翻訳と辞書 Words near each other ・ Anisotenes uniformis ・ Anisotes ・ Anisotes diversifolius ・ Anisothermal plasma ・ Anisothrix ・ Anisothrix (moth) ・ Anisothrix adustalis ・ Anisothrix agamalis ・ Anisothrix grenadensis ・ Anisotoma ・ Anisotome ・ Anisotome latifolia ・ Anisotremus ・ Anisotremus virginicus ・ Anisotropic conductive film ・ Anisotropic diffusion ・ Anisotropic filtering ・ Anisotropic Network Model ・ Anisotropy ・ Anisotropy energy ・ Anisotyma soteri ・ Anisoyl chloride ・ Anissa ・ Anissa Abi-Dargham ・ Anissa Blondin ・ Anissa Helou ・ Anissa Jones ・ Anissa Kate ・ Anissa Khelfaoui ・ Anissa Tann 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 Anisotropic diffusion ： ウィキペディア英語版 Anisotropic diffusion In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image.〔〔〔 Anisotropic diffusion resembles the process that creates a scale space, where an image generates a parameterized family of successively more and more blurred images based on a diffusion process. Each of the resulting images in this family are given as a convolution between the image and a 2D isotropic Gaussian filter, where the width of the filter increases with the parameter. This diffusion process is a ''linear'' and ''space-invariant'' transformation of the original image. Anisotropic diffusion is a generalization of this diffusion process: it produces a family of parameterized images, but each resulting image is a combination between the original image and a filter that depends on the local content of the original image. As a consequence, anisotropic diffusion is a ''non-linear'' and ''space-variant'' transformation of the original image. In its original formulation, presented by Perona and Malik in 1987,〔 the space-variant filter is in fact isotropic but depends on the image content such that it approximates an impulse function close to edges and other structures that should be preserved in the image over the different levels of the resulting scale space. This formulation was referred to as ''anisotropic diffusion'' by Perona and Malik even though the locally adapted filter is isotropic, but it has also been referred to as ''inhomogeneous and nonlinear diffusion''〔 or ''Perona-Malik diffusion''〔 by other authors. A more general formulation allows the locally adapted filter to be truly anisotropic close to linear structures such as edges or lines: it has an orientation given by the structure such that it is elongated along the structure and narrow across. Such methods are referred to as ''shape-adapted smoothing''〔〔 or ''coherence enhancing diffusion''.〔 As a consequence, the resulting images preserve linear structures while at the same time smoothing is made along these structures. Both these cases can be described by a generalization of the usual diffusion equation where the diffusion coefficient, instead of being a constant scalar, is a function of image position and assumes a matrix (or tensor) value (see structure tensor). Although the resulting family of images can be described as a combination between the original image and space-variant filters, the locally adapted filter and its combination with the image do not have to be realized in practice. Anisotropic diffusion is normally implemented by means of an approximation of the generalized diffusion equation: each new image in the family is computed by applying this equation to the previous image. Consequently, anisotropic diffusion is an iterative process where a relatively simple set of computation are used to compute each successive image in the family and this process is continued until a sufficient degree of smoothing is obtained. ==Formal definition== Formally, let $\backslash Omega\; \backslash subset\; \backslash mathbb^2$ denote a subset of the plane and $I(\backslash cdot,t):\; \backslash Omega\; \backslash rightarrow\; \backslash mathbb$ be a family of gray scale images, then anisotropic diffusion is defined as : $\backslash frac\; =\; \backslash mathrm\; \backslash left(\; c(x,y,t)\; \backslash nabla\; I\; \backslash right)=\; \backslash nabla\; c\; \backslash cdot\; \backslash nabla\; I\; +\; c(x,y,t)\; \backslash Delta\; I$ where $\backslash Delta$ denotes the Laplacian, $\backslash nabla$ denotes the gradient, $\backslash mathrm(\backslash dots)$ is the divergence operator and $c(x,y,t)$ is the diffusion coefficient. $c(x,y,t)$ controls the rate of diffusion and is usually chosen as a function of the image gradient so as to preserve edges in the image. Pietro Perona and Jitendra Malik pioneered the idea of anisotropic diffusion in 1990 and proposed two functions for the diffusion coefficient: : $c\backslash left(\backslash |\backslash nabla\; I\backslash |\backslash right)\; =\; e^$ and : $c\backslash left(\backslash |\; \backslash nabla\; I\backslash |\; \backslash right)\; =\; \backslash frac\backslash right)^2\}$ the constant K controls the sensitivity to edges and is usually chosen experimentally or as a function of the noise in the image. 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「Anisotropic diffusion」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.