  2-D complex Gabor filtering has found numerous applications in the fields of
computer vision and image processing. Especially, in some applications, it is
often needed to compute 2-D complex Gabor filter bank consisting of the 2-D
complex Gabor filtering outputs at multiple orientations and frequencies.
Although several approaches for fast 2-D complex Gabor filtering have been
proposed, they primarily focus on reducing the runtime of performing the 2-D
complex Gabor filtering once at specific orientation and frequency. To obtain
the 2-D complex Gabor filter bank output, existing methods are repeatedly
applied with respect to multiple orientations and frequencies. In this paper,
we propose a novel approach that efficiently computes the 2-D complex Gabor
filter bank by reducing the computational redundancy that arises when
performing the Gabor filtering at multiple orientations and frequencies. The
proposed method first decomposes the Gabor basis kernels to allow a fast
convolution with the Gaussian kernel in a separable manner. This enables
reducing the runtime of the 2-D complex Gabor filter bank by reusing
intermediate results of the 2-D complex Gabor filtering computed at a specific
orientation. Furthermore, we extend this idea into 2-D localized sliding
discrete Fourier transform (SDFT) using the Gaussian kernel in the DFT
computation, which lends a spatial localization ability as in the 2-D complex
Gabor filter. Experimental results demonstrate that our method runs faster than
state-of-the-arts methods for fast 2-D complex Gabor filtering, while
maintaining similar filtering quality.
