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Improved Deep Point Cloud Geometry Compression

Maurice Quach, Giuseppe Valenzise, Frederic Dufaux

arXiv:2006.09043v2cs.CVcs.LGeess.IVeess.SPstat.ML

TL;DR

Large point clouds impose substantial storage and transmission costs, motivating lossy geometry compression. The paper improves deep point-cloud compression with several model and decoding changes and an ablation study; its final model reports BD-PSNR gains over G-PCC trisoup and octree on both D1 and D2.

  • Problem

    Large point clouds create substantial storage and transmission costs, making point-cloud compression important in practice.

    Source: §I · p. 1

  • Method

    The paper improves deep convolutional compression of static point-cloud geometry with a scale hyperprior, deeper transforms, focal-loss reweighting, optimal decoding thresholds, and sequential training.

    Source: §I · p. 1, B. Deeper transforms (c3) · p. 3

  • Results

    The final model achieves average BD-PSNR gains over G-PCC trisoup of 5.50 dB on D1 and 6.48 dB on D2, and over G-PCC octree of 6.84 dB on D1 and 5.95 dB on D2.

    Source: B. Experimental results · p. 4, §V · p. 6

  • Takeaways & Limitations

    The ablation study identifies the individual effects of the proposed factors and examines why they improve rate-distortion performance.

    Source: §V · p. 6

Abstract

from arXiv · show

Point clouds have been recognized as a crucial data structure for 3D content and are essential in a number of applications such as virtual and mixed reality, autonomous driving, cultural heritage, etc. In this paper, we propose a set of contributions to improve deep point cloud compression, i.e.: using a scale hyperprior model for entropy coding; employing deeper transforms; a different balancing weight in the focal loss; optimal thresholding for decoding; and sequential model training. In addition, we present an extensive ablation study on the impact of each of these factors, in order to provide a better understanding about why they improve RD performance. An optimal combination of the proposed improvements achieves BD-PSNR gains over G-PCC trisoup and octree of 5.50 (6.48) dB and 6.84 (5.95) dB, respectively, when using the point-to-point (point-to-plane) metric. Code is available at https://github.com/mauriceqch/pcc_geo_cnn_v2 .

I. INTRODUCTION

The paper targets lossy compression of static point-cloud geometry with deep convolutional networks, motivated by the storage and transmission costs of large point clouds. It proposes several ways to improve rate-distortion performance and training efficiency, and evaluates their individual effects.

I. INTRODUCTION

  • The work targets lossy compression of static point-cloud geometry using deep convolutional networks, addressing the storage and transmission costs of large point clouds.The authors also present an ablation study of the proposed factors.Source: §I · p. 1
  • The proposed improvements include a scale hyperprior for entropy coding, deeper transforms, and a changed focal-loss balancing weight.The focal-loss study varies α for the unbalanced voxel classification problem.Source: §I · p. 1
  • The decoding method selects an optimal occupancy threshold to minimize a given distortion metric rather than using a fixed threshold.The fixed-threshold approach is the one used in the cited baseline.Source: §I · p. 1
  • Sequential training fine-tunes the model from the previous rate-distortion point, making training up to 8 times faster than training independently while improving rate-distortion performance.The study also evaluates the individual impact of the proposed factors.Source: §I · p. 1
  • The paper presents an efficient octree partitioning algorithm that is significantly faster than recursive octree partitioning.Source: §I · p. 1

II. RELATED WORK

The related work spans traditional static geometry compression, learned image compression, and deep point-cloud compression. The paper distinguishes its broader study of rate-distortion factors from prior work on DPCC latent-space behavior.

