Gabor filter与Gabor transform

https://en.wikipedia.org/wiki/G%C3%A1bor

Gabor filter：a linear filter used in image processing一种线性滤波器（与卷积的区别？）

In image processing, a Gabor filter, named after Dennis Gabor, is a linear filter used for texture analysis, which means that it basically analyzes whether there are any specific frequency content in the image in specific directions in a localized region around the point or region of analysis. Frequency and orientation representations of Gabor filters are claimed by many contemporary vision scientists to be similar to those of the human visual system, though there is no empirical evidence and no functional rationale to support the idea. They have been found to be particularly appropriate for texture representation and discrimination. In the spatial domain, a 2D Gabor filter is a Gaussian kernel function modulated by a sinusoidal plane wave.

在图像处理中，以Dennis Gabor命名的Gabor滤波器是用于纹理分析的线性滤波器，这意味着它基本上分析图像在分析点或分析区域周围的局部区域中，在特定方向上是否存在任何特定频率内容。许多当代视觉科学家声称Gabor滤波器的频率和方向表示与人类视觉系统的频率和方向表示相似，尽管没有经验证据和功能原理来支持这一观点。他们已被发现是特别适合纹理表示和辨别。在空间域中，二维Gabor滤波器是由正弦平面波调制的高斯核函数。

Gabor transform：

The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform. It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. The function to be transformed is first multiplied by a Gaussian function, which can be regarded as a window function, and the resulting function is then transformed with a Fourier transform to derive the time-frequency analysis.[1] The window function means that the signal near the time being analyzed will have higher weight. The Gabor transform of a signal x(t) is defined by this formula: