A group theoretical approach to filter design

The author investigates the following fundamental pattern recognition problem. He assumes that he has a set of signals or patterns, denoted by S, and an unknown pattern p. The problem is to decide if P∈S or p∉ S. The author assumes further that S is symmetrical or regular in a group-theoretical sense. Harmonic analysis and the theory of group representations are applied to construct filter processes that se the regularity of S in an optimal way. Results are presented for 2-D and 3-D rotation-invariant filters