Deformable models in the ``physically-based'' paradigm are almost always formulated in an ad-hoc fashion and are not related to physical reality. We reinterpret these techniques by putting them into a framework of robust statistics and using this framework to analyze the problems and ad-hoc solutions found in common physically-based formulations. These include incorrect prior shape models; bad relative weights of various energies; and the two-stage approach to minimization (adjusting global, then local shape parameters). We examine the statistical implications of common deformable object formulations. In our reformulation, the units are meaningful, training data plays a fundamental role, different kinds of information may be fused, and certainties can be reported for the segmentation results. We suggest robust statistics to combat interference from the necessarily large amount of unmodeled image information.
Keywords: Active contour model, active shape model, snake, deformable model, deformable contour, deformable surface, potential surface, nonrigid motion, energy-minimizing spline, bayesian formulation, probabilistic formulation, robust statistics, robust estimator, maximum likelihood estimator, uncertainty
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Samuel D. Fenster
Department of Computer Science
Columbia University