Related papers: Polynomial curvelets on higher-dimensional spheres
The present article is the third part of a series of papers devoted to the shallow water wave modelling. In this part, we investigate the derivation of some long wave models on a deformed sphere. We propose first a suitable for our purposes…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
We determine when an exotic sphere $\Sigma$ of dimension $d\not \equiv 1 (4)$ can be detected through the homotopy type of its truncated Disc-presheaf. The latter records the diagram of framed configuration spaces of bounded cardinality in…
Recently, shearlet systems were introduced as a means to derive efficient encoding methodologies for anisotropic features in 2-dimensional data with a unified treatment of the continuum and digital setting. However, only very few…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…
Rotation estimation of high precision from an RGB-D object observation is a huge challenge in 6D object pose estimation, due to the difficulty of learning in the non-linear space of SO(3). In this paper, we propose a novel rotation…
We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such a walk by studying the phase diagram…
While object semantic understanding is essential for most service robotic tasks, 3D object classification is still an open problem. Learning from artificial 3D models alleviates the cost of annotation necessary to approach this problem, but…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
In this paper, we develop a general theoretical framework for constructing Haar-type tight framelets on any compact set with a hierarchical partition. In particular, we construct a novel area-regular hierarchical partition on the 2-sphere…
The objective of this article is to describe a construction of Parseval bandlimited and localized frames on sub-Riemannian compact homogeneous manifolds.
In this paper we provide a characterization for a class of convex curves on the 3-sphere. More precisely, using a theorem that decomposes a locally convex curve on the 3-sphere as a pair of curves on the 2-sphere, one of which is locally…
It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…
We propose a class of spherical wavelet bases for the analysis of geophysical models and forthe tomographic inversion of global seismic data. Its multiresolution character allows for modeling with an effective spatial resolution that varies…
3D shape representation and its processing have substantial effects on 3D shape recognition. The polygon mesh as a 3D shape representation has many advantages in computer graphics and geometry processing. However, there are still some…
The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…
The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…
Category-level object pose estimation aims to determine the pose and size of novel objects in specific categories. Existing correspondence-based approaches typically adopt point-based representations to establish the correspondences between…