Orientation Integrability and Consistency of 3D Cloud Geometry1

Numerous applications processing 3D point data will gain from the ability to estimate reliably normals and differential geometric properties encoding curvature. In general, normal estimation is notoriously unreliable, the errors propagate and lead to unreliable 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 scenes. It provides a tool to quantify the confidence in the estimation of normals, topology, and geometry from a point cloud. The GOC is used in the development of an automatic Cloud-to-Geometry pipeline (C2G) which takes as input an unorganized 3D point cloud and outputs a point-based reconstruction of the scene geometry. Each point is equipped with a normal and a neighborhood in terms of surface distance. The scene is segmented into 0D,1D, and 2D sub-manifold components. Differential geometric properties are estimated at each surface point.