Constructing invariant features by averaging techniques

The paper presents algorithms for the construction of features which are invariant with respect to a given transformation group. The methods are based on integral calculus and are applicable to parametric groups (Lie groups) and finite groups as well. To illustrate the concepts the author discusses in detail how to construct invariant features for the general linear group which is of importance in computer vision applications. The author briefly mentions how to combine the algorithms with Hilbert space techniques for the description of continuous signals. Finally the author applies the presented methods to establish the existence of complete feature sets for arbitrary compact groups.