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Learning Convolutional Transforms for Lossy Point Cloud Geometry Compression
Maurice Quach, Giuseppe Valenzise, Frederic Dufaux
TL;DR
Point clouds can contain millions of points, motivating efficient compression for VR and MR applications. The paper learns convolutional analysis and synthesis transforms with uniform quantization and rate-distortion optimization for static geometry. On MVUB, it reports 51.5% BDBR savings over the MPEG anchor and avoids octree methods’ exponential reduction in output points at lower bitrates.
Problem
Point cloud geometry can be extremely large, while octree-based lossy compression reduces the number of points exponentially at lower bitrates.
Method
The method uses learned convolutional analysis and synthesis transforms, uniform quantization, rate-distortion optimization, and binary voxel-occupancy decoding.
Results
51.5% BDBR savings are reported on average against the MPEG anchor on the MVUB dataset.
Takeaways & Limitations
The method maintains high-resolution outputs at low bitrates without the exponential diminution of output points observed in octree-based methods.
Abstract
from arXiv · showhide
Efficient point cloud compression is fundamental to enable the deployment of virtual and mixed reality applications, since the number of points to code can range in the order of millions. In this paper, we present a novel data-driven geometry compression method for static point clouds based on learned convolutional transforms and uniform quantization. We perform joint optimization of both rate and distortion using a trade-off parameter. In addition, we cast the decoding process as a binary classification of the point cloud occupancy map. Our method outperforms the MPEG reference solution in terms of rate-distortion on the Microsoft Voxelized Upper Bodies dataset with 51.5% BDBR savings on average. Moreover, while octree-based methods face exponential diminution of the number of points at low bitrates, our method still produces high resolution outputs even at low bitrates. Code and supplementary material are available at https://github.com/mauriceqch/pcc_geo_cnn .
1. INTRODUCTION
The paper addresses lossy compression of static point cloud geometry for VR and MR, where point clouds can contain millions of points. It proposes learned transforms that outperform the MPEG anchor while avoiding the exponential point-count reduction of octree methods at lower bitrates.
- Point clouds can contain millions of 3D points and complex attributes, making efficient compression important for practical VR and MR usage.
- The work focuses on lossy compression of static point cloud geometry because precise reconstruction supports high-quality rendering and interactive applications.
- Lossless methods struggle beyond about 2 bits per occupied voxel, creating substantial storage and transmission costs for rich point clouds.
- Octree-based lossy compression reduces point counts exponentially when octree depth is lowered.
- The proposed method learns analysis and synthesis transforms, decodes voxel occupancy through binary classification, and is trained on ModelNet40 but tested on MVUB.
- The method outperforms the MPEG anchor at all tested sequences and bitrates and generalizes across different training and testing datasets.
2. RELATED WORK
Prior point cloud compression research largely used tree-based methods or addressed dynamic point clouds. This work instead learns transforms with a 3D auto-encoder and jointly optimizes rate-distortion performance with a lightweight architecture.
- Point cloud geometry compression has mainly focused on tree-based methods and dynamic point clouds.
- The paper uses a 3D auto-encoder to compress point cloud geometry instead of relying on hand-crafted transforms.
- The method directly learns convolutional filters from data rather than specifying them manually.
- Unlike related 3D-object approaches, the paper incorporates quantization during training to jointly optimize rate-distortion performance.
- Its lightweight architecture supports voxel-grid resolutions an order of magnitude higher than previous art.
3. PROPOSED METHOD
The proposed model uses a 3D convolutional auto-encoder with learned analysis and synthesis transforms, quantization, entropy coding, and occupancy-focused distortion optimization. Training relaxes quantization with uniform noise, while decoding classifies voxel occupancy.
- 3.1. Definitions: The method represents a point cloud as an occupied-voxel grid over the discrete domain Ωr = [0..r]3.
- 3.2. Model: The architecture uses a 3D convolutional auto-encoder consisting of an analysis transform, uniform quantizer, and synthesis transform.
- 3.2. Model: Convolutions and transpose convolutions with same padding and strides form the learned analysis and synthesis transforms.
- 3.2. Model: During training, uniform noise replaces discretization for differentiability; during evaluation, latent values are integer-rounded and compressed with range coding and Deflate.
- 3.2. Model: The decoder treats each voxel as occupied or empty and uses α-balanced focal loss to address the sparsity-driven imbalance between empty and occupied voxels.
- 3.2. Model: The objective is L = λD + R, combining focal-loss distortion D with rate R measured in bits per input occupied voxel.
4. EXPERIMENTAL RESULTS
Experiments train on ModelNet40 and test intraframe compression on MVUB, comparing learned compression against the MPEG anchor using rate-distortion curves. The proposed method achieves substantially better average rate-distortion performance and preserves more output points at low bitrates.
- Datasets: The network is trained and evaluated on ModelNet40, then tested on 1,202 MVUB frames across five sequences at resolution r = 512.ModelNet40 training uses voxel-grid resolution r = 64; MVUB evaluation targets individual frames for intraframe compression.
- Evaluation protocol: Rate-distortion points average bitrate and distortion over time for each λ, while MPEG points use different octree depths.The proposed method evaluates λ values from 10^-4 through 10^-6, and distortion is measured with point-to-plane symmetric PSNR.
- Rate-distortion results: 51.5% BDBR savings are achieved on average against the MPEG anchor across all MVUB sequences and bitrates.The proposed method has mean bitrate 0.691 and mean PSNR 24.11 dB, compared with 0.719 bpov and 16.68 dB for the anchor.
- Qualitative results: At similar bitrates, the proposed method produces lower distortion and 218 times more points than the anchor in the Phil example.The example uses λ = 10^-6 for the proposed method and depth 6 for the octree anchor; their PSNR values are 29.22 dB and 23.98 dB, respectively.
- Qualitative results: The focal loss penalizes false negatives more heavily, so the model produces more points at lower bitrates while avoiding the anchor’s blocking effects.Octree-based output point counts diminish exponentially when reducing octree depth; the decompression threshold is fixed at 0.5 in these experiments.
5. CONCLUSION
The paper presents a data-driven method for lossy static point cloud geometry compression using learned convolutional transforms and uniform quantization. On MVUB, it improves rate-distortion performance over the MPEG anchor while avoiding exponential output-point diminution at lower bitrates.
- The method uses learned convolutional transforms and a uniform quantizer for data-driven point cloud geometry compression.
- 51.5% BDBR savings are achieved on average over the MPEG anchor on the MVUB dataset.
- Unlike octree-based methods, the model does not exhibit exponential diminution in output points at lower bitrates.