[Paper Review] Comments on "Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform"

Gustavo Sandri, Ricado L. de Queiroz+1 more|arXiv (Cornell University)|May 23, 2018

3D Shape Modeling and Analysis3 references17 citations

TL;DR

This paper proposes a depth-based reordering of RAHT (Region-Adaptive Hierarchical Transform) coefficients prior to entropy coding with adaptive run-length Golomb-Rice (RLGR), significantly improving compression efficiency. The reordered RLGR-RAHT outperforms both the original AC-RAHT and state-of-the-art graph transform (GT)-based coders in rate-distortion performance while maintaining low computational complexity.

ABSTRACT

The recently introduced coder based on region-adaptive hierarchical transform (RAHT) for the compression of point clouds attributes, was shown to have a performance competitive with the state-of-the-art, while being much less complex. In the paper "Compression of 3D Point Clouds Using a Region-Adaptive Hierarchical Transform", top performance was achieved using arithmetic coding (AC), while adaptive run-length Golomb-Rice (RLGR) coding was presented as a lower-performance lower-complexity alternative. However, we have found that by reordering the RAHT coefficients we can largely increase the runs of zeros and significantly increase the performance of the RLGR-based RAHT coder. As a result, the new coder, using ordered coefficients, was shown to outperform all other coders, including AC-based RAHT, at an even lower computational cost. We present new results and plots that should enhance those in the work of Queiroz and Chou to include the new results for RLGR-RAHT. We risk to say, based on the results herein, that RLGR-RAHT with sorted coefficients is the new state-of-the-art in point cloud compression.

Motivation & Objective

• To improve the rate-distortion performance of RAHT-based 3D point cloud compression with low-complexity entropy coding.
• To address the suboptimal performance of RLGR-RAHT in the original RAHT work, which underperformed compared to arithmetic coding (AC)-based RAHT.
• To explore coefficient ordering strategies that enhance zero-run length and improve RLGR efficiency.
• To demonstrate that a simple reordering can make RLGR-RAHT competitive with or superior to more complex state-of-the-art coders.

Proposed method

• Reordering RAHT coefficients by their depth in the octree structure, from root to leaves, to group high-frequency coefficients together.
• Applying adaptive run-length Golomb-Rice (RLGR) entropy coding to the depth-sorted RAHT coefficients to exploit longer runs of zeros.
• Using a quantizer with step size Q to produce quantized coefficients before sorting and entropy coding.
• Comparing three sorting strategies: unsorted, depth-sorted, and weight-sorted (where weight reflects the number of voxels involved in coefficient generation).
• Evaluating performance using bits per voxel (bpv) and peak signal-to-noise ratio (PSNR) as metrics.
• Replacing original RAHT rate-distortion curves in [1] with new results from the depth-ordered RLGR-RAHT implementation.

Experimental results

Research questions

• RQ1 Can reordering RAHT coefficients improve the performance of RLGR-based entropy coding in 3D point cloud compression?
• RQ2 Does depth-based sorting of RAHT coefficients lead to longer zero-run lengths compared to unsorted or weight-sorted ordering?
• RQ3 Can RLGR-RAHT with depth-sorted coefficients outperform AC-RAHT in rate-distortion performance while maintaining lower complexity?
• RQ4 Is the proposed RLGR-RAHT with depth sorting competitive with or superior to the state-of-the-art graph transform (GT)-based coder?
• RQ5 Does the improved coefficient ordering reduce the need for complex arithmetic coding in RAHT-based compression?

Key findings

• Depth-sorted RLGR-RAHT achieved the best rate-distortion performance among all tested methods, outperforming both unsorted and weight-sorted variants.
• For Q=10, the depth-sorted RLGR-RAHT reduced bits per voxel from 3.1046 (unsorted) to 2.0581 on the 'Man' point cloud, a 33.7% improvement.
• At Q=40, the depth-sorted method reduced bits per voxel from 0.7638 (unsorted) to 0.5345 on the 'Man' point cloud, a 30.0% reduction.
• The depth-sorted RLGR-RAHT achieved a PSNR of 43.6176 dB on the 'Ricardo' point cloud at Q=10, outperforming the original AC-RAHT and GT-based coders.
• The proposed method achieved superior performance to the GT-based coder while maintaining lower computational complexity than AC-RAHT.
• The rate-distortion curves in Figures 4 and 5 demonstrate that depth-ordered RLGR-RAHT consistently outperforms all other coders across all test point clouds and quantization steps.