Related papers: On an Edge-Preserving Variational Model for Optica…
We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both…
An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…
Conventional image motion based structure from motion methods first compute optical flow, then solve for the 3D motion parameters based on the epipolar constraint, and finally recover the 3D geometry of the scene. However, errors in optical…
High-precision micromanipulation techniques, including optical tweezers and hydrodynamic trapping, have garnered wide-spread interest. Recent advances in optofluidic multiplexed assembly and microrobotics demonstrate significant progress,…
Based on machine learning techniques, we propose a novel method to estimate flow fields using only floating sensor locations. This method does not require either ground-truth velocity fields or governing equations for fluid flows, which is…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
In this paper, a backward Euler method combined with finite element discretization in spatial direction is discussed for the equations of motion arising in the $2D$ Oldroyd model of viscoelastic fluids of order one with the forcing term…
We consider the evolution of an incompressible two-dimensional perfect fluid as the boundary of its domain is deformed in a prescribed fashion. The flow is taken to be initially steady, and the boundary deformation is assumed to be slow…
In recent years, many deep learning-based methods have been proposed to tackle the problem of optical flow estimation and achieved promising results. However, they hardly consider that most videos are compressed and thus ignore the…
In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time in the corresponding Brakke sense using the phase field…
Normalizing flows have grown more popular over the last few years; however, they continue to be computationally expensive, making them difficult to be accepted into the broader machine learning community. In this paper, we introduce a…
Optical flow computation is essential in the early stages of the video processing pipeline. This paper focuses on a less explored problem in this area, the 360$^\circ$ optical flow estimation using deep neural networks to support…
We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
Recently, convolutional networks (convnets) have proven useful for predicting optical flow. Much of this success is predicated on the availability of large datasets that require expensive and involved data acquisition and laborious la-…
Normalizing flow (NF) has gained popularity over traditional maximum likelihood based methods due to its strong capability to model complex data distributions. However, the standard approach, which maps the observed data to a normal…
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper we propose a minimal, local, conservative,…
The Osher-Chakrabarthy family of linear flux-modification schemes is considered. Improved lower bounds on the compression factors are provided, which suggest the viability of using the unlimited version. The LLF flux formula is combined…
We extend the concept of optical flow to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. It is the purpose of this paper to introduce variational motion estimation for images that are…
Flow Matching (FM) models achieve remarkable results in generative tasks. Building upon diffusion models, FM's simulation-free training paradigm enables simplicity and efficiency but introduces a train-inference gap: model outputs cannot be…