Registration is a Powerful Rotation-Invariance Learner for 3D Anomaly Detection

Point-by-Point Response to Reviewer Zbiu

We sincerely appreciate your insightful comments. We believe some concerns may stem from misunderstandings, which we clarify below.

Question-1: " The visualizations in Fig. 1 are not aligned. In addition, the introduction and related work sections could provide a more thorough discussion of the limitations of existing methods and how Reg2Inv addresses these limitations. "

Response: We thank the reviewer for the comment. However, it appears there may have been a misunderstanding regarding the role of Figure 1, as well as the depth of discussion provided in the manuscript.

Figure 1, along with the second through fourth paragraphs of the Introduction, was specifically designed to articulate the motivation behind our work and to highlight the limitations of existing methods. In particular, this section discusses two critical challenges:

1. Unreliable Registration: Traditional methods fail under large pose variations (Fig. 1(a)), preventing accurate spatial alignment.
2. Weak Feature Representation: Methods like PointMAE lack local discriminability and rotation invariance (Fig. 1(b)), leading to inconsistent features and degraded anomaly detection.

Our method, Reg2Inv, is explicitly proposed to overcome these challenges by jointly optimizing registration and feature learning to produce robust, locally discriminative features (Fig. 1(d)), improving both alignment (Fig. 1(c)) and detection performance.

We welcome constructive suggestions to improve the clarity and precision of our writing. However, a single, high-level comment without concrete guidance does not provide actionable feedback for revision and is unlikely to benefit the submission or the broader research community. We are fully committed to improving the manuscript and would greatly appreciate more specific comments on how to strengthen the discussion or presentation.

"Question-2:" " The evaluation metrics lack detailed explanations. It is recommended to supplement with calculation formulas and the set thresholds. "

Response: Thank you for the suggestion. The evaluation metrics we use are standard and widely adopted in the literature, and, in line with common practice, we did not include the calculation formulas in the main paper to preserve space and maintain clarity. However, as suggested, we will provide detailed formulas and threshold settings in the supplementary material.

"Question-3:" " The paper compares its method with several state-of-the-art approaches but does not provide a detailed analysis of why Reg2Inv outperforms these methods. A deeper comparative analysis, including qualitative results and discussions on specific cases where Reg2Inv excels, would enhance the validation of the claims. "

Response: We respectfully disagree with this comment. Due to space constraints, we have made our best effort to provide a detailed comparative analysis throughout the main paper and supplementary material. In addition to the experimental section, we have integrated comparative insights into Figure 1, Figure 3, and conducted extensive experiments in the supplementary material, all of which collectively explain why Reg2Inv outperforms existing methods.

Specifically, Reg2Inv excels by effectively capturing discrepancies in both coordinates and features:

1. Improved Registration Accuracy: As shown in Fig. 1(a) and (c), Reg2Inv achieves better alignment, refining spatial correspondence and reducing false geometric deviations. This allows coordinate differences to more faithfully reflect structural anomalies.

2. Enhanced Feature Discriminability: As demonstrated in Fig. 3, Reg2Inv produces locally discriminative features that remain consistent in normal regions and highlight anomalies more clearly. Competing methods tend to exhibit missed detections or false positives due to weaker local feature modeling.

3. Rotation Invariance without Memory Bank: Table 3 in the main text shows that Reg2Inv outperforms memory bank-based methods using only local features, confirming its robustness to rotation and strong feature consistency.

4. Comprehensive Ablation Studies: The supplementary material includes extensive ablation studies that evaluate the individual contributions of each component in our framework, further validating the effectiveness of our design choices.

We appreciate the suggestion and will further strengthen this analysis in the revised experimental section. However, we believe the current version already provides a thorough and well-supported explanation of Reg2Inv’s advantages.

"Question-4:" " It is not intuitive to verify that the learned features possess stronger rotation invariance and robustness properties through the ablation study on registration. It is suggested that the authors apply different levels of rotation to the two datasets and test the performance changes of different methods. "

Response: We acknowledge that the ablation study on registration does not directly demonstrate the enhanced rotation invariance and robustness of our learned features. To address this, we conducted a rotation experiment on the Real3D-AD dataset. At test time, each point cloud was randomly rotated around one of the X, Y, or Z axes by 90°, 180°, or 270°. We then evaluated the model’s performance using only the learned features under these rotations. The results in Table 1 show consistent performance, confirming that the learned features possess strong rotation invariance and generalization ability.

