Geometric Integrability and Consistency of 3D Point Clouds

Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and differential geometric properties. Normal estimates are notoriously 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 general surfaces, not just graphs. It provides a tool to quantify 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 directly to extract the topology and the geometry of the manifolds underlying 3D point clouds. As an illustration we describe an automatic Cloud-to-Geometry pipeline which exploits the GOC.