Matching LBO eigenspace of non-rigid shapes via high order statistics
Matching LBO eigenspace of non-rigid shapes via high order statistics
复制标题
通过高阶统计匹配非刚性形状的 LBO 特征空间
作者：
A. Shtern;R. Kimmel
形状分析中的一个基本工具是将描述形状几何的黎曼流形虚嵌入到欧几里得空间中。已经提出了几种方法将等距形状嵌入到平坦域中，同时保持在流形上测量的距离。最近，人们已经注意到嵌入形状的Laplace-Beltrami算子的本征空间。Laplace-Beltrami特征空间保持扩散距离，并且在等距变换下不变。然而，Laplace-Beltrami本征函数计算独立的不同形状往往是相互不兼容的。涉及多个形状的应用，如逐点对应，如果它们各自的本征函数以某种方式匹配，将大大受益。在这里，我们介绍了一种统计方法匹配本征函数。我们把流形上特征函数的值看作随机变量的抽样，并试图匹配它们的多元分布。比较分布是间接进行的，使用高阶统计量。我们证明了低阶本征函数的排列和符号模糊性可以通过最小化它们的三阶矩之差来推断。反对称特征函数的符号模糊性可以通过利用特征函数的梯度与表面法线之间的等距不变关系来解决。我们目前的实验证明所提出的方法适用于特征点对应的成功。
A fundamental tool in shape analysis is the virtual embedding of the Riemannian manifold describing the geometry of a shape into Euclidean space. Several methods have been proposed to embed isometric shapes into flat domains, while preserving the distances measured on the manifold. Recently, attention has been given to embedding shapes into the eigenspace of the Laplace–Beltrami operator. The Laplace–Beltrami eigenspace preserves the diffusion distance and is invariant under isometric transformations. However, Laplace–Beltrami eigenfunctions computed independently for different shapes are often incompatible with each other. Applications involving multiple shapes, such as pointwise correspondence, would greatly benefit if their respective eigenfunctions were somehow matched. Here, we introduce a statistical approach for matching eigenfunctions. We consider the values of the eigenfunctions over the manifold as the sampling of random variables and try to match their multivariate distributions. Comparing distributions is done indirectly, using high order statistics. We show that the permutation and sign ambiguities of low order eigenfunctions can be inferred by minimizing the difference of their third order moments. The sign ambiguities of antisymmetric eigenfunctions can be resolved by exploiting isometric invariant relations between the gradients of the eigenfunctions and the surface normal. We present experiments demonstrating the success of the proposed method applied to feature point correspondence.
DOI：
10.1073/pnas.0500334102
发表时间：
2005-05-24
影响因子：
11.1
作者：
Coifman, RR;Lafon, S;Zucker, SW
通讯作者：
Zucker, SW
基于多尺度热核的体积形态特征。
DOI：
10.1007/978-3-319-24574-4_90
发表时间：
2015
期刊：
Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention
影响因子：
--
作者：
Wang,Gang;Wang,Yalin
通讯作者：
Wang,Yalin