CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Vision Research 41 (2001) 3649–3662 www.elsevier.com/locate/visres Darkness filling-in: a neural model of darkness induction Michael E. Rudd a,*, Karl Frederick Arrington b a Department of Psychology, Uni6ersity of Washington, Box 351525, Seattle, WA 98195-1525, USA b Arrington Research, Inc., Mesa, AZ 85206, USA1 Received 14 February 2001; received in revised form 6 August 2001 Abstract A model of darkness induction based on a neural filling-in mechanism is proposed. The model borrows principles from both Land’s Retinex theory and BCS/FCS filling-in model of Grossberg and colleagues. The main novel assumption of the induction model is that darkness filling-in signals, which originate at luminance borders, are partially blocked when they try to cross other borders. The percentage of the filling-in signal that is blocked is proportional to the log luminance ratio across the border that does the blocking. The model is used to give a quantitative account of the data from a brightness matching experiment in which a decremental test disk was surrounded by two concentric rings. The luminances of the rings were independently varied to modulate the brightness of the test. Observers adjusted the luminance of a comparison disk surrounded by a single ring of higher luminance to match the test disk in brightness. © 2001 Published by Elsevier Science Ltd. Keywords: Brightness; Brightness induction; Filling-in; Lightness; Retinex theory 1. Introduction luminance. It was found that the brightnesses of the two disks matched whenever the ratios of their lumi- In the well-known simultaneous contrast illusion, two nances to the luminances of their respective surrounds or more regions of an image that have identical physi- were equal. This result is known as Wallach’s ratio rule. cal luminances differ in brightness because of the differ- The ratio rule has since been shown to hold over a ing luminances of their surrounds. For example, a million-to-one range of illumination (Jacobsen & middle gray paper appears darker when presented Gilchrist, 1988). against a light background than it does when presented Wallach proposed a theoretical account of the ratio against a dark background. Wallach (1948) asked the rule based on the principle of brightness constancy: closely related question: under what conditions will two surface brightness is invariant with respect to changes regions surrounded by different backgrounds appear in illumination. This principle is closely related to the equally bright? To answer this question, he presented idea that brightness is the visual system’s attempt to two disks, each having its own surround annulus represent surface reflectance and discount the illumi- (higher in luminance than the disk), side-by-side in an nant (Helmholtz, 1910/1925). According to the bright- otherwise dark room. The luminance of one of the ness constancy account, when the two disk-and-ring disks was adjusted as a function of its surround lumi- patterns have identical disk/surround luminance ratios, nance to obtain a brightness match to the other disk, they are interpreted by the visual system as two identi- which had both a fixed luminance and fixed surround cal configurations of surfaces illuminated by spotlights of different intensities. The presumed different illumina- The model has been presented earlier at professional conferences tion levels are ‘discounted’ in arriving at the psycho- and published in the form of brief conference abstracts (Rudd & physical brightness match. Arrington, 2000; Rudd, 2000). Although brightness constancy successfully explains * Correponding author. Tel.: +1-206-685-1572; fax: +1-206-685- 3157. why the two disks Wallach’s display appear identical E-mail address: [email protected] (M.E. Rudd). when their disk/surround ratios are equal, it fails to 1 http://www.ArringtonResearch.com. account for the equally important fact that the more 0042-6989/01/$ - see front matter © 2001 Published by Elsevier Science Ltd. PII: S0042-6989(01)00216-4 3650 M.E. Rudd, K.F. Arrington / Vision Research 41 (2001) 3649–3662 luminant surround ring appears brighter than the less Judd, 1940; Land, 1986; Land, Hubel, Livingstone, luminant surround under these same conditions. If, as Perry, & Burns, 1983). The second assumes that the Wallach argued, the visual system interprets the two highest luminance is assigned the value ‘white’ (Land, disk-and-ring configurations as two different objects 1977; Land & McCann, 1971; Wallach, 1948, 1976). having identical ‘paint-jobs’ but illuminated by different The third assumes that a gain control mechanism scales spotlights, then the rings on the two sides of the display brightness according to a measure of space-averaged should also appear equally bright, but they do not. luminance variance (Brown & MacLeod, 1991, 1997). The brightnesses of both the disks and the rings in The results of most of the anchoring experiments have Wallach’s display can be accounted for more parsimo- been interpreted as supporting the highest luminance niously on the basis of local border contrast. The disks rule (Bruno, 1992; Bruno, Bernardis, & Schirillo, 1997; look identical when the disk/annulus luminance ratios Gelb, 1929; Li & Gilchrist, 1993; McCann, 1989, 1992; are the same because, under these conditions, the con- Schirillo & Shevell, 1993, 1996; Schirillo, 1999a,b). trasts at the borders of the two disks are identical. The The process of edge integration (Stage 2) has been more luminant ring looks brighter than the less lumi- investigated in much less detail. However, it is clear nant ring because the contrast of its outer border is that under many stimulus conditions, the visual system greater. However, it is clear from studies carried out does not perfectly integrate luminance steps across the with more complex displays that local contrast alone is entire visual image. The simultaneous contrast illusion, not sufficient to account for brightness perception. In for example, depends on the fact that the contrast of general, brightness also depends on nonlocal influences the disk border has an inordinate influence on disk that are presumably based on the spatial integration of brightness. If all of the luminance steps in a simulta- local contrast information. neous contrast display were perfectly integrated by the A number of theoretical models of have been pro- visual system, there would be no illusion. Instead, the posed to suggest how brightness might be computed on ratios of the brightnesses of various regions within the the basis of a neural process that integrates local lumi- figure would match the actual reflectance ratios of those nance steps across space (Arend, 1985, 1994; Blake, regions. 1985; Horn, 1974; Hurlbert, 1986; Land & McCann, One simple way of modeling the breakdown of per- 1971; Land, 1977, 1986). A common assumption of fect edge integration is to assume that edge integration these models is that the visual system achieves bright- declines with distance. A model of this type was pro- ness constancy by a neural computation involving a posed by Reid and Shapley (1988) to account for their series of subprocesses or stages: (1) extraction of local data on contrast and assimilation. If edge integration luminance ratios at the locations of edges in the image; declines with distance, then the luminance ratio at the (2) spatial integration of these luminance ratios to immediate border of a region should exert a particu- reconstruct a map of relative surface reflectances; and larly important influence on the brightness of that (3) brightness anchoring, to relate the scale of relative region. Edges lying at a greater distance from the surface reflectances to a common absolute brightness region could also affect its brightness, but they should standard. have less of an influence than do nearby edges. Most computational models assume that the lumi- For purposes of exposition, it is useful to consider nance ratios computed by Stage 1 are multiplied across the two limiting cases of the distance-dependent edge space to recover relative surface reflectances in Stage 2 integration hypothesis in which either: (1) edge integra- (Arend, 1985, 1994; Blake, 1985; Gilchrist, Delman, & tion declines very rapidly with spatial distance; or (2) Jacobsen, 1983; Horn, 1974; Hurlbert, 1986; Land & edge integration does not decline with distance at all. In McCann, 1971; Land, 1977, 1986; Whittle & Challands, the limit of very rapid spatial falloff of integration, 1969). Stage 3 is required to relate the scale of relative patch brightness should depend only on the local con- luminances to an absolute standard in order for the trast at the immediate borders of the patch. A model of visual system to assign specific, as opposed to relative, this type would account for simultaneous contrast and brightness values (Cataliotti & Gilchrist, 1995). could be instantiated by a simple lateral inhibitory This basic computational scheme for computing mechanism (Mach, 1865; Ratliff, 1965). brightness, like the principle of brightness constancy In the limit of long-distance edge integration, on the itself, has become a standard working hypothesis within other hand, the visual system would be able to recover the psychophysical brightness literature. A number of the overall pattern of relative reflectances in the image recent psychophysical papers have addressed the prob- and would thus achieve brightness constancy to within lem of brightness anchoring (Stage 3 of the ‘standard’ a constant factor that depends on the anchor point, as model). Three different anchoring rules have been pro- in the computational models cited above. posed in the literature. The first assumes that the space- The current study was designed to pit these two average luminance is assigned the value ‘gray’ (Helson, extreme models against one another and to collect data 1943, 1964; Hurlbert, 1986; Hurlbert & Poggio, 1988; for the purpose of building a quantitative model to M.E. Rudd, K.F.