# Flexible Isosurface Extraction for Gradient-Based Mesh Optimization

arXiv: https://arxiv.org/abs/2308.05371 · HTML: https://mlsanity.com/paper/2308.05371/

## Key facts

- Cited by 139 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 84 references that are in the map.
- First posted on arXiv 10 Aug 2023.

## Builds on (most cited first, 30 of 38)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Magic3D: High-Resolution Text-to-3D Content Creation](https://mlsanity.com/paper/2211.10440/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [StyleNeRF: A Style-based 3D-Aware Generator for High-resolution Image Synthesis](https://mlsanity.com/paper/2110.08985/) (2021)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [NeRD: Neural Reflectance Decomposition from Image Collections](https://mlsanity.com/paper/2012.03918/) (2020)
- [GET3D: A Generative Model of High Quality 3D Textured Shapes Learned from Images](https://mlsanity.com/paper/2209.11163/) (2022)
- [Modular Primitives for High-Performance Differentiable Rendering](https://mlsanity.com/paper/2011.03277/) (2020)
- [Neural 3D Mesh Renderer](https://mlsanity.com/paper/1711.07566/) (2017)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [Extracting Triangular 3D Models, Materials, and Lighting From Images](https://mlsanity.com/paper/2111.12503/) (2021)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Learning to Predict 3D Objects with an Interpolation-based Differentiable Renderer](https://mlsanity.com/paper/1908.01210/) (2019)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Shape, Light, and Material Decomposition from Images using Monte Carlo Rendering and Denoising](https://mlsanity.com/paper/2206.03380/) (2022)
- [PAC-NeRF: Physics Augmented Continuum Neural Radiance Fields for Geometry-Agnostic System Identification](https://mlsanity.com/paper/2303.05512/) (2023)
- [CIPS-3D: A 3D-Aware Generator of GANs Based on Conditionally-Independent Pixel Synthesis](https://mlsanity.com/paper/2110.09788/) (2021)
- [VoxGRAF: Fast 3D-Aware Image Synthesis with Sparse Voxel Grids](https://mlsanity.com/paper/2206.07695/) (2022)
- [MeshSDF: Differentiable Iso-Surface Extraction](https://mlsanity.com/paper/2006.03997/) (2020)

