NeuroGauss4D-PCI: 4D Neural Fields and Gaussian Deformation Fields for Point Cloud Interpolation

We appreciate your meaningful suggestions and questions, and we will address each of them in our response.

Q1.1: Non-traditional writing structure of the introduction.

A1.1: We will rigorously revise our introduction structure according to your recommendations. Due to space constraints, please refer to the end of our response to A1 for the detailed revision plan.

Q1.2: Sporadic PCI challenges and unclear logical relationship to Formula 1.

A2: We appreciate your feedback and will clarify that "multiple unordered point clouds" refers to the inherently unordered nature of input point cloud signals. To enhance clarity and logical flow, we will separate the introduction of PCI concepts from the discussion of current challenges in the main text. Additionally, we will provide a detailed explanation for each term in Equation 1.

Q1.3: Inappropriate introduction of Figure 1 at the beginning.

A3: We greatly appreciate your valuable feedback on Figure 1. We agree that introducing detailed experimental results at the beginning of the paper may not be ideal.

Our original intent was to quickly showcase our method's advantages, including:

1. Interpolation accuracy across various frame intervals
2. Performance with different data sparsity levels
3. Effectiveness on both human body and autonomous driving datasets

To address your concern, we will:

1. Split the existing Figure 1
2. Move qualitative and quantitative results to the experimental section
3. Ensure readers fully understand our method before encountering these results

Regarding the right side of Figure 1, we will provide further explanations in our PDF response (Fig. 4).

The following is the revised Introduction outline, and we will re-revise the text strictly according to your suggestions:

1. Point Cloud Interpolation (PCI)

   • Concept and application scenarios, incorporating Equation 1
   • Clear explanation of each term in Equation 1

2. PCI Challenges and Research Significance

   • Point cloud data characteristics and resulting challenges
   • Complexity of spatio-temporal dynamic modeling
   • Difficulty in generalizing from sparse temporal samples

3. NeuroGauss4D-PCI: Key Components and Their Roles

   a. Iterative Gaussian Cloud Soft Clustering

   • Structured representation for unordered point clouds
   • Geometric feature capture addressing data irregularity

   b. Temporal RBF-GR Module

   • Complex non-linear temporal dynamics modeling
   • Smooth interpolation between sparse temporal samples

   c. 4D Gaussian Deformation Field

   • Long-term motion trend and non-rigid deformation capture
   • Cross-frame geometric consistency maintenance

   d. 4D Neural Field

   • Fine-grained spatiotemporal detail representation
   • Multi-scale dynamic modeling complement to Gaussian representation

   e. Fast Latent-Geometric Feature Fusion Module

   • Adaptive combination of Gaussian and neural features
   • Handling of varying point densities and enhanced spatiotemporal modeling

4. Innovations and Contributions

   • Novel 4D representation combining Gaussian soft clustering and neural field features
   • Continuous time modeling via Temporal RBF-GR module
   • Advanced 4D Gaussian deformation field using graph convolutions

Q2: Unclear flow in the related works section

A2: We will improve the related works section by:

1. Reorganizing the structure of each subsection (neural fields, 3D Gaussian splatting, and point cloud interpolation)
2. Reducing reliance on mathematical formulas
3. Correcting grammatical errors

Q3.1: Unlabeled components in Figure 2

A3.1: We will revise Figure 2's caption to match the module names in the diagram and avoid using numbering:

Figure 2: NeuroGauss4D-PCI architecture. The system processes input point clouds (X, Y, Z, T) and a predicted time T_pred. Latent Feature Learning occurs via Fourier Basis Encoding and Neural Field. Gaussian Representation is achieved using Iterable Gaussian SoftClustering. Temporal Modeling employs the RBF-GR Module. The 4D Deformation Field integrates latent features and temporal information. Feature Fusion is performed by the Fast-LG-Fusion module. Finally, Point Cloud Generation is accomplished using a Prediction Head. This pipeline enables effective spatiotemporal modeling and interpolation of point clouds.

