Optimally Rotation-Equivariant Directional Derivative Kernels

H. Farid and E.P. Simoncelli

Computer Analysis of Images and Patterns (CAIP), Kiel, Germany, 1997

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We describe a framework for the design of directional derivative kernels for two-dimensional discrete signals in which we optimize a measure of rotation-equivariance in the Fourier domain. The formulation is applicable to first-order and higher-order derivatives. We design a set of compact, separable, linear-phase derivative kernels of different orders and demonstrate their accuracy.