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Sparse Tensor-based Multiscale Representation for Point Cloud Geometry Compression

Jianqiang Wang, Dandan Ding, Zhu Li, Xiaoxing Feng, Chuntong Cao, Zhan Ma

arXiv:2111.10633v2cs.CVeess.IV

TL;DR

Point cloud geometry compression must handle irregular, diverse inputs while balancing efficiency, complexity, and generalization. SparsePCGC uses multiscale sparse tensors with SOPA and SLNE to model occupancy from cross-scale and local context, achieving strong lossless and lossy results across dense and LiDAR datasets. Its unified design also reports low computational and storage complexity, though multi-stage SOPA can impose prohibitive runtime.

  • Problem

    Existing learning-based point cloud compression methods face a trade-off among coding efficiency, complexity, and generalization across dense or sparse inputs and lossless or lossy modes.

  • Method

    SparsePCGC compresses multiscale sparse-tensor voxelizations using sparse convolutions, SOPA occupancy estimation, and SLNE local-neighborhood features.

  • Results

    SparsePCGC achieves state-of-the-art lossless and lossy compression across dense and LiDAR datasets, including 95.2% and 90.9% average BD-Rate improvement for dense PCGs under D1 and D2.

  • Takeaways & Limitations

    A shared SparsePCGC model supports diverse point clouds and both compression modes while using sparse computation and shared scale-wise parameters.

  • Takeaways & Limitations

    Multi-stage SOPA relies on strict autoregressive decoding dependencies, yielding unbearable runtime.

Abstract

from arXiv · show

This study develops a unified Point Cloud Geometry (PCG) compression method through the processing of multiscale sparse tensor-based voxelized PCG. We call this compression method SparsePCGC. The proposed SparsePCGC is a low complexity solution because it only performs the convolutions on sparsely-distributed Most-Probable Positively-Occupied Voxels (MP-POV). The multiscale representation also allows us to compress scale-wise MP-POVs by exploiting cross-scale and same-scale correlations extensively and flexibly. The overall compression efficiency highly depends on the accuracy of estimated occupancy probability for each MP-POV. Thus, we first design the Sparse Convolution-based Neural Network (SparseCNN) which stacks sparse convolutions and voxel sampling to best characterize and embed spatial correlations. We then develop the SparseCNN-based Occupancy Probability Approximation (SOPA) model to estimate the occupancy probability either in a single-stage manner only using the cross-scale correlation, or in a multi-stage manner by exploiting stage-wise correlation among same-scale neighbors. Besides, we also suggest the SparseCNN based Local Neighborhood Embedding (SLNE) to aggregate local variations as spatial priors in feature attribute to improve the SOPA. Our unified approach not only shows state-of-the-art performance in both lossless and lossy compression modes across a variety of datasets including the dense object PCGs (8iVFB, Owlii, MUVB) and sparse LiDAR PCGs (KITTI, Ford) when compared with standardized MPEG G-PCC and other prevalent learning-based schemes, but also has low complexity which is attractive to practical applications.

1 INTRODUCTION

Point clouds are flexible but difficult to compress because their irregular 3D occupancy limits spatial-correlation modeling. SparsePCGC addresses this with multiscale sparse tensors, SOPA probability estimation, and SLNE neighborhood features for unified, efficient compression.

  • Motivation: Point clouds encode arbitrary 3D shapes flexibly, but irregularly scattered occupancy complicates efficient geometric coding.The paper targets both lossless and lossy point cloud geometry compression.
  • Motivation: Existing learning-based methods improve coding efficiency but often have high complexity or limited generalization across density and compression modes.The stated need combines coding efficiency, affordable complexity, and robust model generalization.
  • Proposed approach: SparsePCGC represents voxelized point clouds with multiscale sparse tensors and processes only Most-Probable Positively-Occupied Voxels.Dyadic sampling progressively downscales and upscales sparse tensors for hierarchical reconstruction.
  • Proposed approach: SOPA estimates MP-POV occupancy probabilities using cross-scale context and, in multi-stage operation, previously decoded same-scale neighbors.Single-stage and multi-stage SOPA provide a performance-complexity tradeoff.
  • Proposed approach: SLNE embeds local spatial variations as feature attributes so SOPA can use both decoded occupancy status and latent features during upsampling.The module is introduced to improve probability estimation by adding local spatial information.
  • Results: SparsePCGC reports state-of-the-art lossless and lossy performance across dense and LiDAR datasets while maintaining low computational and parameter-storage complexity.The same model is shared across scales, and reported encoding/decoding runtime is about 1–2 seconds per large-scale frame.

