Fast Computation of the Gabor Wavelet Transform

The Gabor filter is a valuable tool in computer vision, however, its high computational load precludes its use in many applications. This paper presents a novel method for approximating Gabor wavelets with a function that can be convolved more efficiently in the spatial domain. The method extends the well known separable nature of the Gabor filter, and demonstrates a means for reducing the computation required when determining the separable 1D convolutions. Experimental results are presented showing the performance of the new method. It is demonstrated that the new method provides an accurate approximation to the convolution with the 1D separated wavelet component of the Gabor kernel, while requiring only 60% of the computation normally required for this operation.