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Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
Spherical $t$-designs on $\mathbb{S}^{d}\subset\mathbb{R}^{d+1}$ provide $N$ nodes for an equal weight numerical integration rule which is exact for all spherical polynomials of degree at most $t$. This paper considers the generation of…
The aim of this paper is to prove that every continuous map from a compact subset of a real algebraic variety into a sphere can be approximated by piecewise-regular maps of class C^k, where k is an arbitrary integer.
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
Most of existing superpixel methods are designed to segment standard planar images as pre-processing for computer vision pipelines. Nevertheless, the increasing number of applications based on wide angle capture devices, mainly generating…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
Sphere fitting is a common problem in almost all science and engineering disciplines. Most of methods available are iterative in behavior. This involves fitting of the parameters in a least square sense or in a geometric sense. Here we…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
The aim of this paper is to give a survey of the known results concerning centrally symmetric polytopes, spheres, and manifolds. We further enumerate nearly neighborly centrally symmetric spheres and centrally symmetric products of spheres…
In a recent article, we have shown that a variety of localized polynomial frames, including isotropic as well as directional systems, are suitable for detecting jump discontinuities along circles on the sphere. More precisely, such edges…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
An efficient technique to solve precision problems consists in using exact computations. For geometric predicates, using systematically expensive exact computations can be avoided by the use of filters. The predicate is first evaluated…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…
Gravitational lensing of luminous matter that surrounds a black hole or some other sufficiently compact object produces an infinite sequence of images. Besides the direct (or primary) image, it comprises demagnified and deformed replicas of…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…