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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 Size function ： ウィキペディア英語版 Size function Size functions are shape descriptors, in a geometrical/topological sense. They are functions from the half-plane ==Formal definition== In size theory, the size function $\backslash ell\_:\backslash Delta^+=\backslash \backslash to\; \backslash mathbb$ associated with the size pair $(M,\backslash varphi:M\backslash to\; \backslash mathbb)$ is defined in the following way. For every $(x,y)\backslash in\; \backslash Delta^+$, $\backslash ell\_(x,y)$ is equal to the number of connected components of the set $\backslash$ that contain at least one point at which the measuring function (a continuous function from a topological space $M\backslash$ to $\backslash mathbb^k\backslash$ 〔Patrizio Frosini and Claudia Landi, ''Size Theory as a Topological Tool for Computer Vision'', Pattern Recognition And Image Analysis, 9(4):596–603, 1999.〕 〔Patrizio Frosini and Michele Mulazzani, ''Size homotopy groups for computation of natural size distances'', Bulletin of the Belgian Mathematical Society, 6:455–464 1999.〕) $\backslash varphi$ takes a value smaller than or equal to $x\backslash$ .〔Michele d'Amico, Patrizio Frosini and Claudia Landi, ''Using matching distance in Size Theory: a survey'', International Journal of Imaging Systems and Technology, 16(5):154–161, 2006.〕 The concept of size function can be easily extended to the case of a measuring function $\backslash varphi:M\backslash to\; \backslash mathbb^k$, where $\backslash mathbb^k$ is endowed with the usual partial order .〔Silvia Biasotti, Andrea Cerri, Patrizio Frosini, Claudia Landi, ''Multidimensional size functions for shape comparison'', Journal of Mathematical Imaging and Vision 32:161–179, 2008.〕 A survey about size functions (and size theory) can be found in .〔Silvia Biasotti, Leila De Floriani, Bianca Falcidieno, Patrizio Frosini, Daniela Giorgi, Claudia Landi, Laura Papaleo, Michela Spagnuolo, ''Describing shapes by geometrical-topological properties of real functions'' ACM Computing Surveys, vol. 40 (2008), n. 4, 12:1–12:87.〕 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「Size function」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.