Shape Invariants and Principal Directions from 3D Points and Normals

George Kamberov  
Gerda Kamberov

Department of Computer Science 
Stevens Institute of Technology 
Hoboken, NJ 07030, USA 

Department of Computer Science 
Hofstra University 
Hempstead, NY 11549, USA

Abstract

A new technique for computing the differential invariants of a surface from 3D sample points and normals is presented. It is based on a new conformal geometric approach to computing shape invariants directly from the Gauss map. In the current implementation we compute the mean curvature, the Gauss curvature, and the principal curvature axes at 3D points reconstructed by area-based stereo. The differential invariants are computed directly from the points and the normals without prior recovery of a 3D surface model and an approximate surface parameterization. The technique is stable computationally.