Scale space semi-local invariants

In this paper we discuss a new approach to invariant signatures for recognizing curves under viewing distortions and partial occlusion. The approach is intended to overcome the ill-posed problem of finding derivatives, on which local invariants usually depend. The basic idea is to use invariant finite differences, with a scale parameter that determines the size of the differencing interval. The scale parameter is allowed to vary so that we obtain a 'scale space'-like invariant representation of the curve, with larger difference intervals corresponding to larger, coarser scales. In this new representation, each traditional local invariant is replaced by a scale-dependent range of invariants. Thus, instead of invariant signature curves we obtain invariant signature surfaces in a 3-D invariant 'scale space'.