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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 Otsu's method ： ウィキペディア英語版 Otsu's method In computer vision and image processing, Otsu's method, named after , is used to automatically perform clustering-based image thresholding, or, the reduction of a graylevel image to a binary image. The algorithm assumes that the image contains two classes of pixels following bi-modal histogram (foreground pixels and background pixels), it then calculates the optimum threshold separating the two classes so that their combined spread (intra-class variance) is minimal, or equivalently (because the sum of pairwise squared distances is constant), so that their inter-class variance is maximal. Consequently, Otsu's method is roughly a one-dimensional, discrete analog of Fisher's Discriminant Analysis. The extension of the original method to multi-level thresholding is referred to as the Multi Otsu method. ==Method== In Otsu's method we exhaustively search for the threshold that minimizes the intra-class variance (the variance within the class), defined as a weighted sum of variances of the two classes: :$\backslash sigma^2\_w(t)=\backslash omega\_1(t)\backslash sigma^2\_1(t)+\backslash omega\_2(t)\backslash sigma^2\_2(t)$ Weights $\backslash omega\_i$ are the probabilities of the two classes separated by a threshold $t$ and $\backslash sigma^2\_\; i$ are variances of these classes. Otsu shows that minimizing the intra-class variance is the same as maximizing inter-class variance:〔 :$\backslash sigma^2\_b(t)=\backslash sigma^2-\backslash sigma^2\_w(t)=\backslash omega\_1(t)\backslash omega\_2(t)\backslash left()^2$ which is expressed in terms of class probabilities $\backslash omega\_i$ and class means $\backslash mu\_i$. The class probability $\backslash omega\_1(t)$ is computed from the histogram as $t$: :$\backslash omega\_1(t)=\backslash Sigma\_0^t\; p(i)$ while the class mean $\backslash mu\_1(t)$ is: :$\backslash mu\_1(t)=\backslash left(p(i)\backslash ,x(i)\backslash right)/\backslash omega\_1$ where $x(i)$ is the value at the center of the $i$th histogram bin. Similarly, you can compute $\backslash omega\_2(t)$ and $\backslash mu\_2$ on the right-hand side of the histogram for bins greater than $t$. The class probabilities and class means can be computed iteratively. This idea yields an effective algorithm. 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「Otsu's method」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.