Boundary Treatment for Young-van Vliet Recursive Zero-Mean Gabor Filtering

Abstract

This paper deals with convolution setting at boundary regions for 1D convolution computed during recursive Gaussian and Gabor filtering as well as staged Gabor filtering computed more efficiently as modulation, recursive Gaussian, and demodulation. These are established fast approximations to their filters. Until recently, all the three applications of recursive filters suffered from distortions near boundary as a result of inappropriate boundary treatment. The extension of input data with constant border value is presumed. We review a recently suggested setting for recursive Gaussian and Gabor filtering. Then, a new convolution setting for the more efficient staged Gabor filtering is presented. We also offer a formula to compute the scale coefficient, using which a zero-mean Gabor filter can be obtained from either recursive or staged Gabor filter.

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