Geometric Integrability and Consistency of 3D Point Clouds

Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and dif-ferential geometric properties. Normal estimates are noto-riously noisy, the errors propagate and may lead to flawed, inaccurate, and inconsistent curvature estimates. Frankot-Chellappa introduced the use of integrability constraints in normal estimation. Their approach deals with graphs z = f(x; y). We present a newly discovered General Orientability Constraint (GOC) for 3D point clouds sampled from gen-eral surfaces, not just graphs. It provides a tool to quan-tify the confidence in the estimation of normals, topology, and geometry from a point cloud. Furthermore, similarly to the Frankot-Chellappa constraint, the GOC can be used di-rectly to extract the topology and the geometry of the man-ifolds underlying 3D point clouds. As an illustration we describe an automatic Cloud-to-Geometry pipeline which exploits the GOC. 1