Related papers: Unstructured to structured: geometric multigrid on…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

In this work, we establish a deformation-based framework for learning solution mappings of PDEs defined on varying domains. The union of functions defined on varying domains can be identified as a metric space according to the deformation,…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…

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,…

Establishing point-to-point correspondences across multiple 3D shapes is a fundamental problem in computer vision and graphics. In this paper, we introduce DcMatch, a novel unsupervised learning framework for non-rigid multi-shape matching.…

This paper explores the problem of reconstructing temporally consistent surfaces from a 3D point cloud sequence without correspondence. To address this challenging task, we propose DynoSurf, an unsupervised learning framework integrating a…

In the domain of geometry and topology optimization, discovering geometries that optimally satisfy specific problem criteria is a complex challenge in both engineering and scientific research. In this work, we propose a new approach for the…

Hexahedral meshes are an ubiquitous domain for the numerical resolution of partial differential equations. Computing a pure hexahedral mesh from an adaptively refined grid is a prominent approach to automatic hexmeshing, and requires the…

Diffeomorphic deformable image registration is one of the crucial tasks in medical image analysis, which aims to find a unique transformation while preserving the topology and invertibility of the transformation. Deep convolutional neural…

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…

In deformable registration, the geometric framework - large deformation diffeomorphic metric mapping or LDDMM, in short - has inspired numerous techniques for comparing, deforming, averaging and analyzing shapes or images. Grounded in…

Reconstruction of tomographic images from boundary measurements requires flexibility with respect to target domains. For instance, when the system equations are modeled by partial differential equations the reconstruction is usually done on…

This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…

Graphs provide a powerful means for representing complex interactions between entities. Recently, deep learning approaches are emerging for representing and modeling graph-structured data, although the conventional deep learning methods…

Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…

Learning inter-domain mappings from unpaired data can improve performance in structured prediction tasks, such as image segmentation, by reducing the need for paired data. CycleGAN was recently proposed for this problem, but critically…

Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are…

Recent point-based differentiable rendering techniques have achieved significant success in high-fidelity reconstruction and fast rendering. However, due to the unstructured nature of point-based representations, they are difficult to apply…

We present a computational approach for unfolding 3D shapes isometrically into the plane as a single patch without overlapping triangles. This is a hard, sometimes impossible, problem, which existing methods are forced to soften by allowing…