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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 Image derivatives ： ウィキペディア英語版 Image derivatives Image derivatives can be computed by using small convolution filters of size 2 x 2 or 3 x 3, such as the Laplacian, Sobel, Roberts and Prewitt operators.〔Pratt, W.K., 2007. Digital image processing (4th ed.). John Wiley & Sons, Inc. pp. 465–522〕 However, a larger mask will generally give a better approximation of the derivative and examples of such filters are Gaussian derivatives 〔H. Bouma, A. Vilanova, J.O. Bescós, B.M.T.H. Romeny, F.A. Gerritsen, Fast and accurate gaussian derivatives based on b-splines, in: Proceedings of the 1st International Conference on Scale Space and Variational Methods in Computer Vision, Springer-Verlag, Berlin, Heidelberg, 2007, pp. 406–417.〕 and Gabor filters.〔P. Moreno, A. Bernardino, J. Santos-Victor, Improving the sift descriptor with smooth derivative filters, Pattern Recognition Letters 30 (2009) 18–26.〕 Sometimes high frequency noise needs to be removed and this can be incorporated in the filter so that the Gaussian kernel will act as a band pass filter.〔J.J. Koenderink, A.J. van Doorn, Generic neighborhood operators, IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 597–605.〕 The use of Gabor filters 〔D. Gabor, Theory of communication, J. Inst. Electr. Eng. 93 (1946) 429–457.〕 in image processing has been motivated by some of its similarities to the perception in the human visual system.〔J.G. Daugman, Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression, IEEE Trans. Acoust. Speech Signal Process. 36 (1988) 1169–1179.〕 The pixel value is computed as a convolution :$$ p'_u=\mathbf \ast G where $\backslash mathbf$ is the derivative kernel and $G$ is the pixel values in a region of the image and $\backslash ast$ is the operator that performs the convolution. == Sobel Derivatives == The derivative kernels, known as the Sobel operator are defined as follows, for the $u$ and $v$ directions respectively: :$$ p'_u = \begin -1 & -2 & -1 \\ 0 & 0 & 0 \\ +1 & +2 & +1 \end * \mathbf \quad \mbox \quad p'_v= \begin -1 & 0 & +1 \\ \ \ -2 & \ \ 0 & \ \ +2 \\ -1 & 0 & +1 \end * \mathbf where $$ * here denotes the 2-dimensional convolution operation. This operator is separable and can be decomposed as the products of an interpolation and a differentiation kernel, so that, $p\text{'}\_v$, for an example can be written as :$$ \begin -1 & 0 & +1 \\ -2 & 0 & +2 \\ -1 & 0 & +1 \end = \begin 1\\ 2\\ 1 \end \begin -1 & 0 & +1 \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「Image derivatives」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.