# MASH: Masked Anchored SpHerical Distances for 3D Shape Representation and Generation

arXiv: https://arxiv.org/abs/2504.09149 · HTML: https://mlsanity.com/paper/2504.09149/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 64 references that are in the map.
- First posted on arXiv 12 Apr 2025.

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

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [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)
- [Zero-1-to-3: Zero-shot One Image to 3D Object](https://mlsanity.com/paper/2303.11328/) (2023)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Point-E: A System for Generating 3D Point Clouds from Complex Prompts](https://mlsanity.com/paper/2212.08751/) (2022)
- [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)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models](https://mlsanity.com/paper/2301.11445/) (2023)
- [CLAY: A Controllable Large-scale Generative Model for Creating High-quality 3D Assets](https://mlsanity.com/paper/2406.13897/) (2024)
- [SDFusion: Multimodal 3D Shape Completion, Reconstruction, and Generation](https://mlsanity.com/paper/2212.04493/) (2022)
- [MeshGPT: Generating Triangle Meshes with Decoder-Only Transformers](https://mlsanity.com/paper/2311.15475/) (2023)
- [Michelangelo: Conditional 3D Shape Generation based on Shape-Image-Text Aligned Latent Representation](https://mlsanity.com/paper/2306.17115/) (2023)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [LN3DIFF++: Scalable Latent Neural Fields Diffusion for Speedy 3D Generation](https://mlsanity.com/paper/2403.12019/) (2024)
- [SpiralNet++: A Fast and Highly Efficient Mesh Convolution Operator](https://mlsanity.com/paper/1911.05856/) (2019)
- [Hunyuan3D 1.0: A Unified Framework for Text-to-3D and Image-to-3D Generation](https://mlsanity.com/paper/2411.02293/) (2024)
- [MeshCNN: A Network with an Edge](https://mlsanity.com/paper/1809.05910/) (2018)
- [Instant-3D: Instant Neural Radiance Field Training Towards On-Device AR/VR 3D Reconstruction](https://mlsanity.com/paper/2304.12467/) (2023)
- [A Simple Approach to Intrinsic Correspondence Learning on Unstructured 3D Meshes](https://mlsanity.com/paper/1809.06664/) (2018)
- [Orienting Point Clouds with Dipole Propagation](https://mlsanity.com/paper/2105.01604/) (2021)
- [Make-A-Shape: a Ten-Million-scale 3D Shape Model](https://mlsanity.com/paper/2401.11067/) (2024)

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

- [FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting](https://mlsanity.com/paper/2602.24084/) (2026)
- [HPR3D: Hierarchical Proxy Representation for High-Fidelity 3D Reconstruction and Controllable Editing](https://mlsanity.com/paper/2507.11971/) (2025)
- [SHARC: Reference point driven Spherical Harmonic Representation for Complex Shapes](https://mlsanity.com/paper/2604.01894/) (2026)
- [Blended Chart Surfaces: A Seamless Explicit Representation for Smooth Surface Fitting](https://mlsanity.com/paper/2606.18069/) (2026)

## Abstract (arXiv)

We introduce Masked Anchored SpHerical Distances (MASH), a novel multi-view and parametrized representation of 3D shapes. Inspired by multi-view geometry and motivated by the importance of perceptual shape understanding for learning 3D shapes, MASH represents a 3D shape as a collection of observable local surface patches, each defined by a spherical distance function emanating from an anchor point. We further leverage the compactness of spherical harmonics to encode the MASH functions, combined with a generalized view cone with a parameterized base that masks the spatial extent of the spherical function to attain locality. We develop a differentiable optimization algorithm capable of converting any point cloud into a MASH representation accurately approximating ground-truth surfaces with arbitrary geometry and topology. Extensive experiments demonstrate that MASH is versatile for multiple applications including surface reconstruction, shape generation, completion, and blending, achieving superior performance thanks to its unique representation encompassing both implicit and explicit features.