Q3.2: Figure 3 fails to visualize component purposes

A3.2: We've enhanced Figure 1 in the PDF reply as follows:

1. Gaussian Ellipsoid Visualization: Added pre- and post-interpolation Gaussian ellipsoids, showing model inputs and outputs.

2. Intermediate Process Visualization: Included visualizations of intermediate products to illustrate data transformation.

3. Component Functionality: Clarified inputs, outputs, and functions of RBF-GR module components.

4. Information Flow Diagram: Will add a flow diagram in the final revision, annotating each component's role and data flow.

Q4: Incorrect terminology in Figure 2.

A4: Using "sphere" to describe soft clustering output is indeed inaccurate.. We will:

• Change "Gaussian spheres" to "Gaussian ellipsoids" in Figure 2's caption and explanation
• Review and correct all related descriptions in the main text

Q5: Impact of outlier removal on other methods

A5: Outlier removal improved results for all tested methods. Here's a comparison:

Note: † indicates results with outlier removal.

NeuroGauss4D-PCI benefits most from outlier removal due to:

1. Our Gaussian representation amplifies the benefits of outlier removal.
2. Clean data significantly enhances our 4D deformation field's accuracy.
3. Outlier removal maximizes our Temporal RBF-GR module's effectiveness.

We sincerely appreciate your positive feedback on our paper's organization, literature review, experimental design, and results. Your recognition of our novel approach using 4D Gaussian deformation fields and temporal radial basis function Gaussian residual modules to capture complex spatiotemporal dynamics is particularly encouraging. We are grateful for your detailed comments and will address each of your concerns in the following responses.

Q1: Discussion on computational efficiency

A1:

• Experimental Platform: Our algorithm was tested on a platform equipped with an NVIDIA RTX 3090 GPU.

• Computational Efficiency: We recorded detailed computational costs for different point cloud sizes:

Table 1: Time consumption statistics (in seconds)

• Efficiency Analysis

1. Single frame processing: Only 0.0118 seconds for 8192 points, demonstrating high efficiency.
2. Sequence processing: 0.1572 seconds for a 4-frame sequence (8192 points/frame), or about 157.2 seconds for 1000 iterations.
3. Preprocessing optimization: Iterative Gaussian Cloud Soft Clustering module moved to preprocessing stage, running once per sequence (~1 second) instead of every iteration.
4. Weight freezing: DGCNN and SelfAttention network weights frozen to reduce updatable parameters.

Q2: Detailed comparison with NeuralPCI.

A2: We appreciate the reviewer's valuable feedback and recognition of NeuroGauss4D-PCI's potential. As requested, we have expanded our comparison with NeuralPCI:

1. Visual comparison in Figures 1, 6 and 7 in the original paper.
2. Quantitative comparisons across various point cloud densities, frame intervals, datasets, and metrics are presented in Tables 1 and 2, and Figure 1 in the original paper.

Key advantages of NeuroGauss4D-PCI over NeuralPCI include:

1. Structured Representation: Our iterative Gaussian soft clustering module provides a structured temporal point cloud representation, better capturing geometric features and spatio-temporal dynamics. NeuralPCI, in contrast, directly inputs spatial and temporal coordinates to an MLP.

2. Spatio-temporal Modeling: Our Temporal RBF-GR module and 4D Gaussian deformation fields enable more precise modeling of complex non-rigid deformations and non-linear trajectories, particularly beneficial for long time spans and complex dynamic scenes.

3. Feature Fusion: Our fast latent-geometry fusion module adaptively combines implicit features from neural fields with explicit geometric features from Gaussian deformation fields, enhancing spatio-temporal correlation modeling.

These improvements collectively contribute to NeuroGauss4D-PCI's superior performance in various challenging scenarios.

Q3: Convincingness of testing on only two open datasets.

A3: Thank you for raising this important question. I understand your concerns about the potential limitations of testing only on two open datasets, as well as the reliability of the experimental design and results of all the work.

