A simple test of the “anchoring account” of simultaneous contrast

Abstract

An “anchoring account” of the classic simultaneous contrast demonstration, first elucidated by Gilchrist et al. (1999) and most recently endorsed by Gilchrist (2014), is tested by adding a small white square to the black half of the display and a small black square to the white half of the display. The alteration should eliminate the effect, which, however, appears unaffected.

In two recent critiques (Maniatis, 2014a, 2014b) I argued that a series of claims addressing the role of perceptual organization in lightness estimation and collected under the rubric of “anchoring theory” are too vague, shifting, and mutually contradictory to be testable. Explanations developed for certain effects often clash with those proposed for others and with various principles expressed at various times. Furthermore, the theory's vagueness as to the degree to which these principles influence lightness means that seemingly contradictory experimental results can be and sometimes are rationalized under the same set of principles—without, however, rationalizing the contradiction. 

The anchoring account of the classic simultaneous contrast illusion (Figure 1) is a case in point. This account was first articulated by Gilchrist et al. (1999) and is reaffirmed by Gilchrist (2014a). Here, two small gray target squares, one lying on a larger white square and the other on a larger black square, appear to differ in their lightness. As I elaborate in Maniatis (2014a), the organizing principles to which anchoring theorists attribute this effect clashes with other theoretical assertions and with accounts offered for other contrast illusions (e.g., the dungeon illusion). 

Figure 1

 

The classic simultaneous contrast demonstration. The two gray squares have the same reflectance, but different lightness values, with the darker background producing a lighter appearance and vice versa.

Though inconsistencies among the principles espoused constitute a logical falsification of the anchoring theory, their vagueness and the ad hoc way in which they are applied makes them difficult to test empirically. The anchoring account for the simultaneous contrast illusion does, however, seem amenable to a straightforward test, presented here. The test involves a change to the original stimulus that should eliminate the difference in the target lightness. 

Gilchrist (2014a) explains the classic simultaneous contrast illusion as follows: 

•  
  In the global framework both squares are assigned the same value of middle gray. The illusion comes from their differing local values. The gray square on the black background, being the highest luminance in its framework, gets a local value of white. This tells us that its perceived value must lie somewhere between white (local value) and middle gray (global value). Because the global framework has twice as many elements … it gets more weight than the local framework. Thus the square should appear closer to middle gray than to white. Thus the illusion is attributed primarily to the lightening of this square due to its local value of white. …
•  
  For the square on the white background, its local value is similar to its global value except that scale normalization in the local framework would darken it slightly. (The luminance range within its framework is about 5:1, so some expansion will occur, expressed as a movement away from the anchor). (p. 888)

If the small target square on the large black square is rated “white” because it has the highest luminance within its black “framework,” then adding a white target to this framework should erase the gray target's local white status. If the target on the white square is darker due to scale normalization within this white framework, then adding a black target should undo this expansion and this darkening. Both gray squares should thus be assigned the same lightness value. 

Below, the standard form of the demonstration has been modified to incorporate this test (Figure 2). (A blue background has been added to the test figures in order to avoid the possibility that the small white square on the black background be interpreted as a hole.) 

Figure 2

 

(a) Test demo: On the basis of the “anchoring account,” the addition of the small black and white squares should make the contrast effect disappear. (b) Control for the test demo.

The effect does not appear to change. It is clearly not eliminated. This result cannot be rationalized by treating each local target pair as the local framework, since, in this case, the effect should reverse. 

Soranzo, Galmonte, and Agostini (2009) performed a similar test using an “articulated simultaneous contrast” demo. In this version of the illusion, the two backgrounds are checkerboards of squares of varying luminance, and one side has a higher average luminance. The authors hypothesized that the presence of a number of ratio-invariant pairs of adjacent checks, differing in their absolute luminance in a manner correlated with the intensity of their respective checkered backgrounds, caused the two halves of the display to appear differently illuminated. Lightness constancy mechanisms may then be invoked to explain the lightening of the target on the darker side and vice versa. 

The investigators reduced the number of ratio-invariant pairs of checks by adding one to four white and black checks to the darker and lighter backgrounds, respectively. The manipulation did not eliminate the effect, which was progressively reduced with each additional black/white check. Soranzo et al. (2009) attributed this gradual attenuation to the reduction of cues to illumination difference. According to the anchoring account, the effect should have been eliminated after the addition of a single white target on the darker side and a single black target on the lighter side. 

Soranzo et al.'s (2009) experiment represents a clear falsification of Gilchrist et al.'s (1999) account, but their explanation in terms of ratio-invariant pairs of checks can obviously not be applied to the classic version of the illusion, in which the backgrounds are homogeneous. Gilchrist (2014b) has also, in the context of a discussion of “anchoring theory,” recently speculated that the classic illusion may be due to illumination cues segregating the black/white backgrounds (i.e., that the dark region is seen as lying in shadow and/or the white region as lying within a highlight). This explicit reference to illumination cues evidently does not change the prediction, which this test has failed to corroborate. 

Acknowledgments

Commercial relationships: none. 

Corresponding author: Lydia M. Maniatis. 

Email: [e-mail]. 

Address: Profitou Ilia 4, Athens, Greece.