Gabor filter

In , a Gabor filter, named after Dennis Gabor, who first proposed it as a 1D filter. The Gabor filter was first generalized to 2D by Gösta Granlund, by adding a reference direction. The Gabor filter is a linear filter used for texture analysis, which essentially means that it analyzes whether there is 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. 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 (see Gabor transform). Some authors claim that simple cells in the visual cortex of mammalian brains can be modeled by Gabor functions. Thus, with Gabor filters is thought by some to be similar to perception in the human visual system. Its impulse response is defined by a sinusoidal wave (a plane wave for 2D Gabor filters) multiplied by a Gaussian function. Because of the multiplication-convolution property (Convolution theorem), the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function (sinusoidal function) and the Fourier transform of the Gaussian function. The filter has a real and an imaginary component representing orthogonal directions. The two components may be formed into a complex number or used individually. Complex Real Imaginary where and . In this equation, represents the wavelength of the sinusoidal factor, represents the orientation of the normal to the parallel stripes of a Gabor function, is the phase offset, is the sigma/standard deviation of the Gaussian envelope and is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function. Gabor filters are directly related to Gabor wavelets, since they can be designed for a number of dilations and rotations.