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Inferring Point Cloud Quality via Graph Similarity

Qi Yang, Zhan Ma, Yiling Xu, Zhu Li, Jun Sun

arXiv:2006.00497v2eess.IVcs.MM

TL;DR

Point-cloud quality assessment needs metrics that better reflect human sensitivity to local structure than point-wise errors alone. GraphSIM addresses this by comparing geometry-defined local graphs through aggregated color-gradient moments, and it reports strong MOS correlation across independent datasets and ablations. Its moment design has scope limits: zeroth- and first-order features do not capture motion-induced geometric variations, motivating higher-order features.

  • Problem

    Point-wise quality metrics do not accurately reflect human perception, while unstructured point clouds combine geometry and color impairments without explicit local relationships.

  • Method

    GraphSIM extracts reference-geometry keypoints, builds corresponding local graphs, aggregates zeroth-, first-, and second-order color-gradient moments, and pools similarities across channels and graphs.

  • Results

    GraphSIM demonstrates state-of-the-art MOS prediction across SJTU-PCQA and IRPC, generalizes to standard-compliant PCC technologies, and shows reliable performance across ablation settings.

  • Takeaways & Limitations

    Graph-based local structure and color-gradient aggregation provide a consistent approach to point-cloud quality assessment across varied impairments, datasets, and model settings.

  • Takeaways & Limitations

    Zeroth- and first-order moments cannot handle motion-induced geometric variations, so second-moment features are needed for such impairments.

Abstract

from arXiv · show

We propose the GraphSIM -- an objective metric to accurately predict the subjective quality of point cloud with superimposed geometry and color impairments. Motivated by the facts that human vision system is more sensitive to the high spatial-frequency components (e.g., contours, edges), and weighs more to the local structural variations rather individual point intensity, we first extract geometric keypoints by resampling the reference point cloud geometry information to form the object skeleton; we then construct local graphs centered at these keypoints for both reference and distorted point clouds, followed by collectively aggregating color gradient moments (e.g., zeroth, first, and second) that are derived between all other points and centered keypoint in the same local graph for significant feature similarity (a.k.a., local significance) measurement; Final similarity index is obtained by pooling the local graph significance across all color channels and by averaging across all graphs. Our GraphSIM is validated using two large and independent point cloud assessment datasets that involve a wide range of impairments (e.g., re-sampling, compression, additive noise), reliably demonstrating the state-of-the-art performance for all distortions with noticeable gains in predicting the subjective mean opinion score (MOS), compared with those point-wise distance-based metrics adopted in standardization reference software. Ablation studies have further shown that GraphSIM is generalized to various scenarios with consistent performance by examining its key modules and parameters.

1 INTRODUCTION

GraphSIM addresses the lack of perceptually effective point-cloud quality metrics by jointly modeling geometry and color through local graph structure. It uses geometry-derived keypoints, color-gradient moments, and pooled graph similarities, achieving strong MOS prediction across independent datasets and settings.

  • Motivation: Point-wise metrics such as PSNR do not accurately reflect human perception, while point clouds lack explicit relationships and combine geometry with attribute distortions.These properties complicate effective objective quality measurement.
  • Motivation: Human vision is frequency-selective and more sensitive to high-spatial-frequency structures, motivating quality assessment based on local structural variations.The paper emphasizes contours, edges, and local neighbor structures rather than individual point intensity.
  • Approach: GraphSIM extracts geometry-based keypoints, constructs local graphs in reference and impaired clouds, aggregates zeroth-, first-, and second-order color-gradient moments, and pools similarities across channels and graphs.Reference-derived keypoints provide a common 3D structure for comparison.
  • Evaluation: GraphSIM is evaluated on SJTU-PCQA and IRPC databases containing re-sampling, compression, additive-noise, and combined impairments using PLCC, SROCC, RMSE, and MOS comparisons.SJTU-PCQA contains 420 processed samples with individual MOS labels.
  • Results: GraphSIM demonstrates state-of-the-art MOS prediction, generalizes to standard-compliant PCC technologies, and remains reliable across ablations of mechanisms, scales, color spaces, parameters, pooling, and signal types.IRPC reports PLCC 0.94, SROCC 0.76, and RMSE 0.21 for joint People and Inanimate contents.

