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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gabor filter ： ウィキペディア英語版 Gabor filter In image processing, a Gabor filter, named after Dennis Gabor, is a linear filter used for edge detection. Frequency and orientation representations of Gabor filters are similar to those of the human visual system, and 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. Simple cells in the visual cortex of mammalian brains can be modeled by Gabor functions.〔J. G. Daugman. Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters. ''Journal of the Optical Society of America A'', 2(7):1160–1169, July 1985.〕 Thus, image analysis with Gabor filters is thought to be similar to perception in the human visual system. == Definition == 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 and the Fourier transform of the Gaussian function. The filter has a real and an imaginary component representing orthogonal directions.〔3D surface tracking and approximation using Gabor filters, Jesper Juul Henriksen, South Denmark University, March 28, 2007〕 The two components may be formed into a complex number or used individually. Complex :$g(x,y;\backslash lambda,\backslash theta,\backslash psi,\backslash sigma,\backslash gamma)\; =\; \backslash exp\backslash left(-\backslash frac\backslash right)\backslash exp\backslash left(i\backslash left(2\backslash pi\backslash frac+\backslash psi\backslash right)\backslash right)$ Real :$g(x,y;\backslash lambda,\backslash theta,\backslash psi,\backslash sigma,\backslash gamma)\; =\; \backslash exp\backslash left(-\backslash frac\backslash right)\backslash cos\backslash left(2\backslash pi\backslash frac+\backslash psi\backslash right)$ Imaginary :$g(x,y;\backslash lambda,\backslash theta,\backslash psi,\backslash sigma,\backslash gamma)\; =\; \backslash exp\backslash left(-\backslash frac\backslash right)\backslash sin\backslash left(2\backslash pi\backslash frac+\backslash psi\backslash right)$ where :$x\text{'}\; =\; x\; \backslash cos\backslash theta\; +\; y\; \backslash sin\backslash theta\backslash ,$ and :$y\text{'}\; =\; -x\; \backslash sin\backslash theta\; +\; y\; \backslash cos\backslash theta\backslash ,$ In this equation, $\backslash lambda$ represents the wavelength of the sinusoidal factor, $\backslash theta$ represents the orientation of the normal to the parallel stripes of a Gabor function, $\backslash psi$ is the phase offset, $\backslash sigma$ is the sigma/standard deviation of the Gaussian envelope and $\backslash gamma$ is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gabor filter」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.