MS-ISSM: Implicit Quality Assessment for Point Clouds

• The paper introduces a novel multi-scale implicit method for quality assessment, bypassing error-prone pointwise matching using RBF interpolation.
• It leverages continuous feature representations across high, medium, and low resolutions, enhancing sensitivity to geometric and attribute distortions.
• A specialized ResGrouped-MLP regression network integrates grouped encoding and channel-wise attention to achieve superior correlation with human perceptual judgments.

Multi-scale Implicit Structural Similarity Measurement (MS-ISSM) is a state-of-the-art approach for objective quality assessment of point clouds, designed to robustly quantify perceptual quality across geometric and attribute distortions. Unlike traditional methods that rely on explicit pointwise correspondence, MS-ISSM leverages continuous implicit feature interpolation via radial basis functions (RBFs), operating across multiple spatial resolutions and perceptual modalities. The framework is tightly integrated with a specialized regression network, ResGrouped-MLP, which is optimized to map complex multiscale distortion patterns to human-aligned quality scores (Chen et al., 3 Jan 2026).

1. Radial Basis Function Implicit Feature Representation and Distortion Measurement

MS-ISSM forgoes explicit point-to-point matching, which is error-prone on unstructured and irregular point cloud data. Instead, for each reference point, a continuous local function is fitted using RBF interpolation over neighboring points. For each feature $F\in\{\mathrm{Cu},Y,\mathrm{Cr}\}$ (curvature, luma, chroma) and spatial scale $\beta\in\{\mathrm{H},\mathrm{M},\mathrm{L}\}$ (high, medium, low), the implicit local feature function is constructed as:

$$f_{F}^{\alpha,\beta}(\hat{p}) = \eta_{F}^{\alpha,\beta}(\hat{p}) + \sum_{n=1}^{N^{\alpha,\beta}} \omega_{F,n}^{\alpha,\beta} \, \phi^{\alpha,\beta}(\|\hat{p} - \hat{p}_n^{\alpha,\beta}\|_2),$$

where $\hat{p}$ are normalized spatial coordinates and $\phi(r)$ is the chosen RBF (such as Gaussian or thin-plate spline). The polynomial term $\eta_{F}^{\alpha,\beta}(\hat{p})$ often takes degree 1–3 forms, ensuring flexibility for local geometry.

The coefficients $\{\omega_{F,n}^{\alpha,\beta},a,b,c,d\}$ are obtained by solving the linear system

$$X^{\alpha,\beta} W_{F}^{\alpha,\beta} = Y_{F}^{\alpha,\beta},$$

where $X$ encodes the RBF kernel matrix and polynomial constraints, and $Y$ contains sampled feature values. The difference between original ($O$) and distorted ($D$) clouds is then captured as relative coefficient differences:

$$d'_k = \frac{|w_k^O - w_k^D|}{\max\{w_k^O, w_k^D\}}$$

for each $k$ in the coefficient vectors.

This method circumvents the combinatorial and geometric ambiguities of explicit matching, yielding stable and spatially-consistent distortion quantification even on irregular point sets.

2. Multi-Scale Feature Extraction and Structural Comparison

MS-ISSM implements a strictly multiscale formulation, utilizing voxel down-sampling to produce three spatial resolutions: High (H, voxel size 2.0), Medium (M, 4.0), and Low (L, 8.0). Each scale allows probing of structural similarity at different spatial frequencies, with high capturing fine details and low emphasizing global shape.

Spatial normalization is employed on each coordinate:

$$\hat{p}_n^\alpha = \frac{1024 (p_n^\alpha - p_{\min})}{L_{\max}}$$

where $L_{\max}$ denotes the largest dimension of the reference bounding box. This normalization harmonizes geometric context across all clouds, a precondition for robust coefficient-based comparison.

For each (feature, scale) tuple, the vector of normalized coefficient differences forms the basis for perceptual similarity assessment. All such vectors are aggregated:

$$D_{\mathrm{pro}} = g\left(\{d'_k\}_{k=1}^K \big|_{L},\; \{d'_k\}_{k=1}^K \big|_{M},\; \{d'_k\}_{k=1}^K \big|_{H}\right)$$

and mapped to a quality score by the downstream regression network.

3. ResGrouped-MLP: Hierarchical Regression Network

The ResGrouped-MLP is a regression architecture specifically designed to interpret the structure of MS-ISSM features. Its design is characterized by the following:

• Log-modulus preprocessing: Coefficient differences are stabilized using

$\tilde{x} = \mathrm{sign}(x) \ln(1 + |x|)$

to compress heavy-tailed distributions prior to normalization.

• Grouped encoding: The $(\text{feature}, \text{scale})$ decomposition (3 features × 3 scales) produces 9 independent "channels," each processed by dedicated small Residual Blocks:

$R(x) = x + \mathcal{F}(x)$

with $\mathcal{F}$ comprising batch normalization (BN), SiLU activations, and linear layers.

