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Differential and semidifferential invariant signature functions for space curve recognition

A space curve distorted by certain transformations may be recognized if an invariant description of it is available. Recent research in this area, primarily dealing with plane curves, has shown that it is possible to identify transformed curves through the use of various combinations of differential invariants and point correspondences. Purely differential invariants usually require very high order derivatives of the space curves. However, taking advantage of point correspondences sharply reduces the order of derivatives necessary, especially when the correspondences are between points on the curves. In this case, invariant signature functions requiring the computation of just first‐order derivatives can be constructed with one point correspondence for similarity transformations and two point correspondences for affine transformations. Determining the equivalence of objects reduces to partial function matching when a suitable invariant is known. A detailed example is provided to illustrate our results.©1994 John Wiley & Sons Inc