1. Dataset Representativeness:

   • DHB (object-level) and NL-Drive (large-scale autonomous driving) represent two major application scenarios in point cloud interpolation.
   • NL-Drive combines KITTI, Argoverse, and Nuscenes datasets, offering diverse, real-world autonomous driving environments.
   • These datasets cover a wide range from fine-grained object deformations to complex, large-scale scenes.

2. Fair Comparison:

   • We benchmark against state-of-the-art methods including IDEA-Net, PointINet, NSFP, PV-RAFT, NeuralPCI, and 3DSFLabelling.
   • We use results provided by Zheng et al. in the NeuralPCI paper, validating their experimental outcomes for consistency.

3. Open-source Verification:

   • All compared algorithms are open-sourced, enhancing result credibility and reproducibility.
   • We conducted independent experiments using NSFP and 3DSFLabelling's open-source code on the test set, further ensuring fair and accurate comparisons.

4. Extensibility Validation:

   • We demonstrate NeuroGauss4D-PCI's potential in related tasks such as auto-labeling and point cloud upsampling, showcasing its versatility and adaptability.

This comprehensive approach aims to establish the reliability and broad applicability of our method across diverse scenarios in point cloud interpolation.

We sincerely thank the reviewer for their insightful questions and provide detailed responses below

Q1: Poor color scheme.

A1: We commit to redesigning the color scheme in our main text to improve visibility and readability. For your reference, we've implemented this new color scheme in our PDF response.

Q2: Emphasize the significance of research direction.

A2: We will reemphasize the research significance of this task in our paper:

1. Bridges the gap between current sensor limitations and high-frequency data demands in autonomous driving and AR.
2. Improves object tracking and motion prediction in dynamic environments.
3. Facilitates world model construction and AI-generated 3D content.
4. Supports multi-sensor synchronization, auto-labeling, and point cloud densification.

Our supplementary materials demonstrate these applications, highlighting PCI's versatility and potential across various 3D vision tasks.

Q3: Latest relevant works.

A3: NeuralPCI (CVPR 2023) is the most recent specialized study on point cloud interpolation in our citations. While 3DSFLabelling (CVPR 2024) addresses related tasks, it focuses on 3D scene flow rather than sequence interpolation. Recent applications of point cloud interpolation include skeletal animation generation (PC-MRL, arXiv 2024) and optimal transport evaluation (CL+SW2, WACV 2024).

Q4: Ensuring robustness to different data sparsities.

A4: NeuroGauss4D-PCI achieves robust performance across data sparsity levels due to:

1. Adaptive Representation: Gaussian soft clustering extracts meaningful features even from sparse data.

2. Flexible Temporal Modeling: RBF-GR module interpolates smoothly between frames, regardless of point density.

3. Multi-scale Capture: 4D Gaussian fields model both global structure and local details, adapting to varying sparsity.

These components synergistically handle different data densities. Our algorithm's robustness across diverse point cloud densities is demonstrated by these results:

Q5: Handling rapidly changing dynamic scenes？

A5: In our response PDF (Fig. 2), we present visualizations of frame interpolation predictions for scenarios involving long intervals and rapid motion patterns. Our predicted results demonstrate strong alignment with ground truth.

Q6: Training and inference costs comparison.

A6: Our model's computation costs for different point cloud sizes are detailed below:

Note: The Iterative Gaussian Cloud Soft Clustering module runs only once in the preprocessing stage, taking about 0.2248 seconds, and is not included in the table.

For 8192 points, our model takes 0.1572 seconds per iteration, or about 157.2 seconds for 1000 iterations. Simpler models like NeuralPCI take about 60 seconds for 1000 iterations, while more complex models like 3DLSFLabelling take over 10 minutes for a single point cloud pair. Our algorithm's time consumption is within an acceptable range for optimization-based methods designed for accuracy.

Q7: Performance under occlusion or sensor noise?

A7: Figures 2 and 3 in our response PDF demonstrate our model's visual results under significant occlusion and various noise conditions, respectively. The results show that our model maintains acceptable accuracy even in these challenging scenarios.