2 RELATED WORK

Prior point-cloud quality assessment includes subjective databases, point-wise geometry and color errors, and projection-based adaptations of image metrics. These approaches motivate graph-based modeling because unstructured points lack explicit local relationships.

  • Assessment resources: Prior work studies subjective assessment protocols, interaction mechanisms, distortion impairments, objective metrics, and publicly accessible databases such as SJTU-PCQA.SJTU-PCQA contains 420 processed samples with associated MOSs.
  • Point-wise metrics: Point-wise methods measure point-to-point, point-to-plane, or point-to-mesh geometry errors and color differences for PSNR, Hausdorff-distance, or MSE-based evaluation.These methods have also been tested under typical compression distortions.
  • Projection-based metrics: Projection-based methods map 3D point clouds to 2D planes so image metrics such as SSIM can be applied, showing improved efficiency for some impairments but requiring deeper investigation for consistent prediction.The related work presents projection as an alternative to direct point-wise measurement.

3 POINT CLOUD VIA GRAPH REPRESENTATION

The paper represents a point cloud as a graph whose vertices are points and whose weighted edges encode local geometric relationships. Graph operators then support density, gradient, and Laplacian processing of point-cloud signals.

  • Graph representation: Graph signal processing represents a point cloud by embedding local neighbor connections that characterize relationships among otherwise unstructured 3D points.This representation is motivated by local visual processing and neighbor structure.
  • Point-cloud signals: The point-cloud tuple includes 3D coordinates and RGB attributes, with geometric occupancy and color intensity treated as separate channels.The formulation allows geometry and color information to be processed distinctly.
  • Graph representation: Each point is modeled as a graph vertex, and positive-weight connections between nearby points are modeled as edges in an adjacency matrix W.The graph uses geometric distance to encode connection weights and a threshold to cluster neighbors.
  • Graph operators: A diagonal degree matrix D records each vertex’s connection density by summing its incident edge weights.D is formed as diag(d1, ..., dN).
  • Graph operators: Graph signals assign values such as RGB color intensity to vertices, while edge derivatives and graph gradients capture differences between neighboring signal values.The framework can also operate on normals or other attributes.
  • Graph operators: The graph Laplacian provides a difference operator for processing signals over the point-cloud graph.It aggregates neighboring differences through the graph’s local connections.

4 POINT CLOUD RE-SAMPLING

The method extracts high-frequency geometric keypoints that form an object's edges, contours, and skeleton, then uses them for quality assessment. A graph-filtering-based resampling strategy orders points by spatial frequency, retaining perceptually important structure while reducing computational complexity.

  • Keypoint extraction: Geometric keypoints represent the object's discriminative skeleton, including edges and contours associated with high spatial-frequency structure.These structures are emphasized because the HVS weighs structural information more heavily than individual point intensity.
  • Keypoint extraction: Keypoints are obtained by resampling the reference point cloud's geometry information and are used to construct local graphs for both point clouds.Using reference-derived keypoints provides a common 3D geometric structure for comparison.
  • Graph filtering: A graph shift operator can be instantiated from an adjacency matrix, transition matrix, or graph Laplacian, and linear shift-invariant filters are polynomial functions of that operator.The filter is written as a polynomial whose coefficients determine the graph-filter length.
  • Graph filtering: A Haar-like graph filter performs high-pass filtering so points can be ordered in the spatial-frequency domain for sampling.The formulation uses A = D^-1W, with eigenvalues and eigenvectors describing the graph-frequency representation.
  • Benefits: Re-sampled high-frequency keypoints fit the perceptual intuition and significantly reduce computational complexity for practical quality-assessment applications.Other resampling methods can also be applied in GraphSIM.

