Abstract

Both the perception of transparency and the estimation of reflectance, given sharp illumination edges, are problems that human observers routinely solve without apparent effort. Although the conditions leading to phenomenal transparency have been thoroughly studied, it has not been clear how to tease apart the transparent from the opaque components of an image. We have modeled the restricted case of the estimation of reflectance in Mondrian images in the presence of multiplicative illuminants with sharp (transparent overlays) or smooth edges. Our computational goal is to find the most probable opaque and transparent components conditional on the image luminance. The posterior probability is the product of three terms: the forward probability of the image conditional on the reflectance and illumination and the prior probabilities of the reflectance and illumination. The priors are modeled as intensity-based Markov random fields with coupled line processes. The landscape of the posterior probability is extremely rugged, leading to multiple stable maxima, a phenomenon human observers also experience. It is also shown that supplementing raw image data with intensity edges considerably improves the solution.

© 1988 Optical Society of America