridge University Press. 45 46 Agostini, T., & Galmonte, A. (1999). Spatial articulation affects lightness. Perception & 47 48 psychophysics, 61(7), 1345-1355. 49 50 Agostini, T., & Galmonte, A. (2002). Perceptual organization overcomes the effects of local 51 52 53 surround in determining simultaneous lightness contrast. Psychological Science, 13(1), 54 55 89–94. 56 57 Agostini, T., & Proffitt, D. R. (1993). Perceptual organization evokes simultaneous lightness 58 59 60 contrast. Perception, 22(3), 263–272.
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1 2 3 Allred, S. R. & Brainard, D. H. (2013). A Bayesian model of lightness perception that 4 5 6 incorporates spatial variation in the illumination. Journal of Vision,13(7:18). 7 8 Anderson, B. & Khang, B. (2010). The role of scission in the perception of color and opacity. 9 10 Journal of Vision, 10(5), 1-16. 11 12 Anderson, B. L. (1999). Stereoscopic surface perception. Neuron, 24(4), 919–928. 13 14 15 Anderson, B. L. (2003). The role of occlusion in the perception of depth, lightness, and 16 17 opacity. Psychological Review, 110(4), 785–801. 18 19 Anderson, B. L. & Winawer, J. (2005). Image segmentation and lightness perception. Nature, 20 21 For Review Only 22 434(7029), 79–83. 23 24 Anderson, B. L., & Winawer, J. (2008). Layered image representations and the computation of 25 26 surface lightness. Journal of Vision, 8(7), 18. 27 28 29 Anderson, B. L., Singh, M., & Meng, J. (2006). The perceived transmittance of 30 31 inhomogeneous surfaces and media. Vision Research, 46(12), 1982–1995. 32 33 Arend, L. (1994). Surface colors, illumination, and surface geometry: Intrinsic-image models 34 35 of human color perception. (A. L. Gilchrist, Ed.). Lawrence Erlbaum Associates, Inc. 36 37 38 Arend, L. E., & Goldstein, R. (1990). Lightness and brightness over spatial illumination 39 40 gradients. Journal of the Optical Society of America A,7, 1929–1936. 41 42 Barrow, H. G., & Tenenbaum, J. M. (1978). Recovering intrinsic scene characteristics from 43 44 45 images. Computer Vision Systems, 3–26. 46 47 Bergström, S. S. (1977). Common and relative components of reflected light as information 48 49 about the illumination, colour, and three-dimensional form of objects. Scandinavian 50 51 52 Journal of Psychology, 18(1), 180–186. 53 54 Blakeslee, B., & McCourt, M. E. (2001). A multiscale spatial filtering account of the 55 56 Wertheimer--Benary effect and the corrugated Mondrian. Vision Research, 41(19), 2487– 57 58 2502. 59 60
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1 2 3 Bloj, M., Ripamonti, C., Mitha, K., Hauck, R., Greenwald, S., & Brainard, D. H. (2004). An 4 5 6 equivalent illuminant model for the effect of surface slant on perceived lightness. Journal 7 8 of Vision, 4, 735-746. 9 10 Bonato, F., & Gilchrist, A. L. (1999). Perceived area and the luminosity threshold. Perception 11 12 & Psychophysics, 61(5), 786-797. 13 14 15 Brainard, D. H., & Maloney, L. (2011). Surface color perception and equivalent illumination 16 17 models. Journal of Vision, 11(5), 1–18. 18 19 Bressan, P., & Actis-Grosso, R. (2001). Simultaneous lightness contrast with double 20 21 For Review Only 22 increments. Perception, 30(7), 889-897. 23 24 Bressan, P. (2006). The place of white in a world of grays: A double-anchoring theory of 25 26 lightness perception. Psychological Review, 113(3), 526. 27 28 29 Burzlaff, W. (1931). Methodologische Beitrage zum Problem der Farbenkonstanz 30 31 [Methodological contributions to the problem of color constancy]. Zeitschriftur 32 33 Psychologie Und Physiologie Der Sinnesorgane. Abt, 1, 177–235. 34 35 Cataliotti, J., & Gilchrist, A. L. (1995). Local and global processes in surface lightness 36 37 38 perception. Perception & Psychophysics, 57(2), 125–135. 