Vision Res. Vol. 28, No. 1, pp. 115-132, 1988 0042-6989/88 $3.00+0.00 Printed in Great Britain. All rights reserved Copyright © 1988 Pergamon Journals Ltd BRIGHTNESS INDUCTION BY LOCAL CONTRAST AND THE SPATIAL DEPENDENCE OF ASSIMILATION R. CLAY REID JR and ROBERT SHAPLEY The Rockefeller University, 1230 York Ave., New York, NY 10021, U.S.A. (Received 16 September 1986; in revised form 28 April 1987) Abstract--Two mechanisms of brightness perception (1) brightness induction by local contrast and (2) assimilation, were examined for a variety of visual stimuli. Local contrast is the primary determinant of brightness perception, making objects appear brighter on a background of lower luminance and darker on a background of greater luminance. Assimilation is the opposite effect, whereby objects on a brighter (but not necessarily more luminant) background appear brighter or on a dark background appear darker. We have compared the relative strength of the two effects using stimuli which permit them to be studied separately. Brightness induction by local contrast is quantitatively stronger in all situations. Further, the strength of assimilation is strongly dependent on spatial parameters in the visual scene. These results are shown to be true both for simple visual stimuli as well as for complicated Mondrian-like patterns. The Retinex theory of brightness perception predicts that the two effects are equal. Our results show a range of relative strengths (assimilation vs brightness induction due to contrast) from 0.59 to 0.63 at 5' down to 0.34 at 4Y. Assimilation Contrast Brightness Retinex Cortex INTRODUCTION The perception of brightness in each region of a visual stimulus is dependent not only on the luminance of each particular region of the stim- ulus considered in isolation, but is influenced by the luminance of adjacent and perhaps distant regions as well. If viewed upon a spatially uniform background, the subjective impression of an object's brightness will vary montonically with its luminance, measured as the amount of physiologically effective light per unit area. If the luminances of other objects in the visual field are varied, however, a region of constant luminance can change significantly in perceived brightness. Rather than luminance determining brightness, there appear to be two antagonistic mechanisms which are responsible for percep- tion of brightness, corresponding to the classical psychological phenomena of brightness in- duction, due to local contrast, and assimilation. It is the relative contribution of the two mechanisms which determine our perceptions of visual stimuli. Numerous studies have quantified the bright- ness induction effect (Heinemann, 1955, 1972), but assimilation has been less well studied. Visual stimuli which minimize contrast differ- ences between test and comparison regions have been used to quantify the strength of assimilation and compare it to the better under- stood effect of brightness induction (Shapley and Reid, 1985). This paper uses similar methods to examine the relative strengths of contrast and assimilation and the dependence of assimilation strength on spatial parameters. The apparent brightness of an object is dependent largely on the physical contrast between it and its surroundings. In this paper we define the physical contrast at a border between areas of luminance Lt and L2 to be C = 2(L2 - LI)/(L2 + L~): the variation of the luminance divided by the average. This is approximately equal to the Weber contrast (Shapley and Enroth-Cugell, 1984) Cw= (Lobject- Lbackgro,.ma)/Lbackg .... d for stimuli of low contrast. The dependence of brightness on contrast alone goes a long way in explaining the effect of brightness (or color) constancy, whereby the brightness (or color) of an object is largely independent of illumination (von Kries, 1905; Hurvich, 1981). As the luminance of a uni- formly illuminated reflecting object is equal to illumination, L times reflectance, R, contrast is independent of illumination Cw = (IRobj~t -- IRbackg~ound)/IRba~kg~ound = (Robject - - Rbackground)/Rbackgrnun d . 115