5 GraphSIM: MEASURING POINT CLOUD QUALITY VIA GRAPH SIMILARITY

GraphSIM measures point-cloud quality by comparing local graphs built around geometry-derived keypoints, combining distance-weighted color-gradient moments to capture density, contrast, and geometric variation.

  • GraphSIM develops a point-cloud quality metric using keypoint resampling, local graph construction, color-gradient aggregation, and similarity derivation.
  • 5.1 Keypoints Resampling: High-pass frequency weighting favors contour- and edge-related points as geometric keypoints, with the sampled reference keypoints reused in reference and distorted clouds.
  • 5.2 Graph Construction and Color Gradients: Distance-weighted graph gradients combine neighbor color differences with Euclidean geometry to represent local attribute variations and jointly assess geometry and color impairments.
  • 5.3.1 Zeroth Moment: Gradient Mass mg: The zeroth gradient moment reflects local point-density changes, such as downsampling-induced point loss, but remains unchanged under some geometric rotations.
  • 5.3.2 First Moment: Gradient Mean µg: The first moment normalizes gradient mass by neighbor count to measure average local contrast when density changes obscure perceptual similarity.
  • 5.3.3 Second Moment: Gradient Variance and Co-variance: The second moment captures relative signal-variation patterns that zeroth and first moments miss under geometric rotation, using point matching for corresponding locations.

6 EXPERIMENTAL EVALUATIONS

This section evaluates GraphSIM alongside five state-of-the-art metrics for predicting point cloud quality using the SJTU-PCQA and IRPC databases.

  • The evaluation compares GraphSIM with five other state-of-the-art point cloud quality metrics.
  • Two publicly accessible databases provide the evaluation data: SJTU-PCQA and IRPC.
  • The assessment focuses on point cloud quality prediction across both databases.

6.1 Subjective Point Cloud Assessment Database

The experiments use SJTU-PCQA and IRPC, which cover diverse point cloud contents, coding settings, and impairment types.

  • SJTU-PCQA: SJTU-PCQA contains five MPEG-recommended People point clouds covering varied content characteristics.The samples include “RedandBlack”, “Loot”, “Soldier”, “LongDress”, and “Hhi”.
  • SJTU-PCQA: SJTU-PCQA augments native samples with seven impairment types at six levels, including individual and combined distortions.The distortions include octree compression, color noise, geometry Gaussian noise, downsampling, and three paired combinations.
  • IRPC: IRPC provides two Inanimate and two People samples, independently collected with emphasis on compression distortions.The Inanimate samples are “Facade” and “House”; the People samples are “LongDress” and “Loot”.
  • IRPC: IRPC samples use three compression methods at three quality levels, with G-PCC and V-PCC selected for evaluation.Octree-based compression is omitted there because it is already included in SJTU-PCQA.
  • IRPC: Both G-PCC and V-PCC increase reconstructed point counts, with G-PCC sometimes doubling the original points and V-PCC adding 40%–50%.

6.2 Gaussian Color Decomposition.

The evaluation begins with Gaussian Color Model decomposition because it is suggested to relate closely to human visual-system color sensation.

  • GraphSIM first uses the Gaussian Color Model to decompose the native RGB signal.
  • The Gaussian Color Model is selected because it is suggested to be more closely related to human visual-system color sensation.
  • The decomposition produces luminance and two chrominance components, denoted bE, bEλ, and bEλλ.

6.3 Model Parameters.

GraphSIM uses parameters associated with resampling, local graph construction, and similarity pooling, with settings intended to balance efficiency, complexity, and color-component importance.

  • GraphSIM has parameters associated with its different processing stages.
  • Resampling: Resampling uses β = N/1000 and L = 4 to balance efficiency and complexity.
  • Local Graph Construction: Local graph construction sets θ from the reference bounding-box scale and determines τ from distances among up to 50 nearest neighbors.σ is then defined as a function of τ for the adjacency matrix and corresponding graphs.
  • Similarity Pooling: Similarity pooling sets T0, T1, and T2 to 0.001 and weights luminance over the two chrominance components as [6, 1, 1].
  • The parameters are fixed constants or can be derived from signal statistics, making GraphSIM lightweight and straightforward for practical applications.

