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Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…

Stitched images provide a wide field-of-view (FoV) but suffer from unpleasant irregular boundaries. To deal with this problem, existing image rectangling methods devote to searching an initial mesh and optimizing a target mesh to form the…

A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…

We present a novel deep architecture termed templateNet for depth based object instance recognition. Using an intermediate template layer we exploit prior knowledge of an object's shape to sparsify the feature maps. This has three…

Deep convolutional neural networks (DCNNs) based remote sensing (RS) image semantic segmentation technology has achieved great success used in many real-world applications such as geographic element analysis. However, strong dependency on…

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…

The scaled boundary finite element method (SBFEM) has recently been employed as an efficient means to model three-dimensional structures, in particular when the geometry is provided as a voxel-based image. To this end, an octree…

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…

Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric…

Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…

We present a novel framework for PDE-constrained $r$-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality…

We present a generalization of the bilateral filter that can be applied to feature-preserving smoothing of signals on images, meshes, and other domains within a single unified framework. Our discretization is competitive with…

Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…

In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream…

This paper proposes a novel discretization workflow for contact problems in which the discretization of the contact interface is decoupled from that of the bulk domain. This separation enables independently tailored meshes for the contact…

We present a scale-invariant, template-based segmentation paradigm that sets up a graph and performs a graph cut to separate an object from the background. Typically graph-based schemes distribute the nodes of the graph uniformly and…

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…

Discrete exterior calculus (DEC) is a structure-preserving numerical framework for partial differential equations solution, particularly suitable for simplicial meshes. A longstanding and widespread assumption has been that DEC requires…

For domains that are easily represented by structured meshes, robust geometric multigrid solvers can quickly provide the numerical solution to many discretized elliptic PDEs. However, for complicated domains with unstructured meshes,…

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…