Tensor Voting : Theory and Applications

Abstract

We present a unified computational framework which properly implementsthe smoothness constraint to generate descriptions in terms of surfaces,regions, curves, and labelled junctions, from sparse, noisy, binarydata in 2-D or 3-D. Each input site can be a point, a point withan associated tangent direction, a point with an associated normaldirection, or any combination of the above. The methodology is groundedon two elements: tensor calculus for representation, and linear votingfor communication: each input site communicates its information (atensor) to its neighborhood through a predefined (tensor) field,and therefore casts a (tensor) vote. Each site collects all the votescast at its location and encodes them into a new tensor. A local,parallel marching process then simultaneously detects features. Theproposed approach is very different from traditional variationalapproaches, as it is non-iterative. Furthermore, the only free parameteris the size of the neighborhood, related to the scale. We have developedseveral algorithms based on the proposed methodology to address anumber of early vision problems, including perceptual grouping in2-D and 3-D, shape from stereo, and motion grouping and segmentation,and the results are very encouraging.