Figure-ground discrimination: a combinatorial optimization approach

Abstract

Abstract-h this paper, we attack the figure-ground discrimination problem from a combinatorial optimization perspective. In general, the solutions proposed in the past solved this problem only partially: Either the mathematical model encoding the figure-ground problem was too simple, the optimization methods that were used were not efficient enough, or they could not guarantee that the global minimum of the cost function describing the figure-ground model would be found. The method that we devised and is describe-d in this paper is tailored around three main contributions.First, we suggest a mathematical model encoding the figureground discrimination problem that makes explicit a definition of shape (or figure) based on cocircularity, smoothness, proximity, and contrast. This model consists of building a cost function on the basis of image element interactions. Moreover, 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 Second, we suggest two combinatorial optimization methods for solving the figure-ground problem, namely i) mean field annealing, which combines mean field approximation theory and annealing, and ii) microcanonical annnealing. Mean field annealing may well be viewed as a deterministic approximation of stochastic methods such as simulated annealing. We describe, in detail, the theoretical bases of these methods, derive computational models, and provide practical algorithms.Third, we provide a comparison of the efficiency of mean field annealing, simulated annealing, and microcanonical annealing algorithms. Within the framework of such a comparison, the figure-ground problem may well be viewed as a benchmark.

Extracting salient curves from images: an analysis of the saliency network

“…We note that, in contrast to other existing methods for grouping that search over the exponentially large space of all possible image curves (e.g., Herault and Horaud, 1993;Jacobs, 1993;Parent and Zucker, 1989;Williams, 1994), the Saliency Network recovers the most salient curve in time complexity that is polynomial in the size of the image. However, the network must take a single choice at every junction, and curves lying near a salient curve tend to merge into the salient curve because they can benefit from its saliency.…”

“…Other tasks in perceptual grouping are image segmentation and gap completion. For instance (Herault and Horaud, 1993;Jacobs, 1993;Martelli, 1976;Nevatia, 1988, 1992;Montanari, 1971;Parent and Zucker, 1989;Pavlidis and Liow, 1990;Weiss, 1988;Williams and Hanson, 1994) extract contours from the image according to certain optimization criteria, (Ullman, 1976;Ruthowski, 1979;Brady et al, 1980;Horn, 1983;Bruckstein and Netravali, 1990) compute optimal curves for filling in gaps, and (Brady and Grimson, 1981;Webb and Pervin, 1984;Finkel and Sajda, 1992;Grossberg and Mingolla, 1987;Heitger and von der Heydt, 1993;Mumford, 1994;Williams and Jacobs, 1995) identify occluded and subjective contours.…”

Applying knowledge to reverse engineering problems

“…There is work on recognizing objects from range data, considering occlusions [36], but here we are attempting to recover from them. The key to reconstruction is the knowledge that the shape of the unobserved surface is usually the same as the observed portion of a surface [23,34]. This allows us to project surfaces into occluded areas.…”

Supervised learning of large perceptual organization: graph spectral partitioning and learning automata

“…Of the work in perceptual organization with extended primitives, such as lines or arcs, the effort has been mostly to form simple, small groups of primitives such as parallels [5], convex outlines [6], ellipses [7], [28], and rectangles [8], [28], [29]. Among the frameworks that can form large groups is the solution suggested by Herault and Horaud [30]. They use simulated annealing to solve the figure ground problem.…”