Tensor Voting: Theory and Applications

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