[Paper Review] Neural Mesh Flow: 3D Manifold Mesh Generation via Diffeomorphic Flows

Kunal Gupta, Manmohan Chandraker|arXiv (Cornell University)|Jul 21, 2020

3D Shape Modeling and Analysis59 references4 citations

TL;DR

Neural Mesh Flow (NMF) is a deep generative model that produces high-quality, two-manifold 3D meshes directly from 2D images or point clouds by learning a diffeomorphic flow from a spherical template using Neural ODEs. The method ensures manifoldness by construction, outperforming prior approaches in geometric accuracy and physical realizability for rendering, simulation, and 3D printing without post-processing.

ABSTRACT

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.

Motivation & Objective

• Address the lack of manifoldness in state-of-the-art 3D mesh generation methods, which hinders their use in physically-based simulations and 3D printing.
• Overcome the limitations of existing mesh generation techniques that require manual post-processing to fix non-manifold defects.
• Develop a deep learning framework that preserves manifold properties during mesh deformation by leveraging the mathematical properties of diffeomorphic flows.
• Enable end-to-end, differentiable mesh generation that is both geometrically accurate and topologically valid for real-world applications.
• Demonstrate that manifoldness is a critical but previously neglected property in 3D mesh generation, especially for downstream physical applications.

Proposed method

• Model the mesh generation process as a diffeomorphic flow from a genus-0 spherical template mesh to the target shape using Neural Ordinary Differential Equations (NODEs).
• Use a series of NODE-based deformation blocks with instance normalization to enable generalization across multiple 3D shape categories.
• Enforce manifoldness through the intrinsic properties of diffeomorphisms—specifically, their orientation-preserving and smooth invertible nature—rather than explicit regularization.
• Train the model using a combination of Chamfer Distance and normal consistency losses to ensure geometric fidelity and consistent surface orientation.
• Apply Laplacian smoothing post-hoc to reduce self-intersections in the generated meshes, improving intersection-free quality.
• Construct the final mesh as a singly connected, non-intersecting, and topologically consistent mesh by ensuring all manifold constraints (edge, vertex, face, and intersection conditions) are satisfied.

Experimental results

Research questions

• RQ1 Can a deep generative model produce 3D meshes that are both geometrically accurate and topologically manifold without requiring post-processing?
• RQ2 Does learning a diffeomorphic flow from a template mesh preserve manifoldness during deformation, and can this be leveraged for end-to-end mesh generation?
• RQ3 How does manifoldness impact the performance of downstream applications such as physically-based simulation, rendering, and 3D printing?
• RQ4 Can a single architecture generalize across multiple 3D shape categories while maintaining high geometric and topological fidelity?
• RQ5 How does the proposed method compare to implicit representation-based approaches (e.g., OccNet) in terms of manifoldness, geometric accuracy, and inference efficiency?

Key findings

• NMF achieves a Chamfer-L2 loss of 7.82 on single-view reconstruction, outperforming the best baseline OccNet-3 (8.33), indicating superior geometric accuracy.
• NMF achieves zero non-manifold vertices and edges (NM-Vertices: 0.00, NM-Edges: 0.00), demonstrating perfect topological consistency by construction.
• The method produces meshes with only 0.83 non-manifold faces and 0.12 self-intersections, significantly outperforming OccNet-3 in manifoldness metrics.
• NMF-generated meshes are directly printable and suitable for physically-based simulation without repair, as validated by 3D printing and simulation results.
• Simulations using NMF-generated meshes show physical behavior closest to ground truth, while MeshRCNN exhibits over-bounciness due to non-manifold artifacts.
• With Laplacian smoothing, NMF reduces self-intersections to zero (0.00) while maintaining high normal consistency (0.837) and competitive inference time (292ms).