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We present a novel shape-approximating anisotropic re-meshing algorithm as a geometric generalization of the adaptive moving mesh method. Conventional moving mesh methods reduce the interpolation error of a mesh that discretizes a given…
This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
We propose a method for fast and automatic estimation of spatially dependent regularization maps for total variation-based (TV) tomography reconstruction. The estimation is based on two distinct sub-networks, with the first sub-network…
With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…
Neural surface reconstruction has been dominated by implicit representations with marching cubes for explicit surface extraction. However, those methods typically require high-quality normals for accurate reconstruction. We propose…
In many applications such as color image processing, data has more than one piece of information associated with each spatial coordinate, and in such cases the classical optimal mass transport (OMT) must be generalized to handle…
Spectrum cartography constructs maps of metrics such as channel gain or received signal power across a geographic area of interest using spatially distributed sensor measurements. Applications of these maps include network planning,…
We present a novel reduced-order Model (ROM) that leverages optimal transport (OT) theory and displacement interpolation to enhance the representation of nonlinear dynamics in complex systems. While traditional ROM techniques face…
Given an unlabeled road map, we consider, from an algorithmic perspective, the cartographic problem to place non-overlapping road labels embedded in their roads. We first decompose the road network into logically coherent road sections,…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
Algorithms for motion planning in unknown environments are generally limited in their ability to reason about the structure of the unobserved environment. As such, current methods generally navigate unknown environments by relying on…
A motion planning algorithm computes the motion of a robot by computing a path through its configuration space. To improve the runtime of motion planning algorithms, we propose to nest robots in each other, creating a nested quotient-space…
The Self-Organizing Map (SOM) is a brain-inspired neural model that is very promising for unsupervised learning, especially in embedded applications. However, it is unable to learn efficient prototypes when dealing with complex datasets. We…
Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. Recently, one line of works propose to solve OT approximately by searching the \emph{transport plan}…
Optimal Transport, a theory for optimal allocation of resources, is widely used in various fields such as astrophysics, machine learning, and imaging science. However, many applications impose elementwise constraints on the transport plan…
In this paper, we propose a new variational model for image reconstruction by minimizing the $L^1$ norm of the \emph{Weingarten map} of image surface $(x,y,f(x,y))$ for a given image $f:{\mathrm{\Omega}}\rightarrow \mathbb R$. We…
Autonomous driving has traditionally relied heavily on costly and labor-intensive High Definition (HD) maps, hindering scalability. In contrast, Standard Definition (SD) maps are more affordable and have worldwide coverage, offering a…
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…