Classification and positioning of algebraic curves and surfaces

An approach to 3-D rigid object recognition and positioning from range data is described. Only piecewise algebraic objects are considered. A piecewise algebraic object is a solid object whose boundary surfaces can be described as finite collections of smooth surface patches, and each of these patches as a subset of an algebraic surface, the set of zeros of a polynomial in three variables. It is shown that the same techniques apply to the recognition and positioning of rigid objects from sparse nonplanar curve data, and to the recognition and positioning of rigid two-dimensional contours from edge maps. New ideas for computationally attractive classification and positioning of 3-D surfaces, 2-D curves, and 3-D curves, based on geometric invariants, are introduced