Related papers: Conforming restricted Delaunay mesh generation for…

We propose a template-driven triangulation framework that embeds raster- or segmentation-derived boundaries into a regular triangular grid for stable PDE discretization on image-derived domains. Unlike constrained Delaunay triangulation…

A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…

This paper addresses the limitations of neural rendering-based multi-view surface reconstruction methods, which require an additional mesh extraction step that is inconvenient and would produce poor-quality surfaces with mesh aliasing,…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…

Generative models that produce point clouds have emerged as a powerful tool to represent 3D surfaces, and the best current ones rely on learning an ensemble of parametric representations. Unfortunately, they offer no control over the…

Remote sensing semantic segmentation must address both what the ground objects are within an image and where they are located. Consequently, segmentation models must ensure not only the semantic correctness of large-scale patches…

This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its…

This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…

Recent advances in the area of plane segmentation from single RGB images show strong accuracy improvements and now allow a reliable segmentation of indoor scenes into planes. Nonetheless, fine-grained details of these segmentation masks are…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

Reliable knowledge of road boundaries is critical for autonomous vehicle navigation. We propose a robust curb detection and filtering technique based on the fusion of camera semantics and dense lidar point clouds. The lidar point clouds are…

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…

We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly…

The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…

This paper presents a RePaint-enhanced framework that integrates a pre-trained performance-guided denoising diffusion probabilistic model (DDPM) for performance- and parameter-constraint engineering design generation. The proposed method…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Shearlet systems have so far been only considered as a means to analyze $L^2$-functions defined on $\R^2$, which exhibit curvilinear singularities. However, in applications such as image processing or numerical solvers of partial…

Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…

Deep learning approaches to 3D shape segmentation are typically formulated as a multi-class labeling problem. Existing models are trained for a fixed set of labels, which greatly limits their flexibility and adaptivity. We opt for top-down…

The paper introduces DelTriC (Delaunay Triangulation Clustering), a clustering algorithm which integrates PCA/UMAP-based projection, Delaunay triangulation, and a novel back-projection mechanism to form clusters in the original…