Related papers: On Artifacts in Limited Data Spherical Radon Trans…
Refraction is a common physical phenomenon and has long been researched in computer vision. Objects imaged through a refractive object appear distorted in the image as a function of the shape of the interface between the media. This hinders…
We consider an area minimizing current $T$ in a $C^2$ submanifold $\Sigma$ of $\mathbb{R}^{m+n}$, with arbitrary integer boundary multiplicity $\partial T = Q [\![ \Gamma ]\!]$ where $\Gamma$ is a $C^2$ submanifold of $\Sigma$. We show that…
Articulated objects, as prevalent entities in human life, their 3D representations play crucial roles across various applications. However, achieving both high-fidelity textured surface reconstruction and dynamic generation for articulated…
In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction…
In this work, we study the problem of reconstructing shapes from simple nonasymptotic densities measured only along shape boundaries. The particular density we study is also known as the integral area invariant and corresponds to the area…
Limited-angle tomography of strongly scattering quasi-transparent objects is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food…
Purpose: To reconstruct artifact-free images from measured k-space data, when the actual k-space trajectory deviates from the nominal trajectory due to gradient imperfections. Methods: Trajectory errors arising from eddy currents and…
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates…
We perform via $\Gamma$-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can…
Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These…
In this work we describe a fast and stable algorithm for the computation of the orthogonal moments of an image. Indeed, orthogonal moments are characterized by a high discriminative power, but some of their possible formulations are…
The paper is devoted to "uniform" reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types $E_6,E_8$ and $A_n$, we…
We consider an inverse problem arising in thermo-/photo- acoustic tomography that amounts to reconstructing a function $f$ from its circular or spherical means with the centers lying on a given measurement surface. (Equivalently, these…
Spatial imaging of magnetic stray fields from magnetic materials is a useful tool for identifying the underlying magnetic configurations of the material. However, transforming the magnetic image into a magnetization image is an ill-poised…
In electrical impedance tomography, algorithms based on minimizing the linearized-data-fit residuum have been widely used due to their real-time implementation and satisfactory reconstructed images. However, the resulting images usually…
Object geometry is key information for robot manipulation. Yet, object reconstruction is a challenging task because cameras only capture partial observations of objects, especially when occlusion occurs. In this paper, we leverage two extra…
The structure of the $(\sqrt{31}\times \sqrt{31})R\pm9^\circ$ reconstructed phase on sapphire (0001) surface is investigated by means of a simulation based on the energy minimization. The interaction between Al adatoms is described with the…
This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and…
Proton deflectometry is increasingly used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The…
A high-order quadrature scheme is constructed for the evaluation of Laplace single and double layer potentials and their normal derivatives on smooth surfaces in three dimensions. The construction begins with a harmonic approximation of the…