# Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows

arXiv: https://arxiv.org/abs/2007.10973 · HTML: https://mlsanity.com/paper/2007.10973/

## Key facts

- Cited by 61 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2020.

## Built on by (most cited first, 30 of 61)

- [Zero-Shot Text-Guided Object Generation with Dream Fields](https://mlsanity.com/paper/2112.01455/) (2021)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Dream3D: Zero-Shot Text-to-3D Synthesis Using 3D Shape Prior and Text-to-Image Diffusion Models](https://mlsanity.com/paper/2212.14704/) (2022)
- [Let 2D Diffusion Model Know 3D-Consistency for Robust Text-to-3D Generation](https://mlsanity.com/paper/2303.07937/) (2023)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [A Deep-Learning Approach For Direct Whole-Heart Mesh Reconstruction](https://mlsanity.com/paper/2102.07899/) (2021)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Neural Template: Topology-aware Reconstruction and Disentangled Generation of 3D Meshes](https://mlsanity.com/paper/2206.04942/) (2022)
- [Vox2Cortex: Fast Explicit Reconstruction of Cortical Surfaces from 3D MRI Scans with Geometric Deep Neural Networks](https://mlsanity.com/paper/2203.09446/) (2022)
- [CortexODE: Learning Cortical Surface Reconstruction by Neural ODEs](https://mlsanity.com/paper/2202.08329/) (2022)
- [Learning Whole Heart Mesh Generation From Patient Images For Computational Simulations](https://mlsanity.com/paper/2203.10517/) (2022)
- [Pixel2Mesh++: 3D Mesh Generation and Refinement from Multi-View Images](https://mlsanity.com/paper/2204.09866/) (2022)
- [Medical Image Registration via Neural Fields](https://mlsanity.com/paper/2206.03111/) (2022)
- [Reinforcement learning for automatic quadrilateral mesh generation: a soft actor-critic approach](https://mlsanity.com/paper/2203.11203/) (2022)
- [Neural Vector Fields: Implicit Representation by Explicit Learning](https://mlsanity.com/paper/2303.04341/) (2023)
- [DeepMesh: Mesh-based Cardiac Motion Tracking using Deep Learning](https://mlsanity.com/paper/2309.14306/) (2023)
- [Neural deformation fields for template-based reconstruction of cortical surfaces from MRI](https://mlsanity.com/paper/2401.12938/) (2024)
- [Landmark-free Statistical Shape Modeling via Neural Flow Deformations](https://mlsanity.com/paper/2209.06861/) (2022)
- [Enabling Uncertainty Estimation in Iterative Neural Networks](https://mlsanity.com/paper/2403.16732/) (2024)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [CLIPXPlore: Coupled CLIP and Shape Spaces for 3D Shape Exploration](https://mlsanity.com/paper/2306.08226/) (2023)
- [Neural Deformable Models for 3D Bi-Ventricular Heart Shape Reconstruction and Modeling from 2D Sparse Cardiac Magnetic Resonance Imaging](https://mlsanity.com/paper/2307.07693/) (2023)
- [Progressive Text-to-3D Generation for Automatic 3D Prototyping](https://mlsanity.com/paper/2309.14600/) (2023)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction](https://mlsanity.com/paper/2305.17555/) (2023)
- [CorticalFlow: A Diffeomorphic Mesh Deformation Module for Cortical Surface Reconstruction](https://mlsanity.com/paper/2206.02374/) (2022)
- [Minimal Neural Atlas: Parameterizing Complex Surfaces with Minimal Charts and Distortion](https://mlsanity.com/paper/2207.14782/) (2022)

## Abstract (arXiv)

Meshes are important representations of physical 3D entities in the virtual world. Applications like rendering, simulations and 3D printing require meshes to be manifold so that they can interact with the world like the real objects they represent. Prior methods generate meshes with great geometric accuracy but poor manifoldness. In this work, we propose Neural Mesh Flow (NMF) to generate two-manifold meshes for genus-0 shapes. Specifically, NMF is a shape auto-encoder consisting of several Neural Ordinary Differential Equation (NODE)[1] blocks that learn accurate mesh geometry by progressively deforming a spherical mesh. Training NMF is simpler compared to state-of-the-art methods since it does not require any explicit mesh-based regularization. Our experiments demonstrate that NMF facilitates several applications such as single-view mesh reconstruction, global shape parameterization, texture mapping, shape deformation and correspondence. Importantly, we demonstrate that manifold meshes generated using NMF are better-suited for physically-based rendering and simulation. Code and data are released.