相关论文: A variational problem arising in registration of d…

Data-driven deep learning approaches to image registration can be less accurate than conventional iterative approaches, especially when training data is limited. To address this whilst retaining the fast inference speed of deep learning, we…

The problem of inpainting involves reconstructing the missing areas of an image. Inpainting has many applications, such as reconstructing old damaged photographs or removing obfuscations from images. In this paper we present the directional…

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local…

Retinal image registration plays an important role in the ophthalmological diagnosis process. Since there exist variances in viewing angles and anatomical structures across different retinal images, keypoint-based approaches become the…

We construct a new kind of encoder, leveraging the expressive power of diffusion models. In a traditional variational autoencoder, the encoder and decoder jointly negotiate a latent representation of the input. This is made possible by the…

We propose here a proof of existence of a minimizer of a segmentation functional based on a priori information on target shapes, and formulated with level sets. The existence of a minimizer is very important, because it guarantees the…

In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…

The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of…

Global existence of very weak solutions to a non-local diffusion-advection-reaction equation is established under no-flux boundary conditions in higher dimensions. The equation features degenerate myopic diffusion and nonlocal adhesion and…

The paper concerns the analysis of global minimizers of a Dirichlet-type energy functional defined on the space of vector fields $H^1(S,T)$, where $S$ and $T$ are surfaces of revolution. The energy functional we consider is closely related…

Most problems in gravitational lensing require numerical solutions. The most frequent types of problems are (1) finding multiple images of a single source and classifying the images according to their properties like magnification or…

We present a detailed analysis of one-dimensional N\'eel walls in thin uniaxial ferromagnetic films in the presence of an in-plane applied external field in the direction normal to the easy axis. Within the reduced one-dimensional thin film…

A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…

Removing or repairing the imperfections of a digital images or videos is a very active and attractive field of research belonging to the image inpainting technique. This later has a wide range of applications, such as removing scratches in…

Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…

We prove a threshold phenomenon for the existence/non-existence of energy minimizing solitary solutions of the diffraction management equation for strictly positive and zero average diffraction. Our methods allow for a large class of…

Diffusion models have achieved remarkable progress in generative modelling, particularly in enhancing image quality to conform to human preferences. Recently, these models have also been applied to low-level computer vision for…

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms…

Conditional image generation has paved the way for several breakthroughs in image editing, generating stock photos and 3-D object generation. This continues to be a significant area of interest with the rise of new state-of-the-art methods…