Related papers: A variational problem arising in registration of d…

Image registration is a key technique in medical image analysis to estimate deformations between image pairs. A good deformation model is important for high-quality estimates. However, most existing approaches use ad-hoc deformation models…

Medical image registration is a difficult problem. Not only a registration algorithm needs to capture both large and small scale image deformations, it also has to deal with global and local image intensity variations. In this paper we…

We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed…

We present our work on scalable, GPU-accelerated algorithms for diffeomorphic image registration. The associated software package is termed CLAIRE. Image registration is a non-linear inverse problem. It is about computing a spatial mapping…

Optimization techniques have been widely used in deformable registration, allowing for the incorporation of similarity metrics with regularization mechanisms. These regularization mechanisms are designed to mitigate the effects of trivial…

In the past, optimization-based registration models have used spatially-varying regularization to account for deformation variations in different image regions. However, deep learning-based registration models have mostly relied on…

This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for…

This paper studies a diffusion-based framework to address the low-light image enhancement problem. To harness the capabilities of diffusion models, we delve into this intricate process and advocate for the regularization of its inherent…

In general, the problem of non-rigid registration is about matching two different scans of a dynamic object taken at two different points in time. These scans can undergo both rigid motions and non-rigid deformations. Since new parts of the…

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV…

We consider a variational problem with a polyconvex integrand and nonstandard boundary conditions that can be treated as minimization of the stress energy during the suturing process in the plastic surgery. Ex- istence of minimizers is…

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

Nematic surfaces are thin liquid films endowed with in-plane orientational order. We study a variational model in which the nematic director is constrained to lie in the tangent space of an axisymmetric surface, and the associated surface…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised…

We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the…

The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…

We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…

Diffusion methods have been proven to be very effective to generate images while conditioning on a text prompt. However, and although the quality of the generated images is unprecedented, these methods seem to struggle when trying to…