# Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction

arXiv: https://arxiv.org/abs/2311.13533 · HTML: https://mlsanity.com/paper/2311.13533/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Graph-based compression of dynamic 3D point cloud sequences](https://mlsanity.com/paper/1506.06096/) (2015)
- [A Volumetric Approach to Point Cloud Compression](https://mlsanity.com/paper/1810.00484/) (2018)
- [Bilateral Filter: Graph Spectral Interpretation and Extensions](https://mlsanity.com/paper/1303.2685/) (2013)
- [Volumetric Attribute Compression for 3D Point Clouds using Feedforward Network with Geometric Attention](https://mlsanity.com/paper/2304.00335/) (2023)

## Built on by (most cited first, 2 of 2)

- [Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding](https://mlsanity.com/paper/2509.08685/) (2025)
- [Transforming harmonic coefficients for 3D splat compression](https://mlsanity.com/paper/2609.15735/) (2026)

## Abstract (arXiv)

We extend a previous study on 3D point cloud attribute compression scheme that uses a volumetric approach: given a target volumetric attribute function f : ℝ3 mapsto ℝ, we quantize and encode parameters θ that characterize f at the encoder, for reconstruction f_hatθ(mathbf(x)) at known 3D points mathbf(x) at the decoder. Specifically, parameters θ are quantized coefficients of B-spline basis vectors Phil (for order p ≥ 2) that span the function space Fl(p) at a particular resolution l, which are coded from coarse to fine resolutions for scalability. In this work, we focus on the prediction of finer-grained coefficients given coarser-grained ones by learning parameters of a polynomial bilateral filter (PBF) from data. PBF is a pseudo-linear filter that is signal-dependent with a graph spectral interpretation common in the graph signal processing (GSP) field. We demonstrate PBF's predictive performance over a linear predictor inspired by MPEG standardization over a wide range of point cloud datasets.