Related papers: Shape Analysis via Functional Map Construction and…
We propose a two-level structural optimization method for obtaining an approximate optimal shape of piecewise developable surface without specifying internal boundaries between surface patches. The condition for developability of a…
Despite the success of deep functional maps in non-rigid 3D shape matching, there exists no learning framework that models both self-symmetry and shape matching simultaneously. This is despite the fact that errors due to symmetry mismatch…
Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specific ellipse that contains the spectrum, we derive an…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
We introduce an algebraic multiscale method for two--dimensional problems. The method uses the generalized multiscale finite element method based on the quadrilateral nonconforming finite element spaces. Differently from the…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
We propose an alternating direction method of multipliers (ADMM) to solve an optimization problem stemming from inverse lithography. The objective functional of the optimization problem includes three terms: the misfit between the imaging…
We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
This paper serves as our first effort to develop a new triangular spectral element method (TSEM) on unstructured meshes, using the rectangle-triangle mapping proposed in the conference note [21]. Here, we provide some new insights into the…
We suggest a novel shape matching algorithm for three-dimensional surface meshes of disk or sphere topology. The method is based on the physical theory of nonlinear elasticity and can hence handle large rotations and deformations.…
Deep functional maps, leveraging learned feature extractors and spectral correspondence solvers, are fundamental to non-rigid 3D shape matching. Based on an analysis of open-source implementations, we find that standard functional map…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
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…