We describe a fast algorithm for Gabor filtering, specially designed for multi-scale image representations. Our proposal is based on three facts: first, Gabor functions can be decomposed in gaussian convolutions and complex multiplications which allows the replacement of Gabor filters by more efficient gaussian filters; second, isotropic gaussian filtering is implemented by separable 1D horizontal/vertical convolutions and permits a fast implementation of the non-separable zero-mean Gabor kernel; third, short FIR filters and the a trous algorithm are utilized to build a recursive multi-scale decomposition, which saves important computational resources. Our proposal reduces to about one half the number of operations with respect to state-of-the-art approaches.
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