Filtering with Anisotropic 3D Gabor Filter Bank Efficiently Computed with 1D Convolutions without Interpolation

V. Ulman (Czech Republic)

Keywords

Gabor filtering, bank filtering, filter design.

Abstract

We present an efficient spatial computational scheme de signed for the convolution with a bank of 3D Gabor filters. The scheme covers most of the state-of-the-art principles. In particular, we start the paper with the staged approach to computing convolution with Gabor filter. It consists of three stages: modulation, IIR Gaussian filtering and demodulation. Two realizations of the IIR Gaussian filtering are considered and discussed: the method of Lampert and Wirjadi, which is efficient in terms of number of multiplications and additions per pixel, and the extension of the method of Lam and Shi. Both methods allow for a convolution of arbitrarily-oriented anisotropic Gaussian. In the proposed scheme the latter method was preferred, inspite of its inherent redundancy. The reason for this choice was its position invariance and higher accuracy. The higher number of operations per pixel is compensated for by applying efficient convolutions with up to four 3D Gabor filters simultaneously. The formal derivation and justification of new constraints as well as experimental results are presented.

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