Related papers: Automatic Target Recognition Using Discrimination …
We study the estimation of optimal transport (OT) maps between an arbitrary source probability measure and a log-concave target probability measure. Our contributions are twofold. First, we propose a new evolution equation in the set of…
This paper connects discrete optimal transport to a certain class of multi-objective optimization problems. In both settings, the decision variables can be organized into a matrix. In the multi-objective problem, the notion of Pareto…
The $L^1$ optimal transport density $\mu^*$ is the unique $L^\infty$ solution of the Monge-Kantorovich equations. It has been recently characterized also as the unique minimizer of the $L^1$ -transport energy functional E. In the present…
Recent transportation research highlights the potential of autonomous vehicles (AV) to improve traffic flow mobility as they are able to maintain smaller car-following distances. However, as a unique class of ground robots, AVs are…
We investigate the small regularization limit of entropic optimal transport when the cost function is the Euclidean distance in dimensions $d > 1$, and the marginal measures are absolutely continuous with respect to the Lebesgue measure.…
Regularized discrete optimal transport (OT) is a powerful tool to measure the distance between two discrete distributions that have been constructed from data samples on two different domains. While it has a wide range of applications in…
We formulate an optimal transport problem for matrix-valued density functions. This is pertinent in the spectral analysis of multivariable time-series. The "mass" represents energy at various frequencies whereas, in addition to a usual…
The inverse reflector problem aims to design a freeform reflecting surface that can direct the light from a specified source to produce the desired illumination in the target area, which is significant in the field of geometrical…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…
Monge map refers to the optimal transport map between two probability distributions and provides a principled approach to transform one distribution to another. Neural network based optimal transport map solver has gained great attention in…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Automated machine learning has been widely researched and adopted in the field of supervised classification and regression, but progress in unsupervised settings has been limited. We propose a novel approach to automate outlier detection…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
Moving target detection plays an important role in computer vision. However, traditional algorithms such as frame difference and optical flow usually suffer from low accuracy or heavy computation. Recent algorithms such as deep…
We present a novel approach for traffic forecasting in urban traffic scenarios using a combination of spectral graph analysis and deep learning. We predict both the low-level information (future trajectories) as well as the high-level…
This article investigates the quality of the estimator of the linear Monge mapping between distributions. We provide the first concentration result on the linear mapping operator and prove a sample complexity of $n^{-1/2}$ when using…
We study the convergence of entropically regularized optimal transport to optimal transport. The main result is concerned with the convergence of the associated optimizers and takes the form of a large deviations principle quantifying the…
In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge-Kantorovich equations, a PDE formulation of the optimal…
Color harmonization adjusts the colors of an inserted object so that it perceptually matches the surrounding image, resulting in a seamless composite. The harmonization problem naturally arises in augmented reality (AR), yet harmonization…