• Scale-wise channel attention: For each scale $\beta$, feature embeddings are concatenated to yield $F_\beta$ and fused by adaptive channel weighting using a bottleneck MLP and sigmoid:

$$F_\beta' = F_\beta \otimes \sigma(\mathrm{MLP}(F_\beta))$$

• Global hierarchical regression: The final global representation is constructed by concatenating $\{F_H', F_M', F_L'\}$ and propagating through fully connected layers (potentially with additional attention). The aggregated output is a single predicted quality score $\hat{y}$.
• Loss function: Training employs a weighted composite loss:

$$\mathcal{L}_{\mathrm{total}} = \mathcal{L}_{\mathrm{MSE}} + \lambda_1\, \mathcal{L}_{\mathrm{PLCC}} + \lambda_2\, \mathcal{L}_{\mathrm{Rank}}$$

to ensure agreement with human perceptual rankings in absolute, correlational, and ordinal terms.

This design preserves the semantics of luma, chroma, and geometric cues, while adaptively emphasizing the scales and features most relevant to the experienced distortion.

4. Empirical Evaluation and Comparative Performance

MS-ISSM has been subjected to rigorous benchmarking across the SJTU, WPC, M-PCCD, ICIP, and the aggregate ALL datasets. The metric is compared against 11 classical and leading perceptual point cloud quality assessment (PCQA) methods, including PSNR-p2p, GraphSIM, MS-GraphSIM, PCQM, MS-PSSIM, and TCDM.

On the ALL dataset (after logistic fitting), the following metrics are achieved:

Metric	MS-ISSM	Next Best (TCDM)
PLCC	0.913	0.847
SROCC	0.914	0.861
KROCC	0.751	0.664
RMSE	0.188	0.204

MS-ISSM achieves superior correlation with human perceptual judgements, ranking first across all criteria and distortion types (down-sampling, noise, Trisoup- and V-PCC compression), and achieving top Kendall correlation on Octree compression.

Ablation studies reveal:

• Fusing all features (Cu, Y, Cr) increases SROCC by >0.10 versus any single feature.
• Multi-scale input (H+M+L) outperforms any single scale by a wide margin (PLCC improves from {0.837, 0.880, 0.855} to 0.913).
• Removing the log-modulus transform, the grouped encoder, or channel-wise attention each yields measurable drops in performance, underscoring their contribution.

Cross-dataset generalization experiments, training on one dataset and testing on another, show minimal degradation, establishing robust domain transferability (e.g., train on SJTU, test on ICIP yields PLCC=0.880, SROCC=0.878).

MS-ISSM is also notably efficient: by bypassing explicit neighbor matching in favor of implicit coefficient comparison, runtime is second only to simple SVR-based metrics and significantly faster than graph-based methods.

5. Algorithmic Workflow and Implementation Details

The MS-ISSM pipeline can be summarized as follows:

1. Multi-scale down-sampling: Generate three resolution levels via voxelization.
2. Neighborhood construction: For each reference point and scale, identify local neighborhoods.
3. Implicit function fitting: Solve for RBF polynomial+kernel coefficients per (feature, scale).
4. Coefficient comparison: Compute normalized coefficient-wise differences between reference and distorted clouds.
5. Preprocessing: Apply log-modulus transform and normalization.
6. Regression: Pass grouped and attention-weighted features through the ResGrouped-MLP.
7. Loss minimization: Train the network with a composite MSE, PLCC, and ranking loss.

The implementation avoids heuristics or dataset-specific parameters, and the approach generalizes without retraining across multiple benchmarks.

6. Significance and Relationship to Broader Structural Similarity Paradigms

MS-ISSM extends the paradigm of structural similarity from traditional 2D images and multiscale SSIM-based frameworks to the domain of irregular, high-dimensional point clouds. Its use of RBF implicit encoding for local features is distinct from discrete matching or voxel-based comparisons. In contrast to methods such as multi-scale structural similarity index measure (M-SSIM) in seismic FWI (He et al., 2 Apr 2025), which focus on local window statistics across scales (mean, variance, covariance), MS-ISSM provides a continuous and spatially-resolved approach anchored in implicit functional representations.

This enables error evaluation that is less sensitive to irregular sampling and spatial jitter—challenges fundamental to point cloud analysis. The multiscale and grouped-encoding strategy of MS-ISSM can be considered an advancement in structurally-aware, data-driven quality assessment for unstructured geometric data.

7. Outlook and Implications

MS-ISSM currently represents the state of the art in PCQA, demonstrated by its strong performance, cross-domain robustness, and computational efficiency (Chen et al., 3 Jan 2026). The methodology suggests applicability to broader classes of unstructured data and may inspire analogous implicit, multiscale similarity frameworks in other domains where explicit matching is unreliable. A plausible implication is that future work may further explore implicit function representations and hierarchical attention in both quality assessment and generative modeling for irregular non-Euclidean domains.