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In this paper, we propose a new framework named Communication Optimal Transport (CommOT) for computing the rate distortion (RD) function. This work is motivated by observing the fact that the transition law and the relative entropy in…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…
Rotational tangle diagrams have been proven to be extremely important in the study of quantum invariants, as they provide a natural passage between topology and quantum algebra. In this paper, we give a detailed description of several…
We introduce the notion of a rigid quasilocal frame (RQF) as a geometrically natural way to define a "system" in general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the…
We propose Pullback Flow Matching (PFM), a novel framework for generative modeling on data manifolds. Unlike existing methods that assume or learn restrictive closed-form manifold mappings for training Riemannian Flow Matching (RFM) models,…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
We propose a novel video frame interpolation algorithm based on asymmetric bilateral motion estimation (ABME), which synthesizes an intermediate frame between two input frames. First, we predict symmetric bilateral motion fields to…
Video stabilization is a fundamental and important technique for higher quality videos. Prior works have extensively explored video stabilization, but most of them involve cropping of the frame boundaries and introduce moderate levels of…
The objective of this study is to enable fast and safe manipulation tasks in home environments. Specifically, we aim to develop a system that can recognize its surroundings and identify target objects while in motion, enabling it to plan…
Dynamic magnetic resonance imaging (dMRI) captures temporally-resolved anatomy but is often challenged by limited sampling and motion-induced artifacts. Conventional motion-compensated reconstructions typically rely on pre-estimated optical…
Video interpolation is an important problem in computer vision, which helps overcome the temporal limitation of camera sensors. Existing video interpolation methods usually assume uniform motion between consecutive frames and use linear…
Accurate object rearrangement from vision is a crucial problem for a wide variety of real-world robotics applications in unstructured environments. We propose IFOR, Iterative Flow Minimization for Robotic Object Rearrangement, an end-to-end…
Nowadays, a lot of old floor plans exist in printed form or are stored as scanned raster images. Slight rotations or shifts may occur during scanning. Bringing floor plans of this form into a machine readable form to enable further use,…
Video frame interpolation (VFI) is a challenging task that aims to generate intermediate frames between two consecutive frames in a video. Existing learning-based VFI methods have achieved great success, but they still suffer from limited…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
Our anatomy is in constant motion. With modern MR imaging it is possible to record this motion in real-time during an ongoing radiation therapy session. In this paper we present an image registration method that exploits the sequential…
Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model…
Many areas in science and engineering now have access to technologies that enable the rapid collection of overwhelming data volumes. While these datasets are vital for understanding phenomena from physical to biological and social systems,…
We introduce several spatially adaptive model order reduction approaches tailored to non-coercive elliptic boundary value problems, specifically, parametric-in-frequency Helmholtz problems. The offline information is computed by means of…
Photo-realistic image restoration algorithms are typically evaluated by distortion measures (e.g., PSNR, SSIM) and by perceptual quality measures (e.g., FID, NIQE), where the desire is to attain the lowest possible distortion without…