Q8: Complex interactions between modules.

A8: Our experiments demonstrate that integrating Gaussian fields with neural network features consistently yields performance improvements, regardless of the specific fusion method employed:

The combination provides: Gaussian fields capture spatial structure and global information, while neural networks learn complex non-linear mappings and local features.

Q9: High computational cost limiting real-time applications.

A9: As shown in the runtime analysis in Answer 6, our algorithm's computational cost falls within an acceptable range. Our approach, similar to NeRF, is a coordinate-based, per-scene fitting method primarily designed for offline optimization of individual scenes.

Thank you for your insightful critique.

Q1: Algorithm complexity and limited contributions

A1: Due to space constraints, we kindly refer you to Reviewer xq5Q's Q1 for the explanation on model complexity. We apologize for any inconvenience.

Design Motivation:

• Gaussian Soft Clustering: Structures multiple unordered point clouds, improving upon methods like NeuralPCI
• Temporal RBF-GR Module: Overcomes linear motion assumptions of methods such as PointINet
• 4D Gaussian Deformation Fields: Captures complex motion patterns over extended time spans, surpassing scene flow-based approaches

Key Innovations

• 4D Gaussian representation for spatiotemporal features
• Temporal RBF-GR for smooth parameter interpolation
• 4D Gaussian Graph Convolutional Deformable module for spatiotemporal learning

Improved Interpretability

• Uses explicit geometric principles: Gaussian means (μ), covariance matrices (Σ), deformation fields

Q2: Long optimization time and suitability for optimization-based approach

A2: Following your Q4 suggestion, we've significantly reduced the algorithm's runtime.

Our core components suit optimization methods because:

Temporal RBF-GR, 4D Gaussian Deformation: Optimize meaningful mathematical parameters.

4D Neural Field: Expresses highly complex non-linear functions through optimization.

Q3: Relationship to 3D Gaussians, splatting, and clustering

A3: Relationship to 3DGS:

• Uses 3D Gaussians, inspired by 3DGS concepts
• Doesn't employ "splatting" techniques
• Will reduce 3DGS discussion in the paper

Our method uses EM-like clustering and GMM concepts, enhanced by DGCNN and self-attention for Gaussian deformation, focusing on point cloud interpolation. Detailed relationships will be clarified in the main text.

Q4: DGCNN training approach

A4:

• Moved Iterative Gaussian Cloud Soft Clustering to preprocessing stage
• Froze weights of DGCNN and SelfAttention networks
• Networks now act as fixed feature extractors

Performance Impact

• Model with frozen weights performs comparably to original model

Efficiency Gains

• Processing time for 4-frame sequence (8192 points) reduced to 0.1572 seconds.
• Iterative Gaussian Cloud Soft Clustering now takes about 0.2248 seconds in preprocessing For detailed timing of individual model components, please refer to our response to Reviewer xq5Q's Q9.

Q5: 3D Gaussian correspondence during interpolation, and residual Gaussian visualization.

A5: Reason:

1. Each Gaussian is uniquely identified and tracked across all timesteps.
2. Gaussian parameters evolve smoothly over time via RBF interpolation.
3. Self-attention mechanism ensures coherent global deformation.

Residual Gaussian visualization provided in Figure 1 of response PDF.

Q6: Model efficiency analysis for more frames/points, and writing corrections

A6:

1. Detailed timing for each module provided in reviewer xq5Q's A9 for 1024 and 8192 points.
2. For optimization time comparisons across models with varying frame counts and point cloud sizes:

The time consumption of our algorithm is within a reasonable range.

3. Writing corrections: "Table 4.2" reference on line 136 and missing arrows for ACC_S and ACC_R in Table 3.

Q7: Framework simplification for improved efficiency

A7: Framework simplified as described in A4, significantly improving efficiency.

Q8: Additional supervision for 3D Gaussian distributions

A9: Explored two additional constraints:

Gaussian Distribution Consistency Constraint: Similar to the Smoothness Loss in the paper, we enforced continuity and consistency between Gaussian distributions of adjacent time steps.

