The talk will describe new results for this classical problem and outlines general principles for the extraction of invariant features from images (Haar integrals, Lie-Theory, Normalization techniques). The nonlinear transforms are able to map the object space of image representation into a canonical frame with invariants and geometrical parameters. Beside the mathematical definition the talk will concentrate on characterizing the properties of the nonlinear mappings with respect to completeness and possible ambiguities, disturbance behavior and computational complexity. We especially investigated Haar integrals for the extraction of invariants based on monomial and relational kernel functions.
Examples and applications will be given for problems in 2D and 3D, namely applications in content-based image and object retrieval and classification tasks in 2D and 3D (classification and retrieval of biological objects and structures).