Fast adaptive calculation of invariant

The paper presents algorithms for the fast adaptive calculation of invariant features. These are pattern characteristics that remain unchanged under the action of a transformation group. First it is explained how to construct such features by integrating complex valued functions over the transformation group. Motivated by this technique we devise algorithms for adaptively calculating invariant features especially suited for a given application. The basic tool is a new network structure with adaptable nodes allowing the fast calculation of an invariant feature with the computational complexity of O(N) (N the size of the input data). The algorithms have been implemented and tested both on real and synthetic data. By an experimental comparison with other techniques for calculating invariants we elucidate the abilities of our adaptive algorithms.