II. RELATED WORK

  • Octree methods efficiently partition 3D space and suit lossless coding, but pruning levels in lossy coding can sharply increase distortion; learned approximation models are another approach.Prior alternatives include triangle and planar surface models, graph-based enhancement layers, and volumetric functions.Source: §II · pp. 1–2
  • Deep image compression introduced learned entropy models and later scale hyperpriors that model spatial correlations in latent representations; this paper applies these techniques to point clouds.The scale hyperprior predicts Gaussian standard deviations with a dedicated network.Source: §II · p. 2
  • Prior DPCC work studies lossy geometry, lossless geometry, and attributes, while the closest study examines latent-space characteristics rather than broad rate-distortion performance factors.The cited work seeks to identify key rate-distortion factors on a larger scale.Source: §II · p. 2

III. PROPOSED IMPROVEMENTS

The proposed improvements build on a baseline deep point-cloud compression network and use octree partitioning to handle large point clouds. The entropy-model variant adds a scale hyperprior to better model spatial dependencies.

III. PROPOSED IMPROVEMENTS

  • Octree partitioning divides point clouds into 64 × 64 × 64 voxel blocks, a trade-off between memory use and coding performance, because the baseline's shallow transforms cannot handle large point clouds within memory limits.The proposed conditions are labeled c2 through c6.Source: §III · p. 2

A. Entropy modeling (c2)

  • The hyperprior model supplements the baseline analysis and synthesis transforms with a quantized hyperprior branch that predicts standard deviations for modeling the latent representation.The model uses a learned density model for z, and the hyperprior is intended to model spatial dependencies better than the baseline learned entropy model.Source: A. Entropy modeling (c2) · p. 2
  • Training jointly optimizes rate and distortion as R + λD, with a model specialized to each rate-distortion trade-off.Because quantization is nondifferentiable, additive uniform noise replaces quantization during training.Source: A. Entropy modeling (c2) · p. 2

B. Deeper transforms (c3)

The method deepens the analysis and synthesis transforms while retaining shallow hyper-analysis and hyper-synthesis transforms. The deep transforms use residual blocks and progressively more filters to compensate for spatial downsampling.

B. Deeper transforms (c3)

  • Hyper-analysis and hyper-synthesis remain shallow while the analysis and synthesis transforms are deepened.Source: B. Deeper transforms (c3) · pp. 2–3
  • Figure 2 specifies each transform layer by convolution type, filter count, filter size, and stride.Source: Figure 2 · p. 3
  • Deep analysis and synthesis transforms use residual blocks and progressively increasing filter counts to compensate for spatial downsampling.The stated filter relationship is N1/4 = N2/2 = N3; experiments set N3 = 64.Source: B. Deeper transforms (c3) · p. 3

C. Changing the balancing weight in the focal loss (c4)

Voxelized point clouds are highly imbalanced, with most voxels empty, so the method uses focal loss and examines its α balancing weight. Experimentally, lower α values can improve coding gains, which the authors hypothesize relates to focal loss’s emphasis on hard examples.

C. Changing the balancing weight in the focal loss (c4)

  • Usually more than 95% of voxels are empty, creating a class imbalance that can lead the network to converge to empty outputs.Source: C. Changing the balancing weight in… · p. 3
  • Focal loss addresses class imbalance through α-balancing and distinguishes easy from hard examples through γ.At γ = 0, focal loss is equivalent to weighted binary cross-entropy.Source: C. Changing the balancing weight in… · p. 3
  • Lower α values experimentally provide better coding gains; the authors hypothesize that γ = 2 already emphasizes hard examples and partly alleviates imbalance.The α parameter governs attention to occupied versus empty voxels; high α makes occupied voxels marked empty more costly and yields denser reconstructions.Source: C. Changing the balancing weight in… · p. 3

D. Optimal thresholding for decoding (c5)

Instead of using the baseline fixed threshold of 0.5, the method selects a threshold for each decoded voxel block by minimizing a distortion metric. The selected threshold is sent as side information with a small bitrate overhead.

D. Optimal thresholding for decoding (c5)

E. Sequential training (c6)

Sequential training initializes each successive rate-distortion model from the previously trained model, addressing the cost of independently training a model for every tradeoff. The c6 condition consistently outperforms the other experimental conditions.

