A system that can be used as a feature extraction unit in a low-level pattern recognition system is described. It is assumed that such a system acts as a linear mapping between the pattern space and the feature space. It can therefore be completely described by a number of filter kernels. These filter kernels are usually constructed by the designer of the system. In the approach to filter design described in this paper, the filter kernels are not created manually. Instead, the authors feed the system during the training period with a representative selection of the patterns that they want to recognize. During the training phase, a learning rule (based on a quality function) is used to update the current form of the filter functions. After the training period, there is a filter system that is is optimally adapted to the recognition of this particular set of patterns of interest. In the first part of the paper, some results from work on group theoretical filter design as described. Within this framework, optimal filter functions can be constructed for a large class of pattern recognition problems. These analytical solutions can then be compared with the filter functions learned by our system. The overall structure of the system and several variations of the basic model are described. A quality function is introduced, and a learning filter system is described as an optimization process. This leads to update rules that are significantly different from other, similar, systems investigated previously. Finally, the performance of the system with the help of several examples is demonstrated.
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