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We present a deformable generator model to disentangle the appearance and geometric information for both image and video data in a purely unsupervised manner. The appearance generator network models the information related to appearance,…
This paper presents a new algorithm for online estimation of a sequence of homographies applicable to image sequences obtained from robotic vehicles equipped with vision sensors. The approach taken exploits the underlying Special Linear…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
The problem of detecting and quantifying the presence of symmetries in datasets is useful for model selection, generative modeling, and data analysis, amongst others. While existing methods for hard-coding transformations in neural networks…
We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the…
The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
In this contribution we are interested in the quantitative homogenization properties of linear elliptic equations with homogeneous Dirichlet boundary data in polygonal domains with corners. To begin our study of this situation, we consider…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct…
The paper is concerned with the finite element solution of the Poisson equation with homogeneous Dirichlet boundary condition in a three-dimensional domain. Anisotropic, graded meshes from a former paper are reused for dealing with the…
We propose and study quantitative measures of smoothness which are adapted to anisotropic features such as edges in images or shocks in PDE's. These quantities govern the rate of approximation by adaptive finite elements, when no constraint…
We provide a statistical analysis of the ability of digitized continuous shearlet systems to detect objects embedded in white noise. We analyze the possibility to subsample the shearlet transform and obtain a subset of significantly reduced…
A stochastic method is introduced for geometric modeling aerosol surface roughness with random field and discrete differential geometry theory. Optical scattering properties are computed for randomly oriented spheroidal particles with…
Weak gravitational lensing provides a unique method to directly measure the distribution of mass in the universe. Because the distortions induced by lensing in the shape of background galaxies are small, the measurement of weak lensing…
Here we present a method of constructing steerable wavelet frames in $L_2(\mathbb{R}^d)$ that generalizes and unifies previous approaches, including Simoncelli's pyramid and Riesz wavelets. The motivation for steerable wavelets is the need…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV)…