Related papers: Optical Flow on Moving Manifolds
Streamflow, as a natural phenomenon, is continuous in time and so are the meteorological variables which influence its variability. In practice, it can be of interest to forecast the whole flow curve instead of points (daily or hourly). To…
Existing methods for the 4D reconstruction of general, non-rigidly deforming objects focus on novel-view synthesis and neglect correspondences. However, time consistency enables advanced downstream tasks like 3D editing, motion analysis, or…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
In this paper, we propose RiemannianFlow, a deep generative model that allows robots to learn complex and stable skills evolving on Riemannian manifolds. Examples of Riemannian data in robotics include stiffness (symmetric and positive…
Event cameras capture brightness changes asynchronously with microsecond resolution, yet existing optical flow methods fail to fully exploit this temporal continuity. Frame-based approaches impose artificial accumulation latency and suffer…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
This is the third paper in a series of four in which a renormalisation flow is introduced which acts directly on the Osterwalder-Schrader data (OS data) without recourse to a path integral. Here the OS data consist of a Hilbert space, a…
It is well-known that natural images possess statistical regularities that can be captured by bandpass decomposition and divisive normalization processes that approximate early neural processing in the human visual system. We expand on…
This paper proposes the first non-flow-based deep framework for high dynamic range (HDR) imaging of dynamic scenes with large-scale foreground motions. In state-of-the-art deep HDR imaging, input images are first aligned using optical flows…
Underwater images suffer from light refraction and absorption, which impairs visibility and interferes the subsequent applications. Existing underwater image enhancement methods mainly focus on image quality improvement, ignoring the effect…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
The Ricci flow is a partial differential equation for evolving the metric in a Riemannian manifold to make it more regular. On the other hand, neural networks seem to have similar geometric behavior for specific tasks. In this paper, we…
The convolutional neural network model for optical flow estimation usually outputs a low-resolution(LR) optical flow field. To obtain the corresponding full image resolution,interpolation and variational approach are the most common…
Over four decades, the majority addresses the problem of optical flow estimation using variational methods. With the advance of machine learning, some recent works have attempted to address the problem using convolutional neural network…
Both optical flow and stereo disparities are image matches and can therefore benefit from joint training. Depth and 3D motion provide geometric rather than photometric information and can further improve optical flow. Accordingly, we design…
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
Generating videos guided by camera trajectories poses significant challenges in achieving consistency and generalizability, particularly when both camera and object motions are present. Existing approaches often attempt to learn these…
Many vesicles have a spherical resting shape and exposure to fluid flows induces an exchange between sub-optical area and visible (systematic) deformation, while the total area is conserved. The dynamics which controls the exchange between…
In this paper, we consider a fully nonlinear curvature flow of a convex hypersurface in the Euclidean n-space. This flow involves k-th elementary symmetric function for principal curvature radii and a function of support function. Under…
This paper addresses the problems of spline interpolation on smooth Riemannian manifolds, with or without the inclusion of least-squares fitting. Our unified approach utilizes gradient flows for successively connected curves or networks,…