Table 1: Results under varying levels of rotation.

rotation angle	O-AUROC	P-AUROC
0°	76.4	83.7
90°	76.3	83.9
180°	76.2	83.6
270°	76.6	84.3

To Reviewer Zbiu: We sincerely thank you for your time and thoughtful comments. However, it seems that some concerns may stem from a partial misunderstanding of our work. In particular, the key issues raised regarding the level of comparative analysis and discussion appear to overlook the efforts we have made throughout the manuscript, including detailed explanations in the main text, visual illustrations in Figures 1 and 3, and extensive experiments and ablation studies in the supplementary material.

We fully respect the importance of constructive critique and welcome suggestions that help improve the quality of the work. However, some of the comments are quite general and would benefit from more specific guidance to better serve both the revision process and the research community.

We have carefully addressed all concerns in our rebuttal and sincerely hope that, with these clarifications, the contributions of our work can be reconsidered in a fair and balanced manner.

Dear Reviewer Zbiu,

Thank you for your thoughtful and constructive feedback. We have provided detailed responses to your concerns above. We notice that you have not yet engaged in further discussion with us. If there are any remaining or unclear issues, we would greatly appreciate the opportunity to clarify or further improve our work. Your feedback is highly valuable, and we are eager to address any remaining points that could help strengthen the paper.

Sincerely,

The Authors

Point-by-Point Response to Reviewer iakd

We sincerely appreciate your insightful comments. We believe some concerns may stem from misunderstandings, which we clarify below.

Question-1: " The overall clarity and readability of the method presentation need improvement, particularly in Figure 2's framework illustration. "

Response: Our intention was to align the architectural diagram with the methodology by illustrating the training/inference procedures, as well as the Rotation-Invariant Feature Extractor. We acknowledge the resulting complexity and will simplify Figure 2 by removing unnecessary lines, standardizing dashed styles, and eliminating redundant labels.

Question-2: " In comparative experiments, the proposed method shows some advantages over others, though the improvements are not statistically significant. "

Response: We respectfully disagree with the statement that the improvements are not statistically significant. As shown in Tables 1 and 2, our method achieves clear and consistent performance gains over existing approaches across both benchmarks:

• On Real3D-AD, our method achieves an average O-AUROC of 78.0% and P-AUROC of 87.8%, outperforming the second-best with 76.5% / 83.6%, a margin of +1.5% and +4.2%, respectively.
• On Anomaly-ShapeNet, our method achieves 86.1% / 88.2%, compared to 83.9% / 89.8% by PO3AD. These improvements in object-level AUROC reflect stronger detection ability on clean and complete shapes.

We believe these gains are significant and reflect the robustness and effectiveness of our approach. Moreover, reconstruction-based methods like PO3AD rely on complete geometry and cannot operate on partial or occluded point clouds. As a result, they struggle to achieve satisfactory performance when computing point-level AUROC on Real3D-AD and are limited to classification only. In contrast, our method processes incomplete inputs and supports both classification and localization, offering broader applicability in real-world scenarios.

In summary, the consistent performance advantage, along with greater flexibility, demonstrates the practical strength and generalization ability of our method.

Question-3: " The presentation of experimental tables has significant issues in Tables 1-3, including overcrowding with too many methods, overly complex content, and suboptimal formatting. Additionally, the experimental analysis needs strengthening to better contextualize these results. "

Response: We thank the reviewer for pointing this out. While the design of Tables 1 and 2 follows common practices in prior work, we agree that the large number of object categories may make the tables appear visually dense. However, this level of detail is necessary for a fair and comprehensive comparison. To aid interpretation, we would like to emphasize that the average scores at the end of each table provide the most intuitive summary of overall performance, and these averages are the key indicators we highlight in the analysis.

To further improve clarity, we will restructure Tables 1 and 2 by grouping methods by category and simplifying the layout of Table 2. Table 3 will be split into two separate tables for easier readability.

In addition, we will expand the experimental analysis with more focused discussion to better contextualize the results and clearly highlight the strengths of our method.

Question-4: " Is the proposed registration-based method still maintains effectiveness in 2D scenarios(e.g., Real-IAD dataset) or multimodal settings (e.g., MVTec3D-AD) ? "

Response: We thank the reviewer for raising this question, and we discuss it from two perspectives to provide a comprehensive response：

1. Application to 2D Anomaly Detection: 2D registration typically involves local, pixel-wise alignment, making it challenging to estimate a reliable global transformation between images captured from different viewpoints. Without consistent global alignment, holistic feature extraction becomes unreliable, and the benefits of 3D registration cannot be achieved. As such, our registration-based approach is not directly applicable to 2D anomaly detection.

