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Diffusion models (DMs) have emerged as powerful generative models for solving inverse problems, offering a good approximation of prior distributions of real-world image data. Typically, diffusion models rely on large-scale clean signals to…

In this paper we present a new method for deformable NeRF that can directly use optical flow as supervision. We overcome the major challenge with respect to the computationally inefficiency of enforcing the flow constraints to the backward…

In this paper, we generalize the normalized gradient flow method which was first applied to computing the least energy ground state to compute the least action ground state. A continuous normalized gradient flow (CNGF) will be presented and…

The goal of this paper is to propose two nonlinear variational models for obtaining a refined motion estimation from an image sequence. Both the proposed models can be considered as a part of a generalized framework for an accurate…

In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…

The numerical modelling of convection dominated high density ratio two-phase flow poses several challenges, amongst which is resolving the relatively thin shear layer at the interface. To this end we propose a sharp discretisation of the…

The present document corresponds to the 4 th chapter of my thesis, the problem setting is not definitive, what matters most here are the mathematical results and the methodology of the existence proofs. In this work, we propose a framework…

Dense pixel matching problems such as optical flow and disparity estimation are among the most challenging tasks in computer vision. Recently, several deep learning methods designed for these problems have been successful. A sufficiently…

Singular Value Decomposition (SVD) has recently emerged as a new paradigm for processing different types of images. SVD is an attractive algebraic transform for image processing applications. The paper proposes an experimental survey for…

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with…

Image denoising is a fundamental challenge in computer vision, with applications in photography and medical imaging. While deep learning-based methods have shown remarkable success, their reliance on specific noise distributions limits…

Recently, the rectified flow (RF) has emerged as the new state-of-the-art among flow-based diffusion models due to its high efficiency advantage in straight path sampling, especially with the amazing images generated by a series of RF…

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…

Normalizing flows (NFs) have become a prominent method for deep generative models that allow for an analytic probability density estimation and efficient synthesis. However, a flow-based network is considered to be inefficient in parameter…

In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…

Denoising generative models, such as diffusion and flow-based models, produce high-quality samples but require many denoising steps due to discretization error. Flow maps, which estimate the average velocity between timesteps, mitigate this…

This work introduces an effective and practical solution to the dense two-view structure from motion (SfM) problem. One vital question addressed is how to mindfully use per-pixel optical flow correspondence between two frames for accurate…

The FlowNet demonstrated that optical flow estimation can be cast as a learning problem. However, the state of the art with regard to the quality of the flow has still been defined by traditional methods. Particularly on small displacements…

We introduce a new non-smooth variational model for the restoration of manifold-valued data which includes second order differences in the regularization term. While such models were successfully applied for real-valued images, we introduce…

Image denoising (removal of additive white Gaussian noise from an image) is one of the oldest and most studied problems in image processing. An extensive work over several decades has led to thousands of papers on this subject, and to many…