Inference of Integrated Surface, Curve, and Junction Descriptions from Sparse 3D Data

Abstract—We are interested in descriptions of 3D data sets, as obtained from stereo or a 3D digitizer. We therefore consider as input a sparse set of points, possibly associated with certain orientation information. In this paper, we address the problem of inferring integrated high-level descriptions such as surfaces, 3D curves, and junctions from a sparse point set. While the method proposed by Guy and Medioni provides excellent results for smooth structures, it only detects surface orientation discontinuities but does not localize them. For precise localization, we propose a noniterative cooperative algorithm in which surfaces, curves, and junctions work together: Initial estimates are computed based on the work by Guy and Medioni, 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 extremal surface and curve algorithms for initial surface and curve extraction. These initial features are refined and integrated by using excitatory and inhibitory fields. Consequently, intersecting surfaces (resp. curves) are fused precisely at their intersection curves (resp. junctions). Results on several synthetic as well as real data sets are presented. Index Terms—Segmentation and feature extraction, integrated shape description, surface orientation discontinuity, surface and curve extremality.