Related papers: A Semi-Lagrangian Scheme with Radial Basis Approxi…

This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…

This paper proposes a novel approach to solving nonlinear programming problems using a sharp augmented Lagrangian method with a smoothing technique. Traditional sharp augmented Lagrangian methods are known for their effectiveness but are…

We propose a numerical method for solving block-structured mesh partitioning problems based on the variational level-set method of (Zhao et al., J Comput Phys 127, 1996) which has been widely used in many partitioning problems such as image…

We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…

Existing 3D surface representation approaches are unable to accurately classify pixels and their orientation lying on the boundary of an object. Thus resulting in coarse representations which usually require post-processing steps to extract…

We present the Multilevel Bregman Proximal Gradient Descent (ML BPGD) method, a novel multilevel optimization framework tailored to constrained convex problems with relative Lipschitz smoothness. Our approach extends the classical…

CNN architectures have terrific recognition performance but rely on spatial pooling which makes it difficult to adapt them to tasks that require dense, pixel-accurate labeling. This paper makes two contributions: (1) We demonstrate that…

The boundary representation (B-Rep) models a 3D solid as its explicit boundaries: trimmed corners, edges, and faces. Recovering B-Rep representation from unstructured data is a challenging and valuable task of computer vision and graphics.…

A key parameter in ice flow modelling is basal slipping at the ice-bed interface as it can have a large effect on the resultant ice thickness. Unfortunately, its contribution to surface observations can be hard to distinguish from that of…

Kernel methods for solving partial differential equations on surfaces have the advantage that those methods work intrinsically on the surface and yield high approximation rates if the solution to the partial differential equation is smooth…

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…

The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…

A robust numerical methodology to predict equilibrium interfaces over arbitrary solid surfaces is developed. The kernel of the proposed method is the distance regularized level set equations (DRLSE) with techniques to incorporate the…

We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity,…

In this paper, we consider the exact continuous relaxation model of $l_0$ regularization problem which was given by Bian and Chen (SIAM J. Numer. Anal 58(1): 858-883, 2020) and propose a smoothing proximal gradient algorithm with…

We study the nonparametric least squares estimator (LSE) of a multivariate convex regression function. The LSE, given as the solution to a quadratic program with $O(n^2)$ linear constraints ($n$ being the sample size), is difficult to…

Binary tomography is concerned with reconstructing a binary image from a very small number or other limited CT projection data. This problem itself not only possesses several medical imaging applications but also can be considered a model…