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Estimating per-pixel motion between video frames, known as optical flow, is a long-standing problem in video understanding and analysis. Most contemporary optical flow techniques largely focus on addressing the cross-image matching with…
This paper studies optical flow estimation, a critical task in motion analysis with applications in autonomous navigation, action recognition, and film production. Traditional optical flow methods require consecutive frames, which are often…
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to possess the exponential decay property, in terms of a…
Modern optical flow methods make use of salient scene feature points detected and matched within the scene as a basis for sparse-to-dense optical flow estimation. Current feature detectors however either give sparse, non uniform point…
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…
Diffusion models have shown great promise for image and video generation, but sampling from state-of-the-art models requires expensive numerical integration of a generative ODE. One approach for tackling this problem is rectified flows,…
The pel-recursive computation of 2-D optical flow has been extensively studied in computer vision to estimate motion from image sequences, but it still raises a wealth of issues, such as the treatment of outliers, motion discontinuities and…
This report presents the results of a partial differential equation (PDE)-based image enhancement algorithm, for dynamic range compression and illumination correction in the absence of the logarithmic function. The proposed algorithm…
Denoising-based models, such as diffusion and flow matching, have been a critical component of robotic manipulation for their strong distribution-fitting and scaling capacity. Concurrently, several works have demonstrated that simple…
Diffusion and flow matching policies have recently demonstrated remarkable performance in robotic applications by accurately capturing multimodal robot trajectory distributions. However, their computationally expensive inference, due to the…
Various research studies indicate that action recognition performance highly depends on the types of motions being extracted and how accurate the human actions are represented. In this paper, we investigate different optical flow, and…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
Akin to many subareas of computer vision, the recent advances in deep learning have also significantly influenced the literature on optical flow. Previously, the literature had been dominated by classical energy-based models, which…
The goal of this paper is to discover, segment, and track independently moving objects in complex visual scenes. Previous approaches have explored the use of optical flow for motion segmentation, leading to imperfect predictions due to…
Rectified flow is a generative model that learns smooth transport mappings between two distributions through an ordinary differential equation (ODE). Unlike diffusion-based generative models, which require costly numerical integration of a…
Learning probabilistic surrogates for partial differential equations remains challenging in data-scarce regimes: neural operators require large amounts of high-fidelity data, while generative approaches typically sacrifice resolution…
We extend the concept of optical flow with spatiotemporal regularisation to a dynamic non-Euclidean setting. Optical flow is traditionally computed from a sequence of flat images. The purpose of this paper is to introduce variational motion…
In most of computer vision applications, motion blur is regarded as an undesirable artifact. However, it has been shown that motion blur in an image may have practical interests in fundamental computer vision problems. In this work, we…
Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings,…