MOTIONS AND PATTERN-ANALYSIS - HARMONIC-ANALYSIS ON MOTION GROUPS AND THEIR HOMOGENEOUS SPACES

Following a previous work, "Fourier like" transforms are presented, 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). These transforms should have many applications in the area of pattern recognition, detection, and the representation of motions in pattern analysis. The method basically comes from 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 illustrative examples are given.