Boundary detection by constrained optimization

Abstract

Abstract-We use a statistical framework for finding boundaries and for partitioning scenes into homogeneous regions. The model is a joint probability distribution for the a r ray of pixel gray levels and an a r ray of “labels. ” In boundary finding, the labels a re binary, zero, or one, representing the absence o r presence of boundary elements. In parti-tioning, the label values a r e generic: two labels a re the same when the corresponding scene locations a r e considered to belong to the same re-gion. The distribution incorporates a measure of disparity between cer-tain spatial features of pairs of blocks of pixel gray levels, using the Kolmogorov-Smirnov nonparametric measure of difference between the distributions of these features. Large disparities encourage inter-vening boundaries and distinct partition labels. The number of model parameters is minimized by forbidding label configurations that a r e in-consistent with prior beliefs, such as those defining very small regions, o r redundant or blindly ending boundary placements. Forbidden con-figurations a re assigned probability zero. We examine the MAP (mar-imum a posterion’) estimator of boundary placements and partition-ings. The forbidden states introduce constraints into the calculation of these configurations. Stochastic relaxation methods a re extended to ac-commodate constrained optimization, and experiments are performed on some texture collages and some natural scenes. i Zndex Terms-Annealing, Bayesian inference, boundary finding,

Keywords

Affiliated Institutions

• Centre National de la Recherche Scientifique FR
• University of Massachusetts Amherst US
• Brown University US
• Mansfield University US
• Université Paris-Sud FR

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