## Built on by (most cited first, 30 of 139)

- [InstantMesh: Efficient 3D Mesh Generation from a Single Image with Sparse-view Large Reconstruction Models](https://mlsanity.com/paper/2404.07191/) (2024)
- [CRM: Single Image to 3D Textured Mesh with Convolutional Reconstruction Model](https://mlsanity.com/paper/2403.05034/) (2024)
- [Native and Compact Structured Latents for 3D Generation](https://mlsanity.com/paper/2512.14692/) (2025)
- [MeshAnything: Artist-Created Mesh Generation with Autoregressive Transformers](https://mlsanity.com/paper/2406.10163/) (2024)
- [MeshLRM: Large Reconstruction Model for High-Quality Meshes](https://mlsanity.com/paper/2404.12385/) (2024)
- [Unique3D: High-Quality and Efficient 3D Mesh Generation from a Single Image](https://mlsanity.com/paper/2405.20343/) (2024)
- [TeCH: Text-guided Reconstruction of Lifelike Clothed Humans](https://mlsanity.com/paper/2308.08545/) (2023)
- [LN3DIFF++: Scalable Latent Neural Fields Diffusion for Speedy 3D Generation](https://mlsanity.com/paper/2403.12019/) (2024)
- [Sparc3D: Sparse Representation and Construction for High-Resolution 3D Shapes Modeling](https://mlsanity.com/paper/2505.14521/) (2025)
- [CAD-MLLM: Unifying Multimodality-Conditioned CAD Generation With MLLM](https://mlsanity.com/paper/2411.04954/) (2024)
- [SparseFlex: High-Resolution and Arbitrary-Topology 3D Shape Modeling](https://mlsanity.com/paper/2503.21732/) (2025)
- [SCube: Instant Large-Scale Scene Reconstruction using VoxSplats](https://mlsanity.com/paper/2410.20030/) (2024)
- [HumanSplat: Generalizable Single-Image Human Gaussian Splatting with Structure Priors](https://mlsanity.com/paper/2406.12459/) (2024)
- [DiffSplat: Repurposing Image Diffusion Models for Scalable Gaussian Splat Generation](https://mlsanity.com/paper/2501.16764/) (2025)
- [LATTICE: Democratize High-Fidelity 3D Generation at Scale](https://mlsanity.com/paper/2512.03052/) (2025)
- [Binary Opacity Grids: Capturing Fine Geometric Detail for Mesh-Based View Synthesis](https://mlsanity.com/paper/2402.12377/) (2024)
- [LATTE3D: Large-scale Amortized Text-To-Enhanced3D Synthesis](https://mlsanity.com/paper/2403.15385/) (2024)
- [SAR3D: Autoregressive 3D Object Generation and Understanding via Multi-scale 3D VQVAE](https://mlsanity.com/paper/2411.16856/) (2024)
- [MILo: Mesh-In-the-Loop Gaussian Splatting for Detailed and Efficient Surface Reconstruction](https://mlsanity.com/paper/2506.24096/) (2025)
- [Garment3DGen: 3D Garment Stylization and Texture Generation](https://mlsanity.com/paper/2403.18816/) (2024)
- [From One to More: Contextual Part Latents for 3D Generation](https://mlsanity.com/paper/2507.08772/) (2025)
- [AvatarGO: Zero-shot 4D Human-Object Interaction Generation and Animation](https://mlsanity.com/paper/2410.07164/) (2024)
- [Ghost on the Shell: An Expressive Representation of General 3D Shapes](https://mlsanity.com/paper/2310.15168/) (2023)
- [MVD2: Efficient Multiview 3D Reconstruction for Multiview Diffusion](https://mlsanity.com/paper/2402.14253/) (2024)
- [Dynamic Gaussians Mesh: Consistent Mesh Reconstruction from Dynamic Scenes](https://mlsanity.com/paper/2404.12379/) (2024)
- [GeoSplatting: Towards Geometry Guided Gaussian Splatting for Physically-based Inverse Rendering](https://mlsanity.com/paper/2410.24204/) (2024)
- [TetSphere Splatting: Representing High-Quality Geometry with Lagrangian Volumetric Meshes](https://mlsanity.com/paper/2405.20283/) (2024)
- [SpaceMesh: A Continuous Representation for Learning Manifold Surface Meshes](https://mlsanity.com/paper/2409.20562/) (2024)
- [Geometry Image Diffusion: Fast and Data-Efficient Text-to-3D with Image-Based Surface Representation](https://mlsanity.com/paper/2409.03718/) (2024)
- [FastMesh: Efficient Artistic Mesh Generation via Component Decoupling](https://mlsanity.com/paper/2508.19188/) (2025)

## Abstract (arXiv)

This work considers gradient-based mesh optimization, where we iteratively optimize for a 3D surface mesh by representing it as the isosurface of a scalar field, an increasingly common paradigm in applications including photogrammetry, generative modeling, and inverse physics. Existing implementations adapt classic isosurface extraction algorithms like Marching Cubes or Dual Contouring; these techniques were designed to extract meshes from fixed, known fields, and in the optimization setting they lack the degrees of freedom to represent high-quality feature-preserving meshes, or suffer from numerical instabilities. We introduce FlexiCubes, an isosurface representation specifically designed for optimizing an unknown mesh with respect to geometric, visual, or even physical objectives. Our main insight is to introduce additional carefully-chosen parameters into the representation, which allow local flexible adjustments to the extracted mesh geometry and connectivity. These parameters are updated along with the underlying scalar field via automatic differentiation when optimizing for a downstream task. We base our extraction scheme on Dual Marching Cubes for improved topological properties, and present extensions to optionally generate tetrahedral and hierarchically-adaptive meshes. Extensive experiments validate FlexiCubes on both synthetic benchmarks and real-world applications, showing that it offers significant improvements in mesh quality and geometric fidelity.