IEEE Trans Image Process. 2018 Apr;27(4):1713-1722. doi: 10.1109/TIP.2017.2783621.
2D 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 2D complex Gabor filter bank consisting of filtering outputs at multiple orientations and frequencies. Although several approaches for fast Gabor filtering have been proposed, they focus primarily on reducing the runtime for performing filtering once at specific orientation and frequency. To obtain the Gabor filter bank, the existing methods are repeatedly applied with respect to multiple orientations and frequencies. In this paper, we propose a novel approach that efficiently computes the 2D complex Gabor filter bank by reducing the computational redundancy that arises when performing filtering at multiple orientations and frequencies. The proposed method first decomposes the Gabor kernel to allow a fast convolution with the Gaussian kernel in a separable manner. This enables reducing the runtime of the Gabor filter bank by reusing intermediate results computed at a specific orientation. By extending this idea, we also propose a fast approach for 2D localized sliding discrete Fourier transform that uses the Gaussian kernel in order to lend spatial localization ability as in the Gabor filter. Experimental results demonstrate that the proposed method runs faster than the state-of-the-art methods, while maintaining similar filtering quality.
二维复 Gabor 滤波在计算机视觉和图像处理领域有广泛的应用。特别是，在某些应用中，经常需要计算由多个方向和频率的滤波输出组成的二维复 Gabor 滤波器组。虽然已经提出了几种快速 Gabor 滤波方法，但它们主要集中在减少特定方向和频率下一次滤波的运行时间。为了获得 Gabor 滤波器组，现有的方法需要针对多个方向和频率进行重复应用。本文提出了一种新的方法，可以通过减少在多个方向和频率上进行滤波时产生的计算冗余来有效地计算二维复 Gabor 滤波器组。该方法首先将 Gabor 核分解，以允许以可分离的方式与高斯核进行快速卷积。这使得通过在特定方向上重新使用计算的中间结果来减少 Gabor 滤波器组的运行时间。通过扩展这个想法，我们还提出了一种使用高斯核的二维局部滑动离散傅里叶变换的快速方法，以便在 Gabor 滤波器中赋予空间局部化能力。实验结果表明，所提出的方法比现有的方法运行速度更快，同时保持类似的滤波质量。