2 RELATED WORK

Prior point cloud compression methods use uniform voxels, octrees, hybrids, or point-wise representations, each with distinct efficiency and complexity trade-offs. SparsePCGC instead exploits sparse tensors and sparse convolutions to reduce computation while retaining spatial context modeling.

  • Existing representations: Uniform-voxel methods apply dense convolutions across all voxels, including empty ones, causing redundant storage and computation.They commonly use dense convolutional autoencoders with entropy coding at quantized latent features.
  • Existing representations: Octree methods progressively represent occupied voxels and model parent-child dependencies, but isolated sparse points create hierarchy-signaling overhead.This overhead constrains octree efficiency despite adaptive decomposition.
  • Existing representations: Hybrid approaches supplement octree dependencies with sibling organization under uniform voxels or sequential processing with Transformers.These methods report compression improvements by combining representation and context-modeling strategies.
  • Existing representations: Point-wise methods avoid voxelization and can have low complexity, but they perform poorly at high bit rates and struggle with large-scale generalization.Their limited generalization also contributes to difficulty supporting diverse compression scenarios.
  • Sparse representation: SparsePCGC uses sparse tensors indexed by MP-POV coordinates and sparse convolutions that operate only on valid sparse voxels.The method uses a hash map and auxiliary structure to index coordinates and manage connections efficiently.
  • Sparse representation: Sparse convolution reduces space and time complexity relative to dense convolution, with the implementation supporting downscaling and upscaling operators.The paper selects MinkowskiEngine for its operator and platform support, while noting other implementations are possible.

3 MULTISCALE SPARSE TENSOR-BASED PCGC

SparsePCGC represents point-cloud geometry with multiscale sparse tensors and estimates MP-POV occupancy probabilities using SparseCNN-based SOPA variants. Multi-Stage SOPA exploits same-scale causal neighbors, while SLNE adds local spatial features as priors.

  • Framework: SparsePCGC uses encoder–decoder processing over a multiscale sparse-tensor representation of point-cloud geometry.Dyadic voxel sampling supports progressive scaling between adjacent resolutions.
  • Framework: Each preceding-scale POV expands into eight MP-POVs whose occupancy statuses are compressed by the encoder and reconstructed by the decoder.MP-POVs form a superset containing possible POVs and NOVs before occupancy decisions are decoded.
  • Basic SparseCNN Blocks: SparseCNN blocks use sparse convolutions, voxel sampling, feature aggregation, and occupancy output layers while computing only on sparse POV or MP-POV locations.The OOL derives occupancy probabilities for dense object point clouds and offsets for sparse LiDAR variants.
  • Multi-Stage SOPA: Multi-Stage SOPA progressively estimates MP-POV probabilities by combining preceding-scale context with already processed same-scale causal neighbors.Groups are processed stage by stage, while elements within the same group can be processed in parallel.
  • Multi-Stage SOPA: Fully autoregressive n-Stage SOPA imposes strict causal dependencies during decoding, producing unbearable runtime according to the supplemental discussion.This motivates practical grouping schemes such as 8-Stage processing with concurrent elements within each stage.
  • SLNE Enhanced SOPA: SLNE aggregates local neighborhood variations into feature attributes that are compressed and decoded as spatial priors to improve SOPA probability estimation.The encoder learns these features from known ground-truth labels at each scale.

4 UNIFIED LOSSLESS AND LOSSY COMPRESSION

SparsePCGC extends its lossless SOPA framework to lossy compression with probability thresholding, while using position-offset adjustment for sparse LiDAR point clouds. The unified system combines lossless low-resolution scales with lossy higher-resolution scales.

  • Unified Lossless and Lossy Compression: SparsePCGC extends lossless SOPA to lossy compression using different strategies for dense and sparse point clouds.The strategies account for their diverse characteristics, including point density and bit precision.
  • Lossy Compression: Lossy SOPA thresholds MP-POV occupancy probabilities to classify voxels as POVs or NOVs, with distortion arising from false classifications.The threshold is adapted according to the number of POVs at each scale.
  • Lossy Compression: One-Stage SOPA is selected for lossy compression because Multi-Stage SOPA can accumulate errors from earlier false classifications across succeeding stages.Succeeding-stage probability estimation depends on preceding-stage outcomes.
  • Sparse LiDAR Compression: Probability-thresholding lossy SOPA works for dense point clouds but fails for LiDAR because extreme sparsity makes higher-scale occupancy estimation inefficient.Sparse LiDAR therefore uses SOPA (Position), which directly estimates coordinate offsets.
  • Sparse LiDAR Compression: SOPA (Position) adjusts coordinates without increasing the number of POVs, reflecting the distribution characteristics of LiDAR sequences.Position-offset adjustment is described as optional post-processing for compression-performance evaluation.
  • Unified Compression Strategy: In lossy mode, the system codes the first m scales losslessly and the remaining N−m scales lossily to balance rate and distortion.The paper states that lossy coding at all scales causes severe reconstruction degradation without noticeable rate benefit.

