Discrete Curvature

Theory and Applications


A colloquium on discrete curvature

Second Order Surface Regularization for Vision Problems

Carl Olsson

Slides can be found by following the link.

In the Computer Vision community it is a common belief that higher order smoothness, such as curvature, should be modeled using higher order interactions. For example, 2nd order derivatives for deformable (active) contours are represented by triple cliques. Similarly, the 2nd order regularization methods in stereo predominantly use MRF models with scalar (1D) disparity labels and triple clique interactions. In this talk we present an energy based framework that uses higher dimensional labels to encode second order smoothness with pairwise interactions. Hence, many generic optimization algorithms (e.g. message passing, graph cut, etc.) can be used to optimize the proposed regularization functionals. The accuracy of our approach for representing curvature is demonstrated by theoretical and empirical results on synthetic and real data sets from multi-view reconstruction and stereo.

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