# McGrids: Monte Carlo-Driven Adaptive Grids for Iso-Surface Extraction

arXiv: https://arxiv.org/abs/2409.06710 · HTML: https://mlsanity.com/paper/2409.06710/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 47 references that are in the map.
- First posted on arXiv 25 Aug 2024.

## Builds on (most cited first, 20 of 20)

- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Scene as Occupancy](https://mlsanity.com/paper/2306.02851/) (2023)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [Recovering Fine Details for Neural Implicit Surface Reconstruction](https://mlsanity.com/paper/2211.11320/) (2022)
- [Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients](https://mlsanity.com/paper/2201.13240/) (2022)
- [Sum-of-Squares Geometry Processing](https://mlsanity.com/paper/2110.08451/) (2021)

## Built on by (most cited first, 4 of 4)

- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes](https://mlsanity.com/paper/2509.21007/) (2025)
- [S2MDF: A Plug-And-Play Layer for Intersection-Free Multi-Object Signed Distance Fields](https://mlsanity.com/paper/2605.29761/) (2026)
- [TetraSDF: Analytic Isosurface Extraction with Multi-resolution Tetrahedral Grid](https://mlsanity.com/paper/2511.16273/) (2025)

## Abstract (arXiv)

Iso-surface extraction from an implicit field is a fundamental process in various applications of computer vision and graphics. When dealing with geometric shapes with complicated geometric details, many existing algorithms suffer from high computational costs and memory usage. This paper proposes McGrids, a novel approach to improve the efficiency of iso-surface extraction. The key idea is to construct adaptive grids for iso-surface extraction rather than using a simple uniform grid as prior art does. Specifically, we formulate the problem of constructing adaptive grids as a probability sampling problem, which is then solved by Monte Carlo process. We demonstrate McGrids' capability with extensive experiments from both analytical SDFs computed from surface meshes and learned implicit fields from real multiview images. The experiment results show that our McGrids can significantly reduce the number of implicit field queries, resulting in significant memory reduction, while producing high-quality meshes with rich geometric details.