Related papers: Nonlinear Evolutionary PDE-Based Refinement of Opt…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
Optical flow is a regression task where convolutional neural networks (CNNs) have led to major breakthroughs. However, this comes at major computational demands due to the use of cost-volumes and pyramidal representations. This was…
We study the extension of the Chambolle--Pock primal-dual algorithm to nonsmooth optimization problems involving nonlinear operators between function spaces. Local convergence is shown under technical conditions including metric regularity…
Diffusion and flow-based generative models have shown strong potential for image restoration. However, image denoising under unknown and varying noise conditions remains challenging, because the learned vector fields may become inconsistent…
Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical…
A novel refinement measure for non-intrusive surrogate modelling of partial differential equations (PDEs) with uncertain parameters is proposed. Our approach uses an empirical interpolation procedure, where the proposed refinement measure…
During the upstroke of a normal eye blink, the upper lid moves and paints a thin tear film over the exposed corneal and conjunctival surfaces. This thin tear film may be modeled by a nonlinear fourth-order PDE derived from lubrication…
We study dynamic measure transport for generative modeling: specifically, flows induced by stochastic processes that bridge a specified source and target distribution. The conditional expectation of the process' velocity defines an ODE…
Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation…
Optical flow provides information on relative motion that is an important component in many computer vision pipelines. Neural networks provide high accuracy optical flow, yet their complexity is often prohibitive for application at the edge…
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this article we study a Horn-Schunck type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying…
We address unsupervised optical flow estimation for ego-centric motion. We argue that optical flow can be cast as a geometrical warping between two successive video frames and devise a deep architecture to estimate such transformation in…
THis work is a survey of a few nonlinear PDE based models in image restoring.
In this paper we propose an efficient second order well balanced finite volume method for modeling complex free surface flows at the aid of a simple diffuse interface method. The employed physical model is a two-phase model derived from the…
We present a pseudo-reversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with different initial distributions. The primary objective is to construct an accurate and…
Diffusion models have achieved significant progress in both image and video generation while still suffering from huge computation costs. As an effective solution, flow matching aims to reflow the diffusion process of diffusion models into…
Optical flow estimation is a widely known problem in computer vision introduced by Gibson, J.J(1950) to describe the visual perception of human by stimulus objects. Estimation of optical flow model can be achieved by solving for the motion…
Continuous normalizing flows (CNFs) construct invertible mappings between an arbitrary complex distribution and an isotropic Gaussian distribution using Neural Ordinary Differential Equations (neural ODEs). It has not been tractable on…
Image enhancement holds extensive applications in real-world scenarios due to complex environments and limitations of imaging devices. Conventional methods are often constrained by their tailored models, resulting in diminished robustness…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…