Efficient matching of space curves

Abstract

The aim is to provide invariant signatures for matching space curves under Euclidean motions. Semi-differential rather than differential invariants can be used for the description and recognition of space curves. They have the advantage of being more robust, but on the other hand introduce the problem of finding good reference points. In order to avoid a search for such points, an alternative scheme is propounded. Strategies are used that make the reference point dependent on the point where the shape is being described. Actually, the reference point is attached to the point under scrutiny in an invariant manner. “Sliding Pairs of Constant Total Curvature” were seen experimentally to provide stable point pairs on all scales allowing to reduce the size of the description from n ² to n, where n is the number of evenly spaced sample points taken from a curve.

This work has been done during the visit of T. Pajdla at ESAT, K.U.Leuven. Support by Esprit Basic Research Action ‘VIVA’ and project IUAP-50 (Inter-Universitaire Attractie-Pool) on Robotics and Industrial Automation, financed by the Belgian Federal Services for Scientific, Technological, and Cultural Affairs, is gratefully acknowledged.