First order tensor voting, and application to 3-D scale analysis

Many computer vision systems depend on reliable detection of 3D boundaries and regions in order to proceed. In the presence of outliers, missing data and orientation discontinuities due to occlusion, it is difficult to detect boundaries and interpolate data without over-smoothing important feature curves. The authora address these problems by incorporating first order tensor information into the tensor voting formalism, which is second-order based. To propagate an adaptive smoothness constraint at a preferred orientation non-iteratively, we vote for a first order tensor (or vector) to capture polarity and orientation information. To integrate first and second order tensors, we propose an algorithm for inferring the proper scale based on the continuity constraint, and preserving the finest details. Given a noisy 3D point set, the new and improved formalism can better localize boundary curves and orientation discontinuities. Unlike many approaches that over-smooth features, or delay the handling of boundaries and discontinuities until model misfit occurs, the interaction of smooth features, boundaries, discontinuities, outliers are encoded at the representation level. We present results from a variety of datasets to show the efficacy of the improved formalism.