5 TRAINING

SparsePCGC training uses ShapeNet and KITTI-derived datasets to cover dense object and sparse LiDAR point clouds, with augmentation across geometry scales. SOPA estimates occupancy probabilities, while SLNE-enhanced variants use combined occupancy and feature-rate objectives; sparse LiDAR position models use coordinate MSE.

  • ShapeNet and KITTI generate training datasets for dense object and sparse LiDAR point clouds, respectively.
  • Geometry precision affects point-cloud variance, density, and compression efficiency, motivating randomized scaling and multiscale supervision.Training applies random scaling followed by dyadic voxel downscaling to produce labels at multiple scales.
  • SOPA models are trained across two consecutive scales and reused across all inference scales, while SLNE parameters are fixed when training multi-stage SOPA.Joint SLNE and SOPA optimization uses a gradually increased feature-rate weight for convergence.
  • SOPA estimates MP-POV occupancy probabilities for lossless coding or lossy binary classification using binary cross-entropy.The occupancy symbol is 1 for a POV and 0 for a NOV.
  • SLNE-enhanced SOPA combines binary cross-entropy with feature-attribute rate, whereas sparse LiDAR SOPA (Position) uses coordinate mean squared error.The Position model directly outputs occupancy position offsets for upscaled sparse tensors.

6.1 Test Setup

Evaluation uses MPEG PCC test content spanning dense objects and sparse LiDAR sequences, with comparisons following MPEG common test conditions. Runtime is measured on specified CPU/GPU hardware, so timing comparisons provide an intuitive rather than implementation-independent complexity reference.

  • MPEG PCC datasets provide evaluation content, including diverse dense-object samples and sparse KITTI and Ford LiDAR sequences.KITTI uses separate training and testing sequences, while all three Ford sequences are tested.
  • G-PCC anchor results follow MPEG common test conditions using reference software TMC13-v14 with the octree codec enabled.Angular coding is disabled for LiDAR compression under the stated evaluation assumption.
  • Table 2 reports lossless compression performance in bits per point and runtime seconds for SOPA variants on 8iVFB samples.Encoding and decoding times are averaged per frame, with sparse convolution settings k = 3 and C = 32.
  • Runtime comparisons use an Intel Xeon Silver 4210 CPU and Nvidia RTX 2080 GPU, and therefore mainly provide an intuitive complexity reference.Implementation differences include CPU versus GPU execution and C/C++ versus Python implementations.

6.2 SparsePCGC Presets

SparsePCGC offers configurable SOPA and SLNE presets that trade compression efficiency against runtime, with different strategies for dense and sparse point clouds. Eight-stage SOPA is selected for lossless coding, while lossy coding uses SLNE-enhanced SOPA for dense PCGs and position prediction for sparse PCGs.

  • Lossless Mode: 8-stage SOPA achieves 38.5% compression gain over the G-PCC anchor, while n-stage SOPA reaches 39.3% but requires approximately 2 hours to decode.The sequential autoregressive dependency makes n-stage decoding impractical despite its slightly better gain.
  • Lossless Mode: 3-stage and 8-stage SOPA require roughly 1–2 seconds to encode or decode an 8iVFB frame, compared with G-PCC times of 5.88 seconds encoding and 3.34 seconds decoding.The comparison is hardware-dependent because SparsePCGC runs on GPU while G-PCC mainly runs on CPU.
  • Lossless Mode: SLNE raises coding efficiency from a 5.5% loss with one-stage SOPA to a 25.1% gain, and to a 35.3% gain when combined with three-stage SOPA.Its improvement over multi-stage SOPA alone becomes negligible at eight stages because both exploit local-neighborhood correlations.
  • Lossless Mode: Eight-stage SOPA is chosen for lossless SparsePCGC because it combines low complexity and superior compression performance, while training SOPA alone is about 2× faster.SLNE-enhanced three-stage SOPA is identified as another promising candidate but is not selected as the lossless default.
  • Configuration Trade-offs: For dense point clouds, k = 3 and C = 32 gives the best tested result, while k = 3 and C = 16 reduces model size from 4.89 MB to 1.31 MB with less than one percentage-point loss.Sparse LiDAR compression benefits from larger kernels; comparing k = 5 with k = 3 yields about 10 absolute percentage points.
  • Lossy Mode: Lossy dense coding uses SLNE-enhanced one-stage SOPA followed by one-stage SOPA, whereas sparse coding uses SOPA (Position) to upscale directly to the highest scale.The scale factor m is varied more extensively for sparse LiDAR point clouds than for dense point clouds.

6.3 Performance Evaluation and Comparison

SparsePCGC improves compression efficiency over G-PCC and several learning-based methods across dense and sparse point clouds, while runtime depends on point-cloud sparsity and compression mode.

  • Comparison to G-PCC: 38.2% average and 42.1% maximum compression-ratio gains over G-PCC are reported for dense point clouds in lossless mode.Gains are lower for sparse point clouds because their spatial distribution makes interpoint correlations harder to capture.
  • Comparison to G-PCC: 95.2% and 90.9% average BD-Rate improvements over G-PCC are achieved for dense PCGs under D1 and D2, respectively.For sparse PCGs, the corresponding gains are 28.6% and 36.2%.
  • Runtime Evaluation: Encoding and decoding are about 2–3× faster than G-PCC on dense object point clouds but about 2–3× slower on sparse LiDAR point clouds in lossless mode.Dense lossy encoding exceeds 9× speedup, whereas sparse LiDAR runtime is favored by G-PCC’s dedicated isolated-point tools.
  • Runtime Evaluation: Runtime comparisons are confounded by different implementations and hardware: G-PCC uses C++/C on CPU, while SparsePCGC uses Python on an RTX 2080 GPU.The authors defer fuller consideration of implementation details and optimization levels to future work.
  • Comparison to other Learning-based Solutions: 44.2% average gain on 8iVFB and 37.7% on MVUB exceed MsVoxelDNN and fNNOC by more than 20 absolute percentage points.Against OctAttention, SparsePCGC gains approximately 7–10 absolute percentage points while using only a limited local receptive field.
  • Comparison to other Learning-based Solutions: SparsePCGC speeds up MsVoxelDNN and fNNOC by at least 20×, while OctAttention decoding is more than 500× slower.OctAttention retains the fastest encoding among the compared learning-based methods.

6.4 Discussion

SparsePCGC addresses the challenge of compressing diverse point clouds with one model by exploiting unstructured-point sparsity and multiscale spatial correlations.

  • Motivation: Diverse acquisition techniques produce point clouds with widely varying density, volume, precision, and noise, making one efficient compression model difficult.Existing solutions therefore use different models or tools for different inputs.
  • Unified Model: SparsePCGC is a unified model that compresses diverse point clouds in both lossy and lossless modes by exploiting the sparsity of unstructured points.The discussion attributes this capability mainly to the proposed representation and context-modeling design.
  • Sparse Representation: Sparse convolutions process points directly without scene priors, reducing complexity while aggregating valid local neighbors within the receptive field.This design is intended to support arbitrarily distributed points in 3D space.
  • Multiscale Representation: Multiscale representation constructs scale-wise data through resolution rescaling and exploits cross-scale correlations to embed local spatial information.The resulting context modeling uses information from multiple resolutions rather than relying only on a single representation scale.
  • Model Sharing: Model sharing across scales reduces parameter storage; the lossless mode uses one 4.9 MB 8-Stage SOPA model for dense and sparse point clouds.Lossy configurations use separate SOPA and SLNE-enhanced components with the reported model sizes.

7 CONCLUSION AND FUTURE WORK

The paper concludes that SparsePCGC combines strong compression performance across diverse point-cloud settings with low computational and parameter-storage demands. Future work targets attributes, dynamic point clouds, and perceptually aligned quality metrics.

  • Conclusion: SparsePCGC achieves state-of-the-art lossless and lossy compression across dense and sparse datasets against G-PCC and learning-based methods.Evaluated datasets include 8iVFB, Owlii, MVUB, KITTI, and Ford.
  • Conclusion: Sparse convolutions lower computational consumption, while sharing one model across scales reduces storage for model parameters.These advantages are identified as practical benefits of the unified approach.
  • Future Work: Future work includes RGB attribute compression, motion capture for dynamic point clouds, and quality metrics closer to human perception for loss optimization.These topics define the stated scope for extending the current geometry-compression study.
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