Object detection based on correlation on transformation groups

In this work, we propose a unified formulation for correlation techniques in a theoretical framework based on group theory. Indeed, correlation on groups can be defined in terms of transformation groups, feature spaces and invariant measures. As an important example, we describe the correlation functions for the affine group and some of its subgroups. Algorithms are illustrated on underwater images to detect and identify specific objects (such as trawl traces) independently of their pose on the sea bottom.