E. Sequential training (c6)

  • Sequential training uses previously trained network weights to speed training and improve rate-distortion performance.Training each tradeoff independently requires a separate model; the abstracted procedure is reported to make training up to 8 times faster.Source: E. Sequential training (c6) · p. 3
  • c6 consistently outperforms all other experimental conditions in BD-PSNR comparisons against G-PCC trisoup and octree.Source: Table II · p. 4
  • Table II reports BD-PSNR for each condition against both G-PCC trisoup and octree, listing the trisoup value before the octree value.Source: Table II · p. 4
  • Each subsequent λ tradeoff is trained from the weights of the preceding model, proceeding from low distortion and high bitrate toward lower bitrates.Source: E. Sequential training (c6) · p. 4

IV. EXPERIMENTS

Experiments evaluate six improvement strategies using four MPEG CTC point clouds, with G-PCC trisoup and octree as baselines. Models are trained on selected ModelNet40 blocks.

A. Experimental setup

  • The evaluation uses “longdress”, “loot”, “redandblack” and “soldier”, four point clouds specified in the MPEG CTCs.Source: A. Experimental setup · p. 4
  • Training data comes from the 4,000 largest blocks, at resolution 64, selected from the 200 largest voxelized ModelNet40 point clouds at resolution 512.Training uses λ values from 5 × 10−6 to 3 × 10−4.Source: A. Experimental setup · p. 4
  • Conditions are evaluated against G-PCC trisoup and octree using G-PCC v10.0 and the “mpeg-pcc-dmetric” tool for D1 and D2.The implementation uses Python 3.6.9, TensorFlow 1.15.0 and the Adam optimizer.Source: A. Experimental setup · p. 4

B. Experimental results

The final condition c6 improves over both G-PCC baselines, while ablations quantify the contributions of the hyperprior, deeper transforms, focal-loss weighting, optimal thresholding and sequential training.

B. Experimental results

  • 1.68 dB (D1) and 2.73 dB (D2) improvement over c4 from optimal thresholding; it selects separate reconstructions for the two distortion metrics.Source: B. Experimental results · p. 4

C. Ablation study

  • 0.47 dB (D1) and 0.77 dB (D2) improvement over c1 from the hyperprior; deeper transforms then add 2.04 dB (D1) and 2.81 dB (D2) over c2.Source: C. Ablation study · p. 4
  • α = 0.75 for D1 and α = 0.50 for D2 increase RD performance across all point clouds; α = 0.75 improves over α = 0.90 by 1.92 dB (D1) and 2.49 dB (D2).Higher α yields denser reconstructions favored by D1, while lower α yields sparser ones favored by D2.Source: C. Ablation study · p. 4

B. Experimental results

  • 5.50 dB (D1) and 6.48 dB (D2) over G-PCC trisoup, and 6.84 dB (D1) and 5.95 dB (D2) over G-PCC octree; c6 consistently outperforms both.The lowest-bitrate c6 point is excluded from BD-PSNR computations to keep integration intervals consistent.Source: B. Experimental results · p. 4, Figure 3 · p. 5

C. Ablation study

  • Fig. 4 compares c6 and G-PCC Trisoup decompressions and D1 squared-error maps for “soldier_vox10_0690”, reporting D1 PSNR and bits per input point.The displayed errors use a color scale and are truncated at the 99th percentile (3.0).Source: Figure 4 · p. 5
  • Up to 8 times faster, sequential training reduces each model’s training time from 4 hours to 30–60 minutes and improves over c5 by 0.11 dB (D1) and 0.06 dB (D2).Fig. 5 compares bits per point and focal loss for independent and sequential training; sequential training reuses previously trained models.Source: C. Ablation study · p. 6, Figure 5 · p. 6

V. CONCLUSION

The conclusion identifies five DPCC performance factors and reports that their final combination c6 outperforms both G-PCC baselines on D1 and D2.

V. CONCLUSION

  • 5.50 dB (D1) and 6.48 dB (D2) average BD-PSNR gains over G-PCC trisoup for c6.Source: §V · p. 6
  • 6.84 dB (D1) and 5.95 dB (D2) average BD-PSNR gains over G-PCC octree for c6.Source: §V · p. 6
  • The ablation study examines scale hyperprior models, deep transforms, focal-loss α, optimal thresholding and sequential training as RD-performance factors.Source: §V · p. 6
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