Continuous Group Averaging and Pattern Classification Problems
J. C. Dunn · SIAM Journal on Computing · 1973
The relationship between pattern classification problems and the elementary theory of group invariants is considered. A general procedure for obtaining quantitative invariants by averaging functionals over the manifold of a continuous group is examined in some detail, and then applied to the classification of plane figures. Specifically, the Fourier transform of a plane figure is averaged over the one-parameter continuous group of dilatations to obtain a pair of interesting scale invariant transforms which tend to pick out corners and flat spots in the figure’s boundary.