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The purpose of this paper is to give a self-contained proof that a complete manifold with more than one end never supports an L-q,L-p-Sobolev inequality (2
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...
A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...
Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equation ...
Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we propose ShapeNet, a generalization of the popular convolutional neural ...
Fluid bridges are ubiquitous soft structures of finite size that conform to and link the surfaces of neighboring objects. Fluid joints, the specific type of fluid bridge with at least one extremity constrained laterally, display even more pronounced reacti ...
We consider total variation (TV) minimization for manifold-valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with l(p) -type data terms in the manifold case. These algorithms are ba ...
We propose a segmentation method based on the geometric representation of images as two-dimensional manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set ...
Institute of Electrical and Electronics Engineers2014
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...
