翻訳と辞書 Words near each other ・ Gabor Fabricius ・ Gabor filter ・ Gabor G. Gyukics ・ Gabor Hamza ・ Gabor Herman ・ Gabor Joo ・ Gabor Kasa ・ Gabor Maté (physician) ・ Gabor Medal ・ Gabor Peterdi ・ Gabor sisters ・ Gabor Steingart ・ Gabor Szabo Live ・ Gabor transform ・ Gabor Varga ・ Gabor wavelet ・ Gaborone ・ Gaborone City Council ・ Gaborone Dam ・ Gaborone Derby ・ Gaborone United S.C. ・ Gabor–Granger method ・ Gabor–Wigner transform ・ Gaboto ・ Gabourey Sidibe ・ Gabow's algorithm ・ Gabowe Grądy ・ Gaboxadol ・ Gaboń ・ Gaboń-Praczka Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gabor wavelet ： ウィキペディア英語版 Gabor wavelet Gabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet wavelets. They are also closely related to Gabor filters (see Gabor filter#Wavelet space). The important property of the wavelet is that it minimizes the product of its standard deviations in the time and frequency domain. Put another way, the uncertainty in information carried by this wavelet is minimized. However they have the downside of being non-orthogonal, so efficient decomposition into the basis is difficult. Since their inception, various applications have appeared, from image processing to analyzing neurons in the human visual system. == Minimal uncertainty property == The motivation for Gabor wavelets comes from finding some function $f(x)$ which minimizes its standard deviation in the time and frequency domains. More formally, the variance in the position domain is: :$(\backslash Delta\; x)^2\; =\; \backslash frac\; (x-\backslash mu)^2\; f(x)f^(x)\; \backslash ,dx\}\; f(x)f^(x)\; \backslash ,\; dx\}$ where $f^(x)$ is the complex conjugate of $f(x)$ and $\backslash mu$ is the arithmetic mean, defined as: :$\backslash mu\; =\; \backslash frac\; x\; f(x)f^(x)\; \backslash ,dx\}\; f(x)f^(x)\backslash ,dx\}$ The variance in the wave number domain is: :$(\backslash Delta\; k)^2\; =\; \backslash frac\; (k-k\_0)^2\; F(k)F^(k)\; \backslash ,\; dk\}\; F(k)F^(k)\; \backslash ,\; dk\}$ Where $k\_0$ is the arithmetic mean of the Fourier Transform of $f(x)$, $F(x)$: :$k\_0\; =\; \backslash frac\; k\; F(k)F^(k)\; \backslash ,dk\}\; F(k)F^(k)\; \backslash ,dk\}$ With these defined, the uncertainty is written as: :$(\backslash Delta\; x)(\backslash Delta\; k)$ This quantity has been shown to have a lower bound of $\backslash frac12$. The quantum mechanics view is to interpret $(\backslash Delta\; x)$ as the uncertainty in position and $\backslash hbar\; (\backslash Delta\; k)$ as uncertainty in momentum. A function $f(x)$ that has the lowest theoretically possible uncertainty bound is the Gabor Wavelet. 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 wavelet」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.