Matrix-valued kernels for shape deformation analysis
Matrix-valued kernels for shape deformation analysis
复制标题
用于形状变形分析的矩阵值核
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J. Glaunès
中科院分区：
文献类型：
--
作者：
M. Micheli;J. Glaunès
本文的主要目的是对再生核Hilbert空间（RKHS）的非标量核进行系统的研究和分类，并用于分析形状空间的形变.在介绍了矩阵值核及其相关的微分性质之后，我们广泛地探索了那些我们称为TRI核的核，这些核在相应的向量场的希尔伯特空间上诱导了一个度量，该度量是平移和旋转不变的。这些都是在傅立叶域，其中的表征RKHS的卷曲自由和发散的矢量场是特别自然的一种有效的方式进行分析。一个简单的技术，用于构建通用的矩阵值核的标量核。我们伴随着几个例子的理论的阐述，并提供数值结果，显示不同的选择TRI内核标记的地标点的流形上引起的动态。
The main purpose of this paper is providing a systematic study and classification of non-scalar kernels for Reproducing Kernel Hilbert Spaces (RKHS), to be used in the analysis of deformation in shape spaces endowed with metrics induced by the action of groups of diffeomorphisms. After providing an introduction to matrix-valued kernels and their relevant differential properties, we explore extensively those, that we call TRI kernels, that induce a metric on the corresponding Hilbert spaces of vector fields that is both translation- and rotation-invariant. These are analyzed in an effective manner in the Fourier domain, where the characterization of RKHS of curl-free and divergence-free vector fields is particularly natural. A simple technique for constructing generic matrix-valued kernels from scalar kernels is also developed. We accompany the exposition of the theory with several examples, and provide numerical results that show the dynamics induced by different choices of TRI kernels on the manifold of labeled landmark points.