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Adaptive block partitioning is responsible for large gains in current image and video compression systems. This method is able to compress large stationary image areas with only a few symbols, while maintaining a high level of quality in…
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…
Vector spherical harmonics on the unit sphere of $\mathbb{R}^3$ have broad applications in geophysics, quantum mechanics and astrophysics. In the representation of a tangent vector field, one needs to evaluate the expansion and the Fourier…
Order-independent transparency schemes rely on low-order approximations of transmittance as a function of depth. We introduce a new wavelet representation of this function and an algorithm for building and evaluating it efficiently on a…
Persistence-based topological optimization deforms a point cloud $X \subset \mathbb{R}^d$ by minimizing objectives of the form $L(X) = \ell(\mathrm{Dgm}(X))$, where $\mathrm{Dgm}(X)$ is a persistence diagram. In practice, optimization is…
We present a novel graph transformer framework, HAMLET, designed to address the challenges in solving partial differential equations (PDEs) using neural networks. The framework uses graph transformers with modular input encoders to directly…
Guided depth map super-resolution (GDSR), as a hot topic in multi-modal image processing, aims to upsample low-resolution (LR) depth maps with additional information involved in high-resolution (HR) RGB images from the same scene. The…
Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…
Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
We investigate stripe patterns formation far from threshold using a combination of topological, analytic, and numerical methods. We first give a definition of the mathematical structure of `multi-valued' phase functions that are needed for…
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.…
Scale-permuted networks have shown promising results on object bounding box detection and instance segmentation. Scale permutation and cross-scale fusion of features enable the network to capture multi-scale semantics while preserving…
The shearlet transform from applied harmonic analysis is currently the state of the art when analyzing multidimensional signals with anisotropic singularities. Its optimal sparse approximation properties and its faithful digitalization…
A fast algorithm for Antoine and Vandergheynst's (1998) directional continuous spherical wavelet transform (CSWT) is presented. Computational requirements are reduced by a factor of O(\sqrt{N}), when N is the number of pixels on the sphere.…
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets --- a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses…
The development of small-angle scattering tensor tomography has enabled the study of anisotropic nanostructures in a volume-resolved manner. It is of great value to have reconstruction methods that can handle many different nanostructural…
Video prediction is a pixel-wise dense prediction task to infer future frames based on past frames. Missing appearance details and motion blur are still two major problems for current predictive models, which lead to image distortion and…
We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus…
We have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, $N$. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere…