Related papers: Convective regularization for optical flow
Characteristic curves of a Hamilton-Jacobi equation can be seen as action minimizing trajectories of fluid particles. However this description is valid only for smooth solutions. For nonsmooth "viscosity" solutions, which give rise to…
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,…
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
We introduce a new modified Navier-Stokes model in $3$ dimensions by modifying the convection term in the ordinary Navier-Stokes equations. This is done by replacing the convective term $(\textbf{u}\cdot \nabla) \textbf{u}$ by…
This paper examines an averaging technique in which the nonlinear flux term is expanded and the convective velocities are passed through a low-pass filter. It is the intent that this modification to the nonlinear flux terms will result in…
Momentum is a popular technique to accelerate the convergence in practical training, and its impact on convergence guarantee has been well-studied for first-order algorithms. However, such a successful acceleration technique has not yet…
The use of convex regularizers allows for easy optimization, though they often produce biased estimation and inferior prediction performance. Recently, nonconvex regularizers have attracted a lot of attention and outperformed convex ones.…
An adaptive regularization algorithm using inexact function and derivatives evaluations is proposed for the solution of composite nonsmooth nonconvex optimization. It is shown that this algorithm needs at most…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
Neural optical flow (NOF) offers improved accuracy and robustness over existing OF methods for particle image velocimetry (PIV). Unlike other OF techniques, which rely on discrete displacement fields, NOF parameterizes the physical velocity…
Reference frame optimization is a generic framework to calculate a spatially-varying observer field that views an unsteady fluid flow in a reference frame that is as-steady-as-possible. In this paper, we show that the optimized vector field…
Existing optical flow methods make generic, spatially homogeneous, assumptions about the spatial structure of the flow. In reality, optical flow varies across an image depending on object class. Simply put, different objects move…
Recently, there has been a great interest in analysing dynamical flows, where the stationary limit is the minimiser of a convex energy. Particular flows of great interest have been continuous limits of Nesterov's algorithm and the Fast…
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…
Online optimisation revolves around new data being introduced into a problem while it is still being solved; think of deep learning as more training samples become available. We adapt the idea to dynamic inverse problems such as video…
The problem of minimization of the least squares functional with a smooth, lower semi-continuous, convex regularizer $J(\cdot)$ is considered to be solved. Over some compact and convex subset $\Omega$ of the Hilbert space $\mathcal{H},$ the…
Particle Image Velocimetry (PIV) has become increasingly popular to study structures in turbulent flows. PIV allows direct extraction and investigation of spatial structures in the given flow field. Increasing temporal resolution of PIV…
We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are…
The computation of 2-D optical flow by means of regularized pel-recursive algorithms raises a host of issues, which include the treatment of outliers, motion discontinuities and occlusion among other problems. We propose a new approach…
We study fully nonlinear geometric flows that deform strictly $k$-convex hypersurfaces in Euclidean space with pointwise normal speed given by a concave function of the principal curvatures. Specifically, the speeds we consider are obtained…