2. Application to Multimodal Anomaly Detection: For multimodal anomaly detection on the MVTec3D-AD dataset, which provides an RGB image and a corresponding point cloud from a single viewpoint, anomaly detection can be performed on the point cloud using our registration-based method, with the results subsequently fused with those from the image modality. However, as MVTec3D-AD provides only partial point clouds, this prevents the use of a complete shape template, potentially leading to less stable registration.

To Reviewer iakd: The primary concern raised appears to be that our performance improvements are not statistically significant. However, this may stem from overlooking the average performance metrics reported in each table, where our method consistently achieves clear and meaningful gains over all baselines. The other concerns, such as the complexity of Figure 2 and the formatting of the tables, are relatively minor and can be readily addressed during revision.

Given that the core issues raised are either not substantiated by the data or are minor in nature, we believe the negative evaluation is not justified. We have addressed all points thoroughly in our rebuttal and sincerely request a reconsideration of the decision in light of the significant, consistent, and practically meaningful improvements demonstrated by our method.

Dear Reviewer iakd,

Thank you for your thoughtful and constructive feedback. We have provided detailed responses to your concerns above. We notice that you have not yet acknowledged the rebuttal, submitted your final recommendation, and engaged in further discussion with us. If there are any remaining or unclear issues, we would greatly appreciate the opportunity to clarify or further improve our work. Your feedback is highly valuable, and we are eager to address any remaining points that could help strengthen the paper.

Sincerely,

The Authors

Dear Reviewer iakd,

With the Reviewer Author Discussion phase nearing its deadline, we kindly noticed that the Discussion, Mandatory Acknowledgement, and Final Rating are still pending on your end. We would be sincerely grateful if you could take a moment to complete these final steps at your earliest convenience.

Sincerely,

The Authors

Dear Reviewer iakd,

As the Reviewer Author Discussion phase is coming to an end, we noticed that you have not yet participated in the discussion, submitted the Mandatory Acknowledgement, or provided the Final Rating.

We would be sincerely grateful if you could kindly take a moment to complete these final steps at your earliest convenience.

Thank you very much for your time and consideration.

Sincerely,

The Authors

Dear Reviewers iakd and BTG1,

Could you please share any additional thoughts you have on the rebuttal and the comments from the other reviewers? Your involvement in this author-reviewer discussion would be greatly appreciated. Thank you very much for your time and effort.

Best,

AC

Point-by-Point Response to Reviewer BTG1

We sincerely appreciate your insightful comments, which significantly improved our paper. In response, we provide our detailed replies to your questions as follows:

Question-1: " The main major weakness is the somewhat weak ablation study. No ablation experiments in the paper for Loss components, filtering, using other extracted features for memory bank computation, etc. "

Response: We thank the reviewer for the valuable feedback on the ablation study. We would like to clarify that several ablations addressing key components of our method are included in the supplementary material. Specifically, Table 1 presents the ablation of the loss component $\mathcal{L}\_{f}$, highlighting its critical contribution to detection performance. Table 2 reports the impact of the filtering strategy, which serves an auxiliary function.

Additionally, we conducted an ablation study on alternative feature representations for memory bank construction using the Real3D-AD dataset. As shown in Table 1 below, KPConv-FPN features $\mathbf{F}'$ are suboptimal due to limited receptive fields and weaker semantics.

Table 1: Ablation study on the use of extracted features for memory bank construction.

Memory Bank Construction	O-AUROC	P-AUROC
$\mathbf{F}'$	51.1	43.8
$\mathcal{P}^{align}$ + $\mathbf{F}'$	54.0	56.1
$\mathbf{F}''$	76.4	83.7
$\mathcal{P}^{align}$ + $\mathbf{F}''$	78.0	87.8

Question-2: " Lacking intuition for some design choices such as various loss components, filtering, etc. Essentially, things that are missing from the ablation study. I know these are present in the quite extensive supplementary material, but it would still be useful for the reader to see more of these in the main paper. "

Response: We appreciate the reviewer’s valuable feedback on the presentation of key design choices. The losses $\mathcal{L}\_{p}$ and $\mathcal{L}\_{oc}$ are standard in point cloud registration, while $\mathcal{L}\_