Abstract
Volterra filters are constructed to recognize images independent of changes caused by a linear transformation group (e.g. rotation, scaling, etc.). Volterra filters are polynomial functions that can model analytic vector functions with arbitrary precision. The theory of invariant Volterra filters is developed for a general polynomial order; however, particular emphasis is given to quadratic filters. Quadratic filters are the lowest order Volterra filter that provide a non-linear response. This suggests a new approach to invariant pattern recognition based upon nearest neighbor classification with respect to an invariant manifold. Both theoretical and simulation results suggest that quadratic filters can provide invariant pattern recognition with high discrimination and robustness to noise.
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