Multilevel computational processes for visual surface reconstruction

Abstract A computational theory of visual surface reconstruction is presented. This theory extends in a natural way the multilevel structure of the earliest processing stages in vision to later stages that reconstruct full, retinocentric surface representations from local information about surface shape at scattered locations. The surface reconstruction problem is formulated as a variational principle describing the equilibria of a thin flexible plate. Optimal discrete approximations to the variational principle are obtained via the finite element method which utilizes local (finite element) representations of surfaces. The resulting discrete problem takes the form of a large, sparse system of linear equations. A multilevel algorithm for quickly solving a hierarchy of discrete problems is described and its performance is demonstrated by examples involving depth constraints from stereopsis.

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