DIFFERENTIAL AND NUMERICALLY INVARIANT SIGNATURE CURVES APPLIED TO OBJECT RECOGNITION

We introduce a new paradigm, the differential invariant signature curv e or manifold, for the invariant recognition of visual objects. A gene ral theorem of E. Cartan implies that two curves are related by a grou p transformation if and only if their signature curves are identical. The important examples of the Euclidean and equi-affine groups are dis cussed in detail. Secondly, we show how a new approach to the numerica l approximation of differential invariants, based on suitable combinat ion of joint invariants of the underlying group action, allows one to numerically compute differential invariant signatures in a fully group -invariant manner. Applications to a variety of fundamental issues in vision, including detection of symmetries, visual tracking, and recons truction of occlusions, are discussed.