# Neural Marching Cubes

arXiv: https://arxiv.org/abs/2106.11272 · HTML: https://mlsanity.com/paper/2106.11272/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 63 references that are in the map.
- First posted on arXiv 21 Jun 2021.

## Builds on (most cited first, 27 of 27)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)
- [Hierarchical Surface Prediction for 3D Object Reconstruction](https://mlsanity.com/paper/1704.00710/) (2017)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [Scan2Mesh: From Unstructured Range Scans to 3D Meshes](https://mlsanity.com/paper/1811.10464/) (2018)
- [Neural Subdivision](https://mlsanity.com/paper/2005.01819/) (2020)
- [Point2Skeleton: Learning Skeletal Representations from Point Clouds](https://mlsanity.com/paper/2012.00230/) (2020)
- [Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks](https://mlsanity.com/paper/2002.06597/) (2020)
- [LOGAN: Unpaired Shape Transform in Latent Overcomplete Space](https://mlsanity.com/paper/1903.10170/) (2019)

## Built on by (most cited first, 30 of 50)

- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [HarmonyView: Harmonizing Consistency and Diversity in One-Image-to-3D](https://mlsanity.com/paper/2312.15980/) (2023)
- [NeuManifold: Neural Watertight Manifold Reconstruction with Efficient and High-Quality Rendering Support](https://mlsanity.com/paper/2305.17134/) (2023)
- [NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud](https://mlsanity.com/paper/2303.16465/) (2023)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)
- [ARMesh: Autoregressive Mesh Generation via Next-Level-of-Detail Prediction](https://mlsanity.com/paper/2509.20824/) (2025)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [CWF: Consolidating Weak Features in High-quality Mesh Simplification](https://mlsanity.com/paper/2404.15661/) (2024)
- [MeshMosaic: Scaling Artist Mesh Generation via Local-to-Global Assembly](https://mlsanity.com/paper/2509.19995/) (2025)
- [DECOLLAGE: 3D Detailization by Controllable, Localized, and Learned Geometry Enhancement](https://mlsanity.com/paper/2409.06129/) (2024)
- [NeuS-PIR: Learning Relightable Neural Surface using Pre-Integrated Rendering](https://mlsanity.com/paper/2306.07632/) (2023)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [ART-DECO: Arbitrary Text Guidance for 3D Detailizer Construction](https://mlsanity.com/paper/2505.20431/) (2025)
- [FACE: A Face-based Autoregressive Representation for High-Fidelity and Efficient Mesh Generation](https://mlsanity.com/paper/2603.01515/) (2026)
- [Neural Volumetric Mesh Generator](https://mlsanity.com/paper/2210.03158/) (2022)
- [Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction](https://mlsanity.com/paper/2504.19545/) (2025)
- [Implicit Conversion of Manifold B-Rep Solids by Neural Halfspace Representation](https://mlsanity.com/paper/2209.10191/) (2022)
- [Neural Surface Detection for Unsigned Distance Fields](https://mlsanity.com/paper/2407.18381/) (2024)
- [McGrids: Monte Carlo-Driven Adaptive Grids for Iso-Surface Extraction](https://mlsanity.com/paper/2409.06710/) (2024)
- [NeuralMeshing: Differentiable Meshing of Implicit Neural Representations](https://mlsanity.com/paper/2210.02382/) (2022)
- [A Review of Deep Learning-Powered Mesh Reconstruction Methods](https://mlsanity.com/paper/2303.02879/) (2023)
- [Text-guided Image-and-Shape Editing and Generation: A Short Survey](https://mlsanity.com/paper/2304.09244/) (2023)
- [Occupancy-Based Dual Contouring](https://mlsanity.com/paper/2409.13418/) (2024)
- [GenUDC: High Quality 3D Mesh Generation with Unsigned Dual Contouring Representation](https://mlsanity.com/paper/2410.17802/) (2024)

## Abstract (arXiv)

We introduce Neural Marching Cubes (NMC), a data-driven approach for extracting a triangle mesh from a discretized implicit field. Classical MC is defined by coarse tessellation templates isolated to individual cubes. While more refined tessellations have been proposed, they all make heuristic assumptions, such as trilinearity, when determining the vertex positions and local mesh topologies in each cube. In principle, none of these approaches can reconstruct geometric features that reveal coherence or dependencies between nearby cubes (e.g., a sharp edge), as such information is unaccounted for, resulting in poor estimates of the true underlying implicit field. To tackle these challenges, we re-cast MC from a deep learning perspective, by designing tessellation templates more apt at preserving geometric features, and learning the vertex positions and mesh topologies from training meshes, to account for contextual information from nearby cubes. We develop a compact per-cube parameterization to represent the output triangle mesh, while being compatible with neural processing, so that a simple 3D convolutional network can be employed for the training. We show that all topological cases in each cube that are applicable to our design can be easily derived using our representation, and the resulting tessellations can also be obtained naturally and efficiently by following a few design guidelines. In addition, our network learns local features with limited receptive fields, hence it generalizes well to new shapes and new datasets. We evaluate our neural MC approach by quantitative and qualitative comparisons to all well-known MC variants. In particular, we demonstrate the ability of our network to recover sharp features such as edges and corners, a long-standing issue of MC and its variants. Our network also reconstructs local mesh topologies more accurately than previous approaches.