6.4 Performance Evaluation.

GraphSIM is evaluated against five MPEG-adopted metrics on SJTU-PCQA and IRPC databases using PLCC, SROCC, and RMSE. It generally provides more consistent MOS prediction, especially for combined geometry and color impairments.

  • SJTU-PCQA Database: GraphSIM leads SJTU-PCQA People-category evaluation across impairments with (PLCC, SROCC, RMSE) = (0.89, 0.88, 1.13).The comparison metrics report lower or less balanced performance, including M-p2po at (0.89, 0.79, 1.11).
  • SJTU-PCQA Database: GraphSIM maintains robust correlations across contents and impairments, whereas competing metrics vary substantially across cases.M-p2po has comparable PLCC for several contents but noticeably lower SROCC than GraphSIM.
  • Impairment Superimposition: Geometry-only metrics cannot evaluate color impairments, while PSNRYUV handles color noise but performs poorly when geometric distortion is present.PSNRYUV reports (PLCC, SROCC, RMSE) = (0.97, 0.94, 0.48) for CN but (0.54, 0.52, 1.52) for OT.
  • Scatter Plot: Scatter plots show GraphSIM predictions closer to the perfect-prediction line than point-wise distance-based metrics.The solid y = x line represents perfect prediction, while many competing predictions lie farther away.

7 ABLATION STUDIES

Ablation studies test GraphSIM across color spaces, resampling methods, graph parameters, pooling strategies, and signal attributes. The model remains broadly robust, with performance depending on parameter and pooling choices.

  • Overview: GraphSIM generalizes across resampling, graph scale, color space, model parameters, pooling methods, and signal types.The ablation program dissects and reassembles the model modules to examine generalization and efficiency.
  • Neighbor Dimension and Graph Scale: Performance improves with larger neighbor dimension θ and becomes stable when θ_B ≥0.05.Graph scale also improves gradually as k increases before stabilizing.
  • Pooling Methods: C1, using averaging for feature and channel pooling, achieves the best quantitative result, while C4 causes PLCC and RMSE degradation.SROCC remains relatively consistent because multiplication and averaging preserve sample monotonicity.
  • Signal Attributes: GraphSIM remains competitive with different signal attributes, achieving (PLCC, SROCC, RMSE) = (0.8836, 0.8028, 1.1557) for normal attributes.Mixed attributes achieve PLCC above 0.93 and SROCC above 0.92, while coordinate signals slightly reduce SROCC.
  • Graph Construction: Geometry-only graph construction performs better than combining geometry and color attributes for graph construction in the tested signal types.The study reports no clear advantage from mixing geometry and attribute information when constructing graphs.

8 CONCLUSION

The paper addresses instability and perceptual limitations in point-wise point-cloud quality metrics by introducing GraphSIM, which jointly models geometry and color through local graph similarities. Evaluations across two independent databases and ablations report reliable MOS correlation and generalization, while geometry-only extension remains future work.

  • Conclusion: Existing MPEG point-wise metrics are unstable across contents and distortions and do not adequately reflect human visual perception.The paper identifies the lack of an efficient objective metric for perceptual point-cloud quality prediction.
  • Conclusion: GraphSIM extracts high-frequency geometric keypoints, constructs local graphs, aggregates color gradients, and pools similarities across channels and graphs.The method jointly considers geometry and color distortions using a common local graph framework.
  • Conclusion: GraphSIM shows consistent MOS correlation on two independent databases with gains over state-of-the-art metrics used in MPEG reference software.Ablation studies support generalization, and parameters are described as fixed or directly dependent on input signals.
  • Future Work: Extending GraphSIM to geometry-only point clouds and applying it to MPEG compression rate-distortion optimization remain future research directions.These directions are presented as avenues for further exploration rather than established capabilities.
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