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It is well known that finite-dimensional polyhedral convex sets can be generated by finitely many points and finitely many directions. Representation formulas in this spirit are obtained for convex polyhedra and generalized convex polyhedra…
We develop a new approximation theory for linear and quadratic interpolation models, suitable for use in convex-constrained derivative-free optimization (DFO). Most existing model-based DFO methods for constrained problems assume the…
In this paper we consider the problem of constructing numerical algorithms for approximating of convex compact bodies in d-dimensional Euclidean space by polytopes with any given accuracy. It is well known that optimal with respect to the…
We consider the offset-deconstruction problem: Given a polygonal shape Q with n vertices, can it be expressed, up to a tolerance \eps in Hausdorff distance, as the Minkowski sum of another polygonal shape P with a disk of fixed radius? If…
This paper presents a new method for 3D shape reconstruction based on two existing methods. A 3D reconstruction from a single photograph is introduced by both papers: the first one uses a photograph and a set of existing 3D model to…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
In this paper we extend the notion of approximate dual to fusion frames and present some approaches to obtain dual and approximate alternate dual fusion frames. Also, we study the stability of dual and approximate alternate dual fusion…
This paper introduces a novel approach to the fine alignment of images in a burst captured by a handheld camera. In contrast to traditional techniques that estimate two-dimensional transformations between frame pairs or rely on discrete…
We study translation invariant, real-valued valuations on the class of convex polytopes in Euclidean space and discuss which continuity properties are sufficient for an extension of such valuations to all convex bodies. For this purpose, we…
In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with metrics of constant curvature.…
Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many…
We study the properties of the multiplicative structure on valuations on convex sets. We prove a new version of the hard Lefschetz theorem for even translation invariant continuous valuations, and discuss related problems of integral…
It is often convenient to use Gaussian blur in studying image quality or in data augmentation pipelines for training convoluional neural networks. Because of their convenience, Guassians are sometimes used as first order approximations of…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
We consider the problem of characterizing the convex hull of the graph of a bilinear function $f$ on the $n$-dimensional unit cube $[0,1]^n$. Extended formulations for this convex hull are obtained by taking subsets of the facets of the…
Numerous applications in signal processing have benefited from the theory of compressed sensing which shows that it is possible to reconstruct signals sampled below the Nyquist rate when certain conditions are satisfied. One of these…
In recent research, Learned Image Compression has gained prominence for its capacity to outperform traditional handcrafted pipelines, especially at low bit-rates. While existing methods incorporate convolutional priors with occasional…
Image completion has made tremendous progress with convolutional neural networks (CNNs), because of their powerful texture modeling capacity. However, due to some inherent properties (e.g., local inductive prior, spatial-invariant kernels),…
Having been studied since long by statisticians, multivariate median concepts found their way into the image processing literature in the course of the last decades, being used to construct robust and efficient denoising filters for…