翻訳と辞書 Words near each other ・ Hermite ring ・ Hermite spline ・ Hermite's cotangent identity ・ Hermite's identity ・ Hermite's problem ・ Hermite–Hadamard inequality ・ Hermite–Minkowski theorem ・ Hermitian adjoint ・ Hermitian connection ・ Hermitian function ・ Hermitian hat wavelet ・ Hermitian manifold ・ Hermitian matrix ・ Hermitian symmetric space ・ Hermitian variety ・ Hermitian wavelet ・ Hermits of Saint William ・ Hermits of St. John the Baptist ・ Hermits of the Most Blessed Virgin Mary of Mount Carmel ・ Hermitude ・ Hermival-les-Vaux ・ Hermle ・ Hermle AG ・ Hermle Clocks ・ Hermleigh Independent School District ・ Hermleigh, Texas ・ Hermlin ・ Hermocrates ・ Hermocrates (dialogue) ・ Hermod (ship) 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 Hermitian wavelet ： ウィキペディア英語版 Hermitian wavelet Hermitian wavelets are a family of continuous wavelets, used in the continuous wavelet transform. The $n^\backslash textrm$ Hermitian wavelet is defined as the $n^\backslash textrm$ derivative of a Gaussian distribution: $\backslash Psi\_(t)=(2n)^\}c\_H\_\backslash left(\backslash fract^\}$ where $H\_\backslash left(\backslash right)$ denotes the $n^\backslash textrm$ Hermite polynomial. The normalisation coefficient $c\_$ is given by: $c\_\; =\; \backslash left(n^-n\}\backslash Gamma(n+\backslash frac)\backslash right)^\}\; =\; \backslash left(n^-n\}\backslash sqrt2^(2n-1)!!\backslash right)^\}\backslash quad\; n\backslash in\backslash mathbb.$ The prefactor $C\_$ in the resolution of the identity of the continuous wavelet transform for this wavelet is given by: $C\_=\backslash frac$ i.e. Hermitian wavelets are admissible for all positive $n$. In computer vision and image processing, Gaussian derivative operators of different orders are frequently used as a basis for expressing various types of visual operations; see scale space and N-jet. Examples of Hermitian wavelets: Starting from a Gaussian function with $\backslash mu=0,\; \backslash sigma=1$: $f(t)\; =\; \backslash pi^e^$ the first 3 derivatives read :$\backslash begin$ f'(t) & = -\pi^te^ \\ f''(t) & = \pi^(t^2 - 1)e^\\ f^(t) & = \pi^(3t - t^3)e^ \end and their $L^2$ norms $||f\text{'}||=\backslash sqrt/2,\; ||f\text{'}\text{'}||=\backslash sqrt/2,\; ||f^||=\; \backslash sqrt/4$ So the wavelets which are the negative normalized derivatives are: :$\backslash begin$ \Psi_(t) &= \sqrt\pi^te^\\ \Psi_(t) &=\frac\sqrt\pi^(1-t^2)e^\\ \Psi_(t) &= \frac\sqrt\pi^(t^3 - 3t)e^ \end 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「Hermitian 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.