Tensor voting in computer vision, visualization, and higher dimensional inferences
Gérard G. Medioni, Chi–Keung Tang · 2000
This dissertation is founded on the basic Tensor Voting Formalism. It provides a unified computational framework, making use of the continuity constraint to generate layered descriptions in terms of surfaces, regions, curves, and labeled junctions, from sparse, noisy, binary data in 2-D or 3-D. The method is non-iterative, does not depend on initialization, robust to spurious outlier noise, and the only free parameter is the size of the neighborhood, or the scale of analysis, which is indeed a property of visual perception. In this thesis, feature extraction from tensor data is first studied. A number of new feature extraction algorithms is designed and implemented. Coherent features, such as a hole-free triangulation mesh, and a curve consisting of connected and oriented curve segments, are typical outputs of these algorithms. While the basic formalism provides excellent results for smooth structures, it only detects discontinuities but does not localize them. A methodology for feature integration is proposed. This extended system is applied in a variety of visualization problems, and very encouraging results are obtained. The feature integration is further upgraded bar the use of second order, curvature information, which is absent from the basic formalism. The tensor voting formalism is also generalized to higher dimensions, and the 8-D version is applied to solve the problem of epipolar geometry estimation. Given a set of noisy point correspondences in two images as obtained from two views of a static scene without correspondences, even in the presence of moving objects, our method extract all good matches while rejecting all outliers. The proposed theory and the implementation consolidate the existing tensor voting foundation. Promising further research and development in a wide variety of applications, and in any dimensions, are possible.