Motions and pattern analysis: harmonic analysis on motion groups and their homogeneous spaces

Fourier-like transforms that are defined on several groups of motions on the plane and on the plane itself (viewed as the homogeneous space of these motion groups) are presented. These transforms should have many applications in the area of pattern recognition, detection, and the representation of motions in pattern analysis. The method is based upon group-representation theory and abstract harmonic analysis on semidirect product groups. However, most of the ideas are generalizations and interpretations of classical concepts and methods such as the Fourier descriptor method used for boundary recognition. Computational aspects are investigated, and examples are given