Related papers: A rigorous analysis using optimal transport theory…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…
Both the backpropagation algorithm in machine learning and the maximum principle in optimal control theory are posed as a two-point boundary problem, resulting in a "forward-backward" lock. We derive a reformulation of the maximum principle…
We propose an algorithm to detect approximate reflection symmetry present in a set of volumetrically distributed points belonging to $\mathbb{R}^d$ containing a distorted reflection symmetry pattern. We pose the problem of detecting…
Designing freeform surfaces to control light based on real-world illumination patterns is challenging, as existing caustic lens designs often assume oversimplified point or parallel light sources. We propose representing surface light…
Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…
From the earth's crust to the human brain, remitted waves are used for sensing and imaging in a diverse range of diffusive media. Separating the source and detector increases the penetration depth of remitted light, yet rapidly decreases…
We experimentally address the wave-vector and polarization dependence of the internal conical refraction phenomenon by demonstrating that an input light beam of elliptical transverse profile refracts into two beams after passing along one…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
We consider an inverse source problem for partially coherent light propagating in the Fresnel regime. The data is the coherence of the field measured away from the source. The reconstruction is based on a minimum residue formulation, which…
We describe a new model for image propagation through open air in the presence of changes in the index of refraction (e.g. due to turbulence) using the theory of optimal transport. We describe the relationship between photon density, or…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…
In this paper, we show that unbalanced optimal transport provides a convenient framework to handle reaction and diffusion processes in a unified metric framework. We use a constructive method, alternating minimizing movements for the…
We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…
Many years ago John Tyrell a lecturer at King's college London challenged his Ph.D. students with the following puzzle: show that there is a unique triangle of minimal perimeter with exactly one vertex to lie on one of three given lines,…
We consider a two-way relay network, where two source nodes, S1 and S2, exchange information through a cluster of relay nodes. The relay nodes receive the sum signal from S1 and S2 in the first time slot. In the second time slot, each relay…
We develop a theory of optimal transport for stationary random measures with a focus on stationary point processes and construct a family of distances on the set of stationary random measures. These induce a natural notion of interpolation…