Local Anisotropy Constraint: We quantified the similarity of local directional and structural features by comparing covariance matrices of corresponding local regions in target and predicted point clouds.

Results:

Precision remains nearly constant, but at the cost of increased computation time.

Q9: Evaluation on more challenging datasets

A10:

1. Evaluated on NL Drive dataset (KITTI, Argoverse, Nuscenes) in Table 2 of paper.
2. Additional testing on Waymo dataset:

These results further validate our model's effectiveness in complex, real-world autonomous driving scenarios.

We appreciate your thorough review and valuable feedback. Here are our responses to your questions:

Weaknesses

Q1: Is the method overly complex with its 5 components?

A1: Our method is designed for efficiency and effectiveness:

1. Parameter Efficiency: NeuroGauss4D-PCI uses only about 0.1 million parameters, significantly fewer than similar methods requiring millions.

2. Logical Pipeline: Our components form a clear sequence:

   a) Structure point clouds

   b) Model temporal evolution

   c) Capture fine details

   d) Fuse information

3. Component Breakdown:

   • Gaussian Soft Clustering: Organizes unstructured point clouds
   • Temporal RBF-GR Module: Enables smooth temporal interpolation
   • 4D Gaussian Deformation Field: Simulates long-term motion trends
   • 4D Neural Field: Captures high-frequency details
   • Fusion Module: Combines geometric and latent features

4. Benefits:

   • Improved Interpretability
   • Reduced Parameter Count Each component addresses specific challenges in point cloud interpolation.

Q2: Is it inefficient that the algorithm must perform operations on each timestamp of the point cloud sequence?

A2: NeuroGauss4D-PCI is designed for per-scene optimization, not real-time processing.

• Processes single-frame point clouds sequentially
• Accumulates loss across the entire sequence
• Performs backpropagation and optimization after processing all frames

Single-frame processing takes about 10ms. The majority of computation time is spent on backpropagation and parameter updates after processing the full sequence. Nevertheless, optimizing a large-scale LiDAR scene requires only 2-3 minutes.

Q3: Can the method handle large point cloud sizes or sequences?

A3: We use different point cloud sizes for distinct scenarios:

• Object-level scenes: 1024 points. (Aligns with Idea-net)
• Autonomous driving scenes: 8192 points. (Consistent with NeuralPCI)

We also provide quantitative comparisons of different point cloud densities:

Table 1: Quantitative comparison results on NLDrive dataset with different input point cloud densities.

Q4: How will you improve writing clarity?

A4: We will:

• Unify to 0-based indexing
• Remove punctuation errors
• Use consistent terminology
• Integrate equations into sentences

Questions

Q5: Clarify "Frame-1, Frame-2, and Frame-3" in Table 2.

A5: We use frames {0, 4, 8, 12} as input and evaluate on frames {5, 6, 7}.

Q6: Explain the training and evaluation process in Table 5.

A6: We optimize on frames {0, 4, 8, 12} and evaluate on {5, 6, 7}. We also present experimental results for both shorter and longer frame intervals:

Table 2: Comparison of CD errors (×10^-2^) for different methods across various time intervals

Our method shows the lowest CD error across all time intervals.

Q7: Explain the time steps "0" and "1" in line 456.

A7: We normalize all input times to 0-1 to handle different sequence lengths, simplify training, and enhance generalization.

Q8: Does the method fit one model per scene?

A8: Yes, NeuroGauss4D-PCI uses per-scene fitting, allowing high-quality interpolation at any time point after a 3-minute optimization.

Q9: Can you provide detailed timing information?

A9: Here's our time consumption breakdown: Table 3: Algorithm Time Consumption Statistics

Note: The Iterative Gaussian Cloud Soft Clustering module runs only once in the preprocessing stage, taking about 0.2248 seconds, and is not included in the table. The total time for one sequence iteration includes the processing time for 4 single frames plus additional sequence-level operations.

I thank the author for the rebuttal responses, where most of my concerns are covered. Score increase 4->5.