39 40 Duncker, K. (1938). Ein Beitrag zur Theorie optisch wahrgenommener Bewegung. Kegan 41 42 Paul, Trench, Trubner & Company. [Original published in 1929]. 43 44 45 Economou, E., Zdravkovic, S., & Gilchrist, A. (2007). Anchoring versus spatial filtering 46 47 accounts of simultaneous lightness contrast. Journal of Vision, 7(12), 1-15. 48 49 Ellis, W. D. (1938/2013). A source book of Gestalt psychology. Routledge. 50 51 52 Gelb, A. (1929). Die "Farbenkonstanz" der Sehdinge (The color of seen things). Handbuch der 53 54 normalen und pathologischen Physiologie. W. A. von Bethe. 12: 594-678. 55 56 Gilchrist A & Soranzo A. (2014). Partial integration versus local/global anchoring: A test. 57 58 Perception, 43, Supplement, 13. 59 60
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1 2 3 Gilchrist, A. L. & Jacobsen, A. (1983). Lightness constancy through a veiling luminance. 4 5 6 Journal of Experimental Psychology: Human Perception and Performance, 9, 936-944. 7 8 Gilchrist, A. L. (1977). Perceived lightness depends on perceived spatial arrangement. 9 10 Science, 195(4274), 185–187. 11 12 Gilchrist, A. L. (1979). The perception of Surface Black and Whites. Scientific American, 13 14 15 24(3), 88–97. 16 17 Gilchrist, A. L. (1980). When does perceived lightness depend on perceived spatial 18 19 arrangement? Perception & Psychophysics, 28(6), 527–538. 20 21 For Review Only 22 Gilchrist, A. L. (1988). Lightness contrast and failures of constancy: a common explanation. 23 24 Perception & Psychophysics, 43(5), 415–424. 25 26 Gilchrist, A. L. (2006). Seeing Black and White. Seeing Black and White. Oxford: Oxford 27 28 29 University Press. 30 31 Gilchrist, A. L. & Ivory, S. (2011). Lightness of a black room seen through a veiling 32 33 luminance. Journal of Vision, 11 (11), 374-374. 34 35 Gilchrist, A. L. & Ivory, S. (2013). Why are lightness values compressed in abnormal 36 37 38 illumination? Perception, 42, 1_Suppl., 87-87. 39 40 Gilchrist, A. L., Delman, S., & Jacobsen, A. (1983). The classification and integration of 41 42 edges as critical to the perception of reflectance and illumination. Perception & 43 44 45 Psychophysics, 33(5), 425–436. 46 47 Gilchrist, A. L., Kossyfidis, C., Bonato, F., Agostini, T., Cataliotti, J., Li, X., Spehar, B., 48 49 Annan. V. & Economou, E. (1999). An anchoring theory of lightness perception. 50 51 52 Psychological Review, 106(4), 795. 53 54 Gilchrist A. & Soranzo A. (2014). Partial integration versus local/global anchoring: A test. 55 56 Perception, 43, Supplement, 13. 57 58 59 60
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 For Review Only 20 21 22 Figure 1a (left): Layer theories split the retinal image into a layer of perceived illumination projected onto a 23 layer of surface reflectance. Figure 1b (right) Framework theories parse the retinal image into frameworks of 24 illumination bounded by corners, occlusion boundaries, and penumbrae. 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 31 of 32 Attention, Perception, & Psychophysics
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Figure 2. In this display (GilchristFor et al.Review 1999; p. 828) the dark Only gray target is the highest luminance in the 20 display, and it appears lighter than the white target, which would be the highest value in the reflectance 21 layer. 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Attention, Perception, & Psychophysics Page 32 of 32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 For Review Only 20 Figure 3. Staircase Gelb illusion. When a series of squares, ranging from black to white, is suspended in 21 mid-air and illuminated by a spotlight, the perceived shades of gray are dramatically compressed relative to 22 their actual shades. 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60