相关论文: Computing Shape DNA using the closest point method

In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate…

In this work, we introduce a novel local pairwise descriptor and then develop a simple, effective iterative method to solve the resulting quadratic assignment through sparsity control for shape correspondence between two approximate…

Computation of the trace of a matrix function plays an important role in many scientific computing applications, including applications in machine learning, computational physics (e.g., lattice quantum chromodynamics), network analysis and…

The Laplace-Beltrami operator has established itself in the field of non-rigid shape analysis due to its many useful properties such as being invariant under isometric transformation, having a countable eigensystem forming an orthornormal…

The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, this eigenvalue problem for a partial differential operator is…

We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…

Clustering is a difficult and widely-studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g. Euclidean distance) to…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

The existing object classification techniques based on descriptive features rely on object alignment to compute the similarity of objects for classification. This paper replaces the necessity of object alignment through sorting of feature.…

Extended target/object tracking (ETT) problem involves tracking objects which potentially generate multiple measurements at a single sensor scan. State-of-the-art ETT algorithms can efficiently exploit the available information in these…

Compressed manifold modes are locally supported analogues of eigenfunctions of the Laplace-Beltrami operator of a manifold. In this paper we describe an algorithm for the calculation of modes for discrete manifolds that, in experiments,…

Diffusion maps is a manifold learning algorithm widely used for dimensionality reduction. Using a sample from a distribution, it approximates the eigenvalues and eigenfunctions of associated Laplace-Beltrami operators. Theoretical bounds on…

We develop a finite element method for the Laplace-Beltrami operator on a surface with boundary and nonhomogeneous Dirichlet boundary conditions. The method is based on a triangulation of the surface and the boundary conditions are enforced…

The Iterative Closest Point (ICP) algorithm is one of the most important algorithms for geometric alignment of three-dimensional surface registration, which is frequently used in computer vision tasks, including the Simultaneous…

We describe a faster and more accurate algorithm for computing the statistical mechanics of DNA denaturation according to the Poland-Scheraga type. Nearest neighbor thermodynamics is included in a complete and general way. The algorithm…

Evaluating the similarity of non-rigid shapes with significant partiality is a fundamental task in numerous computer vision applications. Here, we propose a novel axiomatic method to match similar regions across shapes. Matching similar…

This paper deals with the numerical optimization of the first three eigenvalues of the Laplace-Beltrami operator of domain in the Euclidean sphere in $\mathbb{R}^3$ with Neumann boundary conditions. We address two approaches : the first one…

In this paper we develop proximal methods for statistical learning. Proximal point algorithms are useful in statistics and machine learning for obtaining optimization solutions for composite functions. Our approach exploits closed-form…

To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. The objective of this research work is to extend this method…

The current capacity of computers makes it possible to perform simulations of small systems with portable, explicit-solvent potentials achieving high degree of accuracy. However, simplified models must be employed to exploit the behaviour…