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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 Matching distance ： ウィキペディア英語版 Matching distance In mathematics, the matching distance〔Michele d'Amico, Patrizio Frosini, Claudia Landi, ''Using matching distance in Size Theory: a survey'', International Journal of Imaging Systems and Technology, 16(5):154–161, 2006.〕〔Michele d'Amico, Patrizio Frosini, Claudia Landi, ''Natural pseudo-distance and optimal matching between reduced size functions'', Acta Applicandae Mathematicae, 109(2):527-554, 2010.〕 is a metric on the space of size functions. The core of the definition of matching distance is the observation that the information contained in a size function can be combinatorially stored in a formal series of lines and points of the plane, called respectively ''cornerlines'' and ''cornerpoints''. Given two size functions $\backslash ell\_1$ and $\backslash ell\_2$, let $C\_1$ (resp. $C\_2$) be the multiset of all cornerpoints and cornerlines for $\backslash ell\_1$ (resp. $\backslash ell\_2$) counted with their multiplicities, augmented by adding a countable infinity of points of the diagonal $\backslash$. The ''matching distance'' between $\backslash ell\_1$ and $\backslash ell\_2$ is given by $d\_\backslash text(\backslash ell\_1,\; \backslash ell\_2)=\backslash min\_\backslash sigma\backslash max\_\backslash delta\; (p,\backslash sigma(p))$ where $\backslash sigma$ varies among all the bijections between $C\_1$ and $C\_2$ and : $\backslash delta\backslash left((x,y),(x\text{'},y\text{'})\backslash right)=\backslash min\backslash left\backslash ,\backslash frac\backslash right\backslash \}\backslash right\backslash \}.$ Roughly speaking, the matching distance $d\_\backslash text$ between two size functions is the minimum, over all the matchings between the cornerpoints of the two size functions, of the maximum of the $L\_\backslash infty$-distances between two matched cornerpoints. Since two size functions can have a different number of cornerpoints, these can be also matched to points of the diagonal $\backslash Delta$. Moreover, the definition of $\backslash delta$ implies that matching two points of the diagonal has no cost. ==References== 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「Matching distance」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.