Inference of surfaces, 3-D curves, and junctions from sparse 3-D data

Addresses the problem of obtaining surface information from a sparse set of 3-D data in the presence of spurious noise samples. The input can be in the form of points, or points with an associated normal, allowing for both position and direction to be corrupted by noise. This is the typical input obtained from matching sparse features in stereo or motion, assuming that the observed scene is rigid. Most approaches treat the problem as an interpolation problem, solved by fitting a surface such as a membrane or thin plate which minimizes some functional. The authors argue that these physical constraints are not sufficient and propose to impose additional perceptual constraints such as good continuation and "co-surfacity". These constraints allow the authors to not only infer surfaces, but also detect surface discontinuities at the same time. The method imposes no restriction on genus, number of discontinuities, number of objects, and is non-iterative. The result is in the form of three dense saliency maps for surfaces, intersections between surfaces, and 3-D junctions. These saliency maps can then be used to guide a 'marching' process to generate a description (e.g. a triangulated mesh) making information about surfaces, space curves, and 3-D junctions explicit. The authors present results on computer-generated and real data having multiple objects, varying curvature, and of different genus.