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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 Mumford–Shah functional ： ウィキペディア英語版 Mumford–Shah functional The Mumford–Shah functional is a functional that is used to establish an optimality criterion for segmenting an image into sub-regions. An image is modeled as a piecewise-smooth function. The functional penalizes the distance between the model and the input image, the lack of smoothness of the model within the sub-regions, and the length of the boundaries of the sub-regions. By minimizing the functional one may compute the best image segmentation. The functional was proposed by mathematicians David Mumford and Jayant Shah in 1989.〔.〕 == Definition of the Mumford–Shah functional == Consider an image ''I'' with a domain of definition ''D'', call ''J'' the image's model, and call ''B'' the boundaries that are associated with the model: the Mumford–Shah functional ''E''(''J'',''B'' ) is defined as :$$ E() = C \int (I(\vec x) - J(\vec x))^2 d\vec x + A \int _ \vec \nabla J(\vec x) \cdot \vec \nabla J(\vec x) d \vec x + B \int _B ds Optimization of the functional may be achieved by approximating it with another functional, as proposed by Ambrosio and Tortorelli.〔See .〕 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「Mumford–Shah functional」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.