Visual filling-in for computing perceptual surface properties

The visual system is constantly confronted with the problem of integrating local signals into more global arrangements. This arises from the nature of early cell responses, whether they signal localized measures of luminance, motion, retinal position differences, or discontinuities. Consequently, from sparse, local measurements, the visual system must somehow generate the most likely hypothesis that is consistent with them. In this paper, we study the problem of determining achromatic surface properties, namely brightness. Mechanisms of brightness filling-in have been described by qualitative as well as quantitative models, such as by the one proposed by Cohen and Grossberg [Cohen and Grossberg (1984) Percept Psychophys 36: 428-456]. We demonstrate that filling-in from contrast estimates leads to a regularized solution for the computational problem of generating brightness representations from sparse estimates. This provides deeper insights into the nature of filling-in processes and the underlying objective function one wishes to compute. This particularly guided the proposal of a new modified version of filling-in, namely confidence-based filling-in which generates more robust brightness representations. Our investigation relates the modeling of perceptual data for biological vision to the mathematical frameworks of regularization theory and linear spatially variant diffusion. It therefore unifies different research directions that have so far coexisted in different scientific communities.