# Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression

arXiv: https://arxiv.org/abs/2311.13539 · HTML: https://mlsanity.com/paper/2311.13539/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 22 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Learning End-to-End Lossy Image Compression: A Benchmark](https://mlsanity.com/paper/2002.03711/) (2020)
- [Improved Deep Point Cloud Geometry Compression](https://mlsanity.com/paper/2006.09043/) (2020)
- [Deep Implicit Volume Compression](https://mlsanity.com/paper/2005.08877/) (2020)
- [Sparse Tensor-based Point Cloud Attribute Compression](https://mlsanity.com/paper/2204.01023/) (2022)
- [LVAC: Learned Volumetric Attribute Compression for Point Clouds using Coordinate Based Networks](https://mlsanity.com/paper/2111.08988/) (2021)
- [An Algorithm Unrolling Approach to Deep Image Deblurring](https://mlsanity.com/paper/1902.05399/) (2019)
- [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)
- [Transform-Aligned Learned Features for Lossy Point Cloud Attribute Compression](https://mlsanity.com/paper/2609.34834/) (2026)

## Abstract (arXiv)

We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters θ of a continuous attribute function f: ℝ3 mapsto ℝ are quantized to hatθ and encoded, so that discrete samples f_hatθ(xi) can be recovered at known 3D points xi ∈ ℝ3 at the decoder. Specifically, we consider a nested sequences of function subspaces F(p)l0 subseteq cdots subseteq F(p)L, where Fl(p) is a family of functions spanned by B-spline basis functions of order p, fl^* is the projection of f on Fl(p) represented as low-pass coefficients Fl^*, and gl^* is the residual function in an orthogonal subspace Gl(p) (where Gl(p) oplus Fl(p) = Fl+1(p)) represented as high-pass coefficients Gl^*. In this paper, to improve coding performance over citedo2023volumetric, we study predicting fl+1^* at level l+1 given fl^* at level l and encoding of Gl^* for the p=1 case (RAHT(1)). For the prediction, we formalize RAHT(1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients Gl^* amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperforms the MPEG G-PCC predictor by 11%--12% in bit rate.