Computation of surface geometry and segmentation using covariance techniques

In this correspondence, the application of covariance techniques to surface representation of 3-D objects is discussed and such ways of computing surface geometry are compared with traditional methods using differential geometry. It is shown how the covariance method provides surface descriptors that are invariant to rigid motions without explicitly using surface parameterizations or derivatives. Analogous covariance operators for both the Gauss and Weingarten maps are defined and a range image segmentation technique is presented that labels pixels as jump or crease discontinuities or planar, parabolic or curved region types