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, fr om sparse, local measurements, the visual system must somehow generate the most likely hypothesis that is consistent with them. In this paper, we stud y the problem of determining achromatic surface properties, namely brightne ss. Mechanisms of brightness filling-in have been described by qualitative as well as quantitative models, such as by the one proposed by Cohen and Gr ossberg [Cohen and Grossberg (1984) Percept Psychophys 36: 428-456]. We dem onstrate that filling-in from contrast estimates leads to a regularized sol ution for the computational problem of generating brightness representation s from sparse estimates. This provides deeper insights into the nature of f illing-in processes and the underlying objective function one wishes to com pute. This particularly guided the proposal of a new modified version of fi lling-in, namely confidence-based filling-in which generates more robust br ightness representations. Our investigation relates the modeling of percept ual data for biological vision to the mathematical frameworks of regulariza tion theory and linear spatially variant diffusion. It therefore unifies di fferent research directions that have so far coexisted in different scienti fic communities.