# A Volumetric Approach to Point Cloud Compression

arXiv: https://arxiv.org/abs/1810.00484 · HTML: https://mlsanity.com/paper/1810.00484/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2018.

## Built on by (most cited first, 10 of 10)

- [OctAttention: Octree-Based Large-Scale Contexts Model for Point Cloud Compression](https://mlsanity.com/paper/2202.06028/) (2022)
- [LVAC: Learned Volumetric Attribute Compression for Point Clouds using Coordinate Based Networks](https://mlsanity.com/paper/2111.08988/) (2021)
- [Neural 3D Scene Compression via Model Compression](https://mlsanity.com/paper/2105.03120/) (2021)
- [Improving 3D Gaussian Splatting Compression by Scene-Adaptive Lattice Vector Quantization](https://mlsanity.com/paper/2509.13482/) (2025)
- [Volumetric Attribute Compression for 3D Point Clouds using Feedforward Network with Geometric Attention](https://mlsanity.com/paper/2304.00335/) (2023)
- [Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction](https://mlsanity.com/paper/2311.13533/) (2023)
- [Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression](https://mlsanity.com/paper/2311.13539/) (2023)
- [Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding](https://mlsanity.com/paper/2509.08685/) (2025)
- [DALD-PCAC: Density-Adaptive Learning Descriptor for Point Cloud Lossless Attribute Compression](https://mlsanity.com/paper/2601.12261/) (2026)
- [Transforming harmonic coefficients for 3D splat compression](https://mlsanity.com/paper/2609.15735/) (2026)

## Abstract (arXiv)

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Geometry is represented implicitly as the level set of a volumetric function (the signed distance function or similar). Attributes are represented by a volumetric function whose coefficients can be regarded as a critically sampled orthonormal transform that generalizes the recent successful region-adaptive hierarchical (or Haar) transform to higher orders. Experimental results show that both geometry and attribute compression using volumetric functions improve over those used in the emerging MPEG Point Cloud Compression standard.