Related papers: MeshODE: A Robust and Scalable Framework for Mesh …

Mesh models are a promising approach for encoding the structure of 3D objects. Current mesh reconstruction systems predict uniformly distributed vertex locations of a predetermined graph through a series of graph convolutions, leading to…

Mesh processing pipelines are mature, but adapting them to newer non-mesh surface representations -- which enable fast rendering with compact file size -- requires costly meshing or transmitting bulky meshes, negating their core benefits…

In this article we propose a scalable shape optimization algorithm which is tailored for large scale problems and geometries represented by hierarchically refined meshes. Weak scalability and grid independent convergence is achieved via a…

Mesh-agnostic models have advantages in terms of processing unstructured spatial data and incorporating partial differential equations. Recently, they have been widely studied for constructing physics-informed neural networks, but they need…

High-order implicit shock tracking is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features. These methods align elements of the computational mesh with non-smooth features to represent them…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…

Establishing character shape correspondence is a critical and fundamental task in computer vision and graphics, with diverse applications including re-topology, attribute transfer, and shape interpolation. Current dominant functional map…

Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural…

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…

Dense 3D shape correspondence remains a central challenge in computer vision and graphics as many deep learning approaches still rely on intermediate geometric features or handcrafted descriptors, limiting their effectiveness under…

Manipulating deformable and fragile objects remains a fundamental challenge in robotics due to complex contact dynamics and strict requirements on object integrity. Existing approaches typically optimize either end-effector design or…

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label…

This paper puts forth a new formulation and algorithm for the elastic matching problem on unparametrized curves and surfaces. Our approach combines the frameworks of square root normal fields and varifold fidelity metrics into a novel…

Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…

Partitioning a polygonal mesh into meaningful parts can be challenging. Many applications require decomposing such structures for further processing in computer graphics. In the last decade, several methods were proposed to tackle this…

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

The dominant paradigm for high-fidelity 3D generation relies on a VAE-Diffusion pipeline, where the VAE's reconstruction capability sets a firm upper bound on generation quality. A fundamental challenge limiting existing VAEs is the…

The superior performance of Deformable Convolutional Networks arises from its ability to adapt to the geometric variations of objects. Through an examination of its adaptive behavior, we observe that while the spatial support for its neural…

We devise and evaluate numerically a Hybrid High-Order (HHO) method for incremental associative plasticity with small deformations. The HHO method uses as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton,…