# ASH: A Modern Framework for Parallel Spatial Hashing in 3D Perception

arXiv: https://arxiv.org/abs/2110.00511 · HTML: https://mlsanity.com/paper/2110.00511/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 70 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Deep Global Registration](https://mlsanity.com/paper/2004.11540/) (2020)
- [Voxblox: Incremental 3D Euclidean Signed Distance Fields for On-Board MAV Planning](https://mlsanity.com/paper/1611.03631/) (2016)
- [Intrinsic3D: High-Quality 3D Reconstruction by Joint Appearance and Geometry Optimization with Spatially-Varying Lighting](https://mlsanity.com/paper/1708.01670/) (2017)
- [Self-supervised Geometric Perception](https://mlsanity.com/paper/2103.03114/) (2021)
- [InfiniTAM v3: A Framework for Large-Scale 3D Reconstruction with Loop Closure](https://mlsanity.com/paper/1708.00783/) (2017)
- [PSDF Fusion: Probabilistic Signed Distance Function for On-the-fly 3D Data Fusion and Scene Reconstruction](https://mlsanity.com/paper/1807.11034/) (2018)
- [An Efficient Volumetric Mesh Representation for Real-time Scene Reconstruction using Spatial Hashing](https://mlsanity.com/paper/1803.03949/) (2018)
- [stdgpu: Efficient STL-like Data Structures on the GPU](https://mlsanity.com/paper/1908.05936/) (2019)
- [WarpCore: A Library for fast Hash Tables on GPUs](https://mlsanity.com/paper/2009.07914/) (2020)
- [A Dynamic Hash Table for the GPU](https://mlsanity.com/paper/1710.11246/) (2017)
- [Data-Parallel Hashing Techniques for GPU Architectures](https://mlsanity.com/paper/1807.04345/) (2018)

## Built on by (most cited first, 11 of 11)

- [Drivable Avatar Clothing: Faithful Full-Body Telepresence with Dynamic Clothing Driven by Sparse RGB-D Input](https://mlsanity.com/paper/2310.05917/) (2023)
- [Parametric Encoding with Attention and Convolution Mitigate Spectral Bias of Neural Partial Differential Equation Solvers](https://mlsanity.com/paper/2403.15652/) (2024)
- [Fast Monocular Scene Reconstruction with Global-Sparse Local-Dense Grids](https://mlsanity.com/paper/2305.13220/) (2023)
- [On the Overconfidence Problem in Semantic 3D Mapping](https://mlsanity.com/paper/2311.10018/) (2023)
- [pySLAM: An Open-Source, Modular, and Extensible Framework for SLAM](https://mlsanity.com/paper/2502.11955/) (2025)
- [Revisiting LiDAR Registration and Reconstruction: A Range Image Perspective](https://mlsanity.com/paper/2112.02779/) (2021)
- [Minuet: Accelerating 3D Sparse Convolutions on GPUs](https://mlsanity.com/paper/2401.06145/) (2023)
- [Multi-robot autonomous 3D reconstruction using Gaussian splatting with Semantic guidance](https://mlsanity.com/paper/2412.02249/) (2024)
- [PointCNN++: Performant Convolution on Native Points](https://mlsanity.com/paper/2511.23227/) (2025)
- [Gaussian-Voxel Duet: A Dual-Scaffolding Hybrid Representation for Fast and Accurate Monocular Surface Reconstruction](https://mlsanity.com/paper/2605.26616/) (2026)
- [Test-Time Spatial Reasoning for Robot Manipulation Using Generative Real-to-Sim](https://mlsanity.com/paper/2609.33982/) (2026)

## Abstract (arXiv)

We present ASH, a modern and high-performance framework for parallel spatial hashing on GPU. Compared to existing GPU hash map implementations, ASH achieves higher performance, supports richer functionality, and requires fewer lines of code (LoC) when used for implementing spatially varying operations from volumetric geometry reconstruction to differentiable appearance reconstruction. Unlike existing GPU hash maps, the ASH framework provides a versatile tensor interface, hiding low-level details from the users. In addition, by decoupling the internal hashing data structures and key-value data in buffers, we offer direct access to spatially varying data via indices, enabling seamless integration to modern libraries such as PyTorch. To achieve this, we 1) detach stored key-value data from the low-level hash map implementation; 2) bridge the pointer-first low level data structures to index-first high-level tensor interfaces via an index heap; 3) adapt both generic and non-generic integer-only hash map implementations as backends to operate on multi-dimensional keys. We first profile our hash map against state-of-the-art hash maps on synthetic data to show the performance gain from this architecture. We then show that ASH can consistently achieve higher performance on various large-scale 3D perception tasks with fewer LoC by showcasing several applications, including 1) point cloud voxelization, 2) retargetable volumetric scene reconstruction, 3) non-rigid point cloud registration and volumetric deformation, and 4) spatially varying geometry and appearance refinement. ASH and its example applications are open sourced in Open3D (http://www.open3d.org).