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General Geometric Good Continuation: A Biologically Plausible Network Model

Good continuation is the Gestalt observation that parts often group to form coherent wholes. Perceptual integration of edges, for example, involves orientation good continuation, and has been widely exploited computationally. But more general local-global relationships, such as for shading, have been elusive. While Taylor's Theorem suggests certain modeling and smoothness criteria, the consideration of levelset geometry indicates a different approach. Using such first principles we derive, for the first time, a generalization of good continuation to all those visual structures that can be abstracted as scalar functions over the image plane. Our model yields a coupled system of partial differential equations, which leads to a unique class of harmonic models and a network-based cooperative algorithm for structure inference which we apply to shading and intensity distributions. We demonstrate how this approach eliminates spurious measurements while preserving both singularities and regular structure, a property that facilitates higher level processes which depend so critically on both aspects of visual structures