Lie transformation groups, integral transforms, and invariant pattern recognition

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Abstract
This paper considers image representations based on integral transforms which are invariant under certain transformations, while preserving the uniqueness of the encoding. Necessary and sufficient conditions are determined for the existence of such representations and a method to determine the kernels of the related integral transforms is presented. Finally, the possible relevance of such considerations for the understanding of invariant recognition systems in biological vision is also explored.

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