Contrasting theories of White's illusion.

Howe (2001) presents a new variant of White's illusion and asserts that it demonstrates the failures of a number of models of White's illusion, including my own (Anderson 1997). He also argues that the FACADE model of Grossberg can explain this effect, as well as the other published variants of White's illusion (Grossberg 1997; Kelly and Grossberg 2000). My response has two parts. First, although Howe's display does reveal the need to go beyond the local properties of T-junctions, I contend that it does not provide a critical test of the two competing explanations of White's effect (namely, a contrast theory, and a scission theory). Second, I will argue that although the FACADE model can provide some insight into this particular variant of White's illusion, it actually fails to account for White's original effect or variants of the illusion I have published previously (Anderson 1997). Howe's demonstration consists of a very weak version of White's effect containing a single target bar. The main change to White's stimulus is the addition of extended black and white horizontal bands that cut across the image. In his display, the contours of these bands are carefully aligned with the stems of the targets' T-junctions. Howe finds that observers report that the illusion is either greatly reduced or inverted by this manipulation. He argues that this impacts negatively on T-junction-based theories of this illusion, since the local T-junctions are unchanged in the top and bottom figure. This seems fair enough, and points to a need to consider other, nonlocal properties to account for the effect. The main change introduced by Howe's variant of White's illusion is the presence of aligned contours at the T-junctions from the horizontally extended bars in his pattern. Although Howe did not actually demonstrate that the alignment of these contours is critical for his effect, it can be easily demonstrated; see figure 1. When the horizontal bands are aligned with the stems of the T-junction, the illusion is greatly reduced (as Howe reports); however, when they are misaligned, the illusion returns to normal (which he did not). Why would this be so? The simplest and most obvious answer is that the extended horizontal contours effectively transform the local T-junctions into X-junctions, which is precisely how Howe tries to explain the new effect. The question is whether this provides any conceptual leverage into the two competing theories of this illusion that Howe discusses: contrast theory, and scission theory [see also Gilchrist et al (1999) for an anchoring account of this illusion]. Contrast-based models attribute White's effect to a selective contrast between the gray target bars and the stripes on which the targets are embedded. Scission theory (Anderson 1997) attributes this illusion to mechanisms that are responsible for decomposing images into multiple layers. The theoretical problem created by White's illusion for contrast theories is that the perceived lightness difference is in the wrong direction. One way to `solve' this problem is to assert that the edges that would drive the illusion in the wrong direction are somehow discounted. Such models essentially reduce White's illusion to a form of simultaneous contrast: a gray bar in a white stripe becomes equivalent to a gray target on a white background; and a gray bar in a black stripe becomes equivalent to a gray target on a black background. My scission-based account was motivated (in part) by a significant shortcoming of such theories. By reducing White's illusion to a variant of simultaneous contrast, such theories place an upper bound on the strength of the illusion: White's effect can only be as large as a comparable simultaneous-contrast display. But even White's original Discussion Perception, 2001, volume 30, pages 1499 ^ 1507