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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 Kuwahara filter ： ウィキペディア英語版 Kuwahara filter The Kuwahara filter is a non-linear smoothing filter used in image processing for adaptive noise reduction. Most filters that are used for image smoothing are linear low-pass filters that effectively reduce noise but also blur out the edges. However the Kuwahara filter is able to apply smoothing on the image while preserving the edges. == The Kuwahara Operator == Suppose that $I(x,y)$ is a grey scale image and that we take a square window of size $2a+1$ centered around a point $(x,y)$ in the image. This square can be divided in to four smaller square regions $Q\_$ each of which will be 〔 :$$ Q_i (x,y) = \begin \left(x,x+a \right ) \times \left(y,y+a \right ) & \mboxi = 1\\ \left(x-a,x \right ) \times \left(y,y+a \right ) & \mboxi = 2\\ \left(x-a,x \right ) \times \left(y-a,y \right ) & \mboxi = 3\\ \left(x,x+a \right ) \times \left(y-a,y \right ) & \mboxi = 4\\ \end where $\backslash times$ is the cartesian product. It must be noted that pixels located on the borders between two regions belong to both regions so there is a slight overlap between subregions. The arithmetic mean $m\_i(x,y)$ and standard deviation $\backslash sigma\; \_i(x,y)$ of the four regions centered around a pixel (x,y) are calculated and used to determine the value of the central pixel. The output of the kuwahara filter $\backslash Phi(x,y)$ for any point $(x,y)$ is then given by $\backslash Phi(x,y)\; =\; \backslash begin$ m_1(x,y) & \mbox\sigma_1(x,y) = min_ \mbox \sigma_i(x,y) \\ m_2(x,y) & \mbox\sigma_2(x,y) = min_ \mbox \sigma_i(x,y) \\ m_3(x,y) & \mbox\sigma_3(x,y) = min_ \mbox \sigma_i(x,y) \\ m_4(x,y) & \mbox\sigma_4(x,y) = min_ \mbox \sigma_i(x,y) \\ \end This means that the central pixel will take the mean value of the area that is most homogenous. The location of the pixel in relation to an edge plays a great role in determining which region will have the greater standard deviation. If for example the pixel is located on a dark side of an edge it will most probably take the mean value of the dark region. On the other hand should the pixel be on the lighter side of an edge it will most probably take a light value. On the event that the pixel is located on the edge it will take the value of the more smooth, least textured region. The fact that the filter takes into account the homogeneity of the regions ensures that it will preserve the edges while using the mean creates the blurring effect. Similarly to the Median filter the Kuwahara filter uses a sliding window approach to access every pixel in the image. The size of the window is chosen in advance and may vary depending on the desired level of blur in the final image. Bigger windows typically result in the creation of more abstract images whereas small windows produce images that retain their detail. Typically windows are chose to be square with sides that have an odd number of pixels for symmetry. However, there are variations of the Kuwahara filter that use rectangular windows. Additionally, the subregions do not need to overlap or have the same size as long as they cover all of the window. 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「Kuwahara filter」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.