# Region adaptive graph fourier transform for 3d point clouds

arXiv: https://arxiv.org/abs/2003.01866 · HTML: https://mlsanity.com/paper/2003.01866/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [3DAC: Learning Attribute Compression for Point Clouds](https://mlsanity.com/paper/2203.09931/) (2022)
- [Rendering-Oriented 3D Point Cloud Attribute Compression using Sparse Tensor-based Transformer](https://mlsanity.com/paper/2411.07899/) (2024)
- [Fractional Motion Estimation for Point Cloud Compression](https://mlsanity.com/paper/2202.00172/) (2022)
- [4DAC: Learning Attribute Compression for Dynamic Point Clouds](https://mlsanity.com/paper/2204.11723/) (2022)
- [Motion estimation and filtered prediction for dynamic point cloud attribute compression](https://mlsanity.com/paper/2210.08262/) (2022)
- [Joint Graph and Vertex Importance Learning](https://mlsanity.com/paper/2303.08552/) (2023)
- [Motion Estimation Techniques for Volumetric Video Attribute Compression](https://mlsanity.com/paper/2607.03576/) (2026)
- [Transform-Aligned Learned Features for Lossy Point Cloud Attribute Compression](https://mlsanity.com/paper/2609.34834/) (2026)

## Abstract (arXiv)

We introduce the Region Adaptive Graph Fourier Transform (RA-GFT) for compression of 3D point cloud attributes. The RA-GFT is a multiresolution transform, formed by combining spatially localized block transforms. We assume the points are organized by a family of nested partitions represented by a rooted tree. At each resolution level, attributes are processed in clusters using block transforms. Each block transform produces a single approximation (DC) coefficient, and various detail (AC) coefficients. The DC coefficients are promoted up the tree to the next (lower resolution) level, where the process can be repeated until reaching the root. Since clusters may have a different numbers of points, each block transform must incorporate the relative importance of each coefficient. For this, we introduce the Q-normalized graph Laplacian, and propose using its eigenvectors as the block transform. The RA-GFT achieves better complexity-performance trade-offs than previous approaches. In particular, it outperforms the Region Adaptive Haar Transform (RAHT) by up to 2.5 dB, with a small complexity overhead.