Inference of Surfaces, 3D Curves, and Junctions From Sparse, Noisy, 3D Data

We address the problem of obtaining dense surface information from a sparse set of 3D data in the presence of spurious noise samples. The input can be in the form of points, or points with an associated tangent or normal, allowing both position and direction to be corrupted by noise. Most approaches treat the problem as an interpolation problem, which is solved by fitting a surface such as a membrane or thin plate to minimize some function. We argue that these physical constraints are not sufficient, and propose to impose additional perceptual constraints such as good continuity and "cosurfacity". These constraints allow us to not only infer surfaces, but also to detect surface orientation discontinuities, as well as junctions, all at the same time. The approach imposes no restriction on genus, number of discontinuities, number of objects, and is noniterative. The result is in the form of three dense saliency maps for surfaces, intersections between surfaces (i.e., 3D curves), and 3D junctions, respectively. These saliency maps are then used to guide a "marching" process to generate a description (e.g., a triangulated mesh) making information about surfaces, space curves, and 3D junctions explicit. The traditional marching process needs to be refined as the polarity of the surface orientation is not necessarily locally consistent. These three maps are currently not integrated, and this is the topic of our ongoing research. We present results on a variety of computer-generated and real data, having varying curvature, of different genus, and multiple objects.