Related papers: Multiscale Strategies for Computing Optimal Transp…

We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set…

This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…

Sampling-based Motion Planners (SMPs) have become increasingly popular as they provide collision-free path solutions regardless of obstacle geometry in a given environment. However, their computational complexity increases significantly…

Hierarchical, multi-resolution volumetric mapping approaches are widely used to represent large and complex environments as they can efficiently capture their occupancy and connectivity information. Yet widely used path planning methods…

Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…

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…

Brain pathologies often manifest as partial or complete loss of tissue. The goal of many neuroimaging studies is to capture the location and amount of tissue changes with respect to a clinical variable of interest, such as disease…

In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…

We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…

We propose a scalable, distributed algorithm for the optimal transport of large-scale multi-agent systems. We formulate the problem as one of steering the collective towards a target probability measure while minimizing the total cost of…

Point sets matching problems can be handled by optimal transport. The mechanism behind it is that optimal transport recovers the point-to-point correspondence associated with the least curl deformation. Optimal transport is a special form…

The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…

For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…

Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…

This paper introduces a multiscale analysis based on optimal piecewise linear approximations of time series. An optimality criterion is formulated and on its base a computationally effective algorithm is constructed for decomposition of a…