Related papers: Relaxed Total Generalized Variation Regularized Pi…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
Moving mesh methods (also called r-adaptive methods) are space-adaptive strategies used for the numerical simulation of time-dependent partial differential equations. These methods keep the total number of mesh points fixed during the…
Despite recent progress on semantic segmentation, there still exist huge challenges in medical ultra-resolution image segmentation. The methods based on multi-branch structure can make a good balance between computational burdens and…
Mass abnormality segmentation is a vital step for the medical diagnostic process and is attracting more and more the interest of many research groups. Currently, most of the works achieved in this area have used the Gray Level Co-occurrence…
Phase-field models of fracture introduce smeared cracks of width commensurate with a regularisation length parameter $\epsilon$ and obeying a minimum energy principle. Mesh adaptivity naturally suggests itself as a means of supplying…
Given a tetrahedral mesh and objective functionals measuring the mesh quality which take into account the shape, size, and orientation of the mesh elements, our aim is to improve the mesh quality as much as possible. In this paper, we…
Reconstructing high-quality 3D meshes and visuals from 3D Gaussian Splatting(3DGS) still remains a central challenge in computer graphics. Although existing models such as SuGaR offer effective solutions for rendering, there is is still…
This paper introduces a novel method for the efficient second-order accurate computation of normal fields from volume fractions on unstructured polyhedral meshes. Locally, i.e. in each mesh cell, an averaged normal is reconstructed by…
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…
Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
Despite rapid progress in scene segmentation in recent years, 3D segmentation methods are still limited when there is severe occlusion. The key challenge is estimating the segment boundaries of (partially) occluded objects, which are…
Magnetic resonance imaging (MRI) is the non-invasive modality of choice for body tissue composition analysis due to its excellent soft tissue contrast and lack of ionizing radiation. However, quantification of body composition requires an…
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…
We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local…
In this work, we develop efficient solvers for linear inverse problems based on randomized singular value decomposition (RSVD). This is achieved by combining RSVD with classical regularization methods, e.g., truncated singular value…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend regular simplicial meshes by allowing for overlapping elements…
The reliability of Deep Learning systems depends on their accuracy but also on their robustness against adversarial perturbations to the input data. Several attacks and defenses have been proposed to improve the performance of Deep Neural…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…