Sliding Pairs -a Method for Finding Reference Points on Curves

The aim is to provide invariant signatures for matching space curves under Euclidean motions. Semi-diierential rather than diierential 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 nding 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. The results of experiments are reported, that corroborate the method's feasibility.