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<p>The figure-ground discrimination problem is considered from a combinatorial optimization perspective. A mathematical model encoding the figure-ground discrimination problem that makes explicit a definition of shape based on cocircularity, smoothness, proximity, and contrast is presented. This model consists of building a cost function on the basis of image element interactions. This cost function fits the constraints of an interacting spin system that, in turn, is a well suited physical model that solves hard combinatorial optimization problems. Two combinatorial optimization methods for solving the figure-ground problem, namely mean field annealing, which combines mean field approximation theory and annealing, and microcanonical annealing, are discussed. Mean field annealing may be viewed as a deterministic approximation of stochastic methods such as simulated annealing. The theoretical bases of these methods are described, and the computational models are derived. The efficiencies of mean field annealing, simulated annealing, and microcanonical annealing algorithms are compared. Within the framework of such a comparison, the figure-ground problem may be viewed as a benchmark.</p>
combinatorial optimization; figure-ground discrimination; shape; cocircularity; smoothness; proximity; contrast; image element interactions; cost function; interacting spin system; mean field annealing; mean field approximation theory; microcanonical annealing; deterministic approximation; stochastic methods; simulated annealing; combinatorial mathematics; image processing; simulated annealing

R. Horaud and L. Hérault, "Figure-Ground Discrimination: A Combinatorial Optimization Approach," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 15, no. , pp. 899-914, 1993.
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