Recognizing surfaces using curve invariants and differential properties of curves and surfaces

Abstract

A general paradigm for recognizing 3D objects is offered, and applied to some geometric primitives (spheres, cylinders, cones, and tori). The assumption is that a curve on the surface was measured with high accuracy (for instance, by a sensory robot). Differential invariants of the curve in one method and differential properties of curves and surfaces in the other are then used to recognize the surface. The motivation is twofold: the output of some devices is not surface range data, but such curves. So, surface invariants, which may be simpler in some cases, cannot always be obtained. Also, a considerable speedup is obtained by using curve data, as opposed to surface data which usually contains a much higher number of points.