Related papers: Multigrid Algorithm Based on Hybrid Smoothers for …

This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…

Vertex-patch smoothers are essential for the robust convergence of geometric multigrid methods in high-order finite element applications, yet their adoption is traditionally hindered by the prohibitive cost of solving local patch problems.…

Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there…

An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergence…

Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional…

Shape priors have been widely utilized in medical image segmentation to improve segmentation accuracy and robustness. A major way to encode such a prior shape model is to use a mesh representation, which is prone to causing…

This paper proposes a novel heterogeneous grid convolution that builds a graph-based image representation by exploiting heterogeneity in the image content, enabling adaptive, efficient, and controllable computations in a convolutional…

We introduce a geometric multigrid method for solving linear systems arising from variational problems on surfaces in geometry processing, Gravo MG. Our scheme uses point clouds as a reduced representation of the levels of the multigrid…

Partial Differential Equations (PDEs) underpin many scientific phenomena, yet traditional computational approaches often struggle with complex, nonlinear systems and irregular geometries. This paper introduces the AMG method, a Multi-Graph…

Each year, numerous segmentation and classification algorithms are invented or reused to solve problems where machine vision is needed. Generally, the efficiency of these algorithms is compared against the results given by one or many human…

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…

The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

We introduce a novel Unsmoothed Aggregation (UA) Algebraic Multigrid (AMG) method combined with Preconditioned Conjugate Gradient (PCG) to overcome the limitations of Extended Position-Based Dynamics (XPBD) in high-resolution and…

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…

Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…

This paper presents a comprehensive evaluation framework for image segmentation algorithms, encompassing naive methods, machine learning approaches, and deep learning techniques. We begin by introducing the fundamental concepts and…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

In this paper we develop a data-driven smoothing technique for high-dimensional and non-linear panel data models. We allow for individual specific (non-linear) functions and estimation with econometric or machine learning methods by using…

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class…