相关论文: PDE-constrained optimization in medical image anal…

Medical image segmentation is a relevant task as it serves as the first step for several diagnosis processes, thus it is indispensable in clinical usage. Whilst major success has been reported using supervised techniques, they assume a…

Finding optimal data for inpainting is a key problem in the context of partial differential equation based image compression. The data that yields the most accurate reconstruction is real-valued. Thus, quantisation models are mandatory to…

Regularization strategies in medical image registration often take a one-size-fits-all approach by imposing uniform constraints across the entire image domain. Yet biological structures are anything but regular. Lacking structural…

Deformable image registration (DIR), aiming to find spatial correspondence between images, is one of the most critical problems in the domain of medical image analysis. In this paper, we present a novel, generic, and accurate diffeomorphic…

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…

Image normalization is a building block in medical image analysis. Conventional approaches are customarily utilized on a per-dataset basis. This strategy, however, prevents the current normalization algorithms from fully exploiting the…

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and…

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…

In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…

Class imbalance and the difficulty imbalance are the two types of data imbalance that affect the performance of neural networks in medical segmentation tasks. In class imbalance the loss is dominated by the majority classes and in…

Motivation: Medical image analysis involves tasks to assist physicians in qualitative and quantitative analysis of lesions or anatomical structures, significantly improving the accuracy and reliability of diagnosis and prognosis.…

Segmentation maps of medical images annotated by medical experts contain rich spatial information. In this paper, we propose to decompose annotation maps to learn disentangled and richer feature transforms for segmentation problems in…

In this thesis I explore challenging discrete energy minimization problems that arise mainly in the context of computer vision tasks. This work motivates the use of such "hard-to-optimize" non-submodular functionals, and proposes methods…

Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) automatic 3-D registration is implemented and validated for small animal image volumes so that the high-resolution anatomical MRI information can be fused with the low…

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer…

Image registration is a critical component in the applications of various medical image analyses. In recent years, there has been a tremendous surge in the development of deep learning (DL)-based medical image registration models. This…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

Machine learning techniques used in computer-aided medical image analysis usually suffer from the domain shift problem caused by different distributions between source/reference data and target data. As a promising solution, domain…

Medical image fusion is the process of registering and combining multiple images from single or multiple imaging modalities to improve the imaging quality and reduce randomness and redundancy in order to increase the clinical applicability…

Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…