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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 Thin plate spline ： ウィキペディア英語版 Thin plate spline Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. They were introduced to geometric design by Duchon. 〔J. Duchon, 1976, Splines minimizing rotation invariant semi-norms in Sobolev spaces. pp 85–100, In: Constructive Theory of Functions of Several Variables, Oberwolfach 1976, W. Schempp and K. Zeller, eds., Lecture Notes in Math., Vol. 571, Springer, Berlin, 1977〕 ==Physical analogy== The name ''thin plate spline'' refers to a physical analogy involving the bending of a thin sheet of metal. Just as the metal has rigidity, the TPS fit resists bending also, implying a penalty involving the smoothness of the fitted surface. In the physical setting, the deflection is in the $z$ direction, orthogonal to the plane. In order to apply this idea to the problem of coordinate transformation, one interprets the lifting of the plate as a displacement of the $x$ or $y$ coordinates within the plane. In 2D cases, given a set of $K$ corresponding points, the TPS warp is described by $2(K+3)$ parameters which include 6 global affine motion parameters and $2K$ coefficients for correspondences of the control points. These parameters are computed by solving a linear system, in other words, TPS has closed-form solution. 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「Thin plate spline」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.