翻訳と辞書 Words near each other ・ Spectral noise logging ・ Spectral phase interferometry for direct electric-field reconstruction ・ Spectral power distribution ・ Spectral printing ・ Spectral purity ・ Spectral pygmy chameleon ・ Spectral radius ・ Spectral regrowth ・ Spectral rendering ・ Spectral resolution ・ Spectral risk measure ・ Spectral Sciences Incorporated ・ Spectral sensitivity ・ Spectral sequence ・ Spectral set ・ Spectral shape analysis ・ Spectral signal-to-noise ratio ・ Spectral signature ・ Spectral slope ・ Spectral Sound ・ Spectral space ・ Spectral splatter ・ Spectral tarsier ・ Spectral test ・ Spectral theorem ・ Spectral theory ・ Spectral theory of compact operators ・ Spectral theory of ordinary differential equations ・ Spectral triple ・ Spectral Visions of Mental Warfare Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Spectral shape analysis ： ウィキペディア英語版 Spectral shape analysis Spectral shape analysis relies on the spectrum (eigenvalues and/or eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under isometries, it is well suited for the analysis or retrieval of non-rigid shapes, i.e. bendable objects such as humans, animals, plants, etc. == Laplace == The Laplace–Beltrami operator is involved in many important differential equations, such as the heat equation and the wave equation. It can be defined on a Riemannian manifold as the divergence of the gradient of a real-valued function ''f'': :$\backslash Delta\; f\; :=\; \backslash operatorname\backslash ;\; \backslash operatorname\; f.$ Its spectral components can be computed by solving the Helmholtz equation (or Laplacian eigenvalue problem): :$$ \Delta \phi_i + \lambda_i \phi_i = 0. \, The solutions are the eigenfunctions $\backslash phi\_i$ (modes) and corresponding eigenvalues $\backslash lambda\_i$, representing a diverging sequence of positive real numbers. The first eigenvalue is zero for closed domains or when using the Neumann boundary condition. For some shapes, the spectrum can be computed analytically (e.g. rectangle, flat torus, cylinder, disk or sphere). For the sphere, for example, the eigenfunctions are the spherical harmonics. The most important properties of the eigenvalues and eigenfunctions are that they are isometry invariants. In other words, if the shape is not stretched (e.g. a sheet of paper bent into the third dimension), the spectral values will not change. Bendable objects, like animals, plants and humans, can move into different body postures with only minimal stretching at the joints. The resulting shapes are called near-isometric and can be compared using spectral shape analysis. However, the isometric deformation of surfaces in 3D in the strict sense are rigid transformations. To characterize the actual deformation undergoing for the interest of nonrigid shape analysis, smooth deformations are introduced as an alternative family of deformation to isometry, where eigenvalues are allowed to perturb with finite error bounds.〔 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「Spectral shape analysis」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.