相关论文: Shape Partitioning via L$_p$ Compressed Modes

This work develops an algorithm for PDE-constrained shape optimization based on Lipschitz transformations. Building on previous work in this field, the $p$-Laplace operator is utilized to approximate a descent method for Lipschitz shapes.…

In this paper we consider general l0-norm minimization problems, that is, the problems with l0-norm appearing in either objective function or constraint. In particular, we first reformulate the l0-norm constrained problem as an equivalent…

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization, which is of great importance in many scientific areas such as image and signal processing, medical…

In this paper, we propose compactly supported radial basis functions for solving some well- known classes of astrophysics problems categorized as non-linear singular initial ordinary dif- ferential equations on a semi-infinite domain. To…

In this paper, we focus on a class of constrained nonlinear optimization problems (NLP), where some of its equality constraints define a closed embedded submanifold $\mathcal{M}$ in $\mathbb{R}^n$. Although NLP can be solved directly by…

This paper proposes an improved quasi-Newton penalty decomposition algorithm for the minimization of continuously differentiable functions, possibly nonconvex, over sparse symmetric sets. The method solves a sequence of penalty subproblems…

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…

Non-isometric shape correspondence remains a fundamental challenge in computer vision. Traditional methods using Laplace-Beltrami operator (LBO) eigenmodes face limitations in characterizing high-frequency extrinsic shape changes like…

Particle-based shape modeling (PSM) is a popular approach to automatically quantify shape variability in populations of anatomies. The PSM family of methods employs optimization to automatically populate a dense set of corresponding…

Although many machine learning algorithms involve learning subspaces with particular characteristics, optimizing a parameter matrix that is constrained to represent a subspace can be challenging. One solution is to use Riemannian…

We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compression is achieved by using localized basis functions, which…

This paper develops a convex approach for sparse one-dimensional deconvolution that improves upon L1-norm regularization, the standard convex approach. We propose a sparsity-inducing non-separable non-convex bivariate penalty function for…

This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding…

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…

This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…

Eigenanalysis of differential operators, such as the Laplace operator or elastic energy Hessian, is typically restricted to a single shape and its discretization, limiting reduced order modeling (ROM). We introduce the first eigenanalysis…

In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…

We explore an optimal partition problem on surfaces using a computational approach. The problem is to minimise the sum of the first Dirichlet Laplace--Beltrami operator eigenvalues over a given number of partitions of a surface. We consider…

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback…

We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…