Invariants for 2d and 3d Pattern Recognition Problems

 

By Hans Burkhardt

(Professor, Albert-Ludwigs-University, Germany)

Review by:

Jean-Pierre Salmon

LORIA, France

 

New results for a classical problem

Professor Burkhardt presented general principles for the extraction of invariant features from images and described new results obtained. The aim is to classify images independently of the current position and orientation of the pattern to recognize.

 

Burkhardt began his talk by showing the drawbacks (for computation time, among others) of comparing a measured pattern in all possible locations against the prototypes. The solution proposed is to extract position-invariant and intrinsic features and to classify the objects in the feature space. Mathematically speaking, patterns form an equivalence class with respect to a geometric coordinate transform describing the motion. Invariant transforms are able to map such equivalence classes into one point of an appropriate feature space.

 

Burkhardt used Haar integrals, Lie-Theory and normalization techniques to extract the invariant features. He especially investigated Haar Integrals for the extraction of invariants based on monomial and relational kernel functions. The nonlinear transforms are able to map the object space of image representation into a canonical frame with invariants and geometrical parameters. Integration over the transformation group is based on Haar Integrals. The Haar Integrals are estimated by Monte-Carlo Methods to reduce the complexity (sublinear or even constant complexity).

 

Burkhardt explained the advantages of this method: 1)robustness against topological deformations, 2) robustness to scaling by using multi-scale kernels, 3) using functions of local support allows the recognition of articulated objects, 4) additivity in the Haar Integral for separate data regions allows the recognition of two objects in one scene without segmentation.

 

Finally, he showed that this method works on numerous problems in 2D and 3D through examples and applications, namely applications in content-based image and object retrieval and classification tasks (classification and retrieval of biological objects and structures).

 

More information on Burkhardt’s work can be found at, http://lmb.informatik.uni-freiburg.de/

Example from image retrieval system using invariant features.