# Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes

arXiv: https://arxiv.org/abs/2509.21007 · HTML: https://mlsanity.com/paper/2509.21007/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 79 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem](https://mlsanity.com/paper/1812.05720/) (2018)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Bounding and Counting Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1711.02114/) (2017)
- [Deep ReLU Networks Have Surprisingly Few Activation Patterns](https://mlsanity.com/paper/1906.00904/) (2019)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [Reachable Polyhedral Marching (RPM): A Safety Verification Algorithm for Robotic Systems with Deep Neural Network Components](https://mlsanity.com/paper/2011.11609/) (2020)
- [SplineCam: Exact Visualization and Characterization of Deep Network Geometry and Decision Boundaries](https://mlsanity.com/paper/2302.12828/) (2023)
- [Three Decades of Activations: A Comprehensive Survey of 400 Activation Functions for Neural Networks](https://mlsanity.com/paper/2402.09092/) (2024)
- [Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks](https://mlsanity.com/paper/2002.06597/) (2020)
- [Polyhedral Complex Extraction from ReLU Networks using Edge Subdivision](https://mlsanity.com/paper/2306.07212/) (2023)
- [Spelunking the Deep: Guaranteed Queries on General Neural Implicit Surfaces via Range Analysis](https://mlsanity.com/paper/2202.02444/) (2022)
- [Reach For the Spheres: Tangency-Aware Surface Reconstruction of SDFs](https://mlsanity.com/paper/2308.09813/) (2023)
- [Learning and Meshing from Deep Implicit Surface Networks Using an Efficient Implementation of Analytic Marching](https://mlsanity.com/paper/2106.10031/) (2021)

## Built on by (most cited first, 3 of 3)

- [TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid](https://mlsanity.com/paper/2511.16273/) (2025)
- [Recent Advances and Trends in Learning-based 3D Representations](https://mlsanity.com/paper/2606.04871/) (2026)
- [DiffGI: Differentiable Geometry Images for High-Fidelity Thin-Shell 3D Generation](https://mlsanity.com/paper/2607.13365/) (2026)

## Abstract (arXiv)

Accurate surface geometry representation is crucial in 3D visual computing. Explicit representations, such as polygonal meshes, and implicit representations, like signed distance functions, each have distinct advantages, making efficient conversions between them increasingly important. Conventional surface extraction methods for implicit representations, such as the widely used Marching Cubes algorithm, rely on spatial decomposition and sampling, leading to inaccuracies due to fixed and limited resolution. We introduce a novel approach for analytically extracting surfaces from neural implicit functions. Our method operates natively in parallel and can navigate large neural architectures. By leveraging the fact that each neuron partitions the domain, we develop a depth-first traversal strategy to efficiently track the encoded surface. The resulting meshes faithfully capture the full geometric information from the network without ad-hoc spatial discretization, achieving unprecedented accuracy across diverse shapes and network architectures while maintaining competitive speed.