Integrated surface, curve and junction inference from sparse 3-D data sets

We are interested in descriptions of 3-D data sets, as obtained from stereo or a 3-D digitizer. We therefore consider as input a sparse set of points, possibly associated with orientation information. In this paper, we address the problem of inferring integrated high-level descriptions such as surfaces, curves, and junctions from a sparse point set. While the method described previously provides excellent results for smooth structures, it only detects discontinuities, but does not localize them. For precise localization, we propose a non-iterative cooperative algorithm in which surfaces, curves, and junctions work together: Initial estimates are computed based on previous results, where each point in the given sparse and possibly noisy point set is convolved with a predefined vector mask to produce dense saliency maps. These maps serve as input to our novel maximal surface and curve marching algorithms for initial surface and curve extraction. Refinement of initial estimates is achieved by hybrid voting using excitatory and inhibitory fields for inferring reliable and natural extension so that surface/curve and curve/junction discontinuities are preserved. Results on several synthetic as well as real data sets are presented.