相关论文: Geometric primitive feature extraction - concepts,…

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…

We overview a series of recent works addressing numerical simulations of partial differential equations in the presence of some elements of randomness. The specific equations manipulated are linear elliptic, and arise in the context of…

We develop efficient and high-order accurate finite difference methods for elliptic partial differential equations in complex geometry in the Difference Potentials framework. The main novelty of the developed schemes is the use of local…

In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…

Feature curves are largely adopted to highlight shape features, such as sharp lines, or to divide surfaces into meaningful segments, like convex or concave regions. Extracting these curves is not sufficient to convey prominent and…

Numerical computation of shortest paths or geodesics on curved domains, as well as the associated geodesic distance, arises in a broad range of applications across digital geometry processing, scientific computing, computer graphics, and…

This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node…

Head pose estimation plays a vital role in various applications, e.g., driverassistance systems, human-computer interaction, virtual reality technology, and so on. We propose a novel geometry based algorithm for accurately estimating the…

One of the fundamental problems in computer vision is the two-frame relative pose optimization problem. Primarily, two different kinds of error values are used: photometric error and re-projection error. The selection of error value is…

We present an efficient algorithm designed for and capable of detecting elongated, thin features such as lines and curves in astronomical images, and its application to the automatic detection of gravitational arcs. The algorithm is…

This paper proposes a fast and unsupervised scheme for the polygonal approximation of a closed digital curve. It is demonstrated that the approximation scheme is faster than state-of-the-art approximation and is competitive with Rosin's…

Many recent problems in signal processing and machine learning such as compressed sensing, image restoration, matrix/tensor recovery, and non-negative matrix factorization can be cast as constrained optimization. Projected gradient descent…

The computation of the geometric transformation between a reference and a target image, known as registration or alignment, corresponds to the projection of the target image onto the transformation manifold of the reference image (the set…

This article considers the extension of two-grid $hp$-version discontinuous Galerkin finite element methods for the numerical approximation of second-order quasilinear elliptic boundary value problems of monotone type to the case when…

Power systems with high penetration of inverter-based resources (IBR) present significant challenges for conventional protection schemes, with traditional distance protection methods failing to detect line-to-line faults during asymmetric…

Deep learning method is of great importance in solving partial differential equations. In this paper, inspired by the failure-informed idea proposed by Gao et.al. (SIAM Journal on Scientific Computing 45(4)(2023)) and as an improvement, a…

Object detection and recognition are important problems in computer vision. Since these problems are meta-heuristic, despite a lot of research, practically usable, intelligent, real-time, and dynamic object detection/recognition methods are…

We study the problem of aligning two sets of 3D geometric primitives given known correspondences. Our first contribution is to show that this primitive alignment framework unifies five perception problems including point cloud registration,…