Refereed full papers (journals, book chapters, international conferences)

1993

A group theoretic approach to image representation and analysis is presented. The concept of a wavelet transform is extended to incorporate different types of groups. The wavelet approach is generalized to Lie groups that satisfy conditions of compactness and commutability and to groups that are determined in a particular way by subgroups that satisfy these conditions. These conditions are fundamental to finding the invariance measure for the admissibility condition of a mother wavelet-type transform. The following special cases of interest in image representation in biological and computer vision are discussed: 2- and 3-D rigid motion, similarity and Lorentzian groups, and 2-D projective groups obtained from 3-D camera rotation.