Recognizing 3D objects using tactile sensing and curve invariants

A general paradigm for recognizing 3D objects is offered, and applied to so me geometric primitives (spheres, cylinders, cones, and tori). The assumpti on is that a curve on the surface, or a pair of intersecting curves, was me asured with high accuracy (for instance, by a sensory robot). Differential invariants of the curve(s) are then used to recognize the surface. The moti vation is twofold: the output of some devices is not surface range data, bu t such curves. Also, a considerable speedup is obtained by using curve data , as opposed to surface data which usually contains a much higher number of points. We survey global, algebraic methods for recognizing surfaces, and point out their limitations. After introducing some notions from differential geomet ry and elimination theory, the differential and "semi-differential" approac hes to the problem are described, and novel invariants which are based on t he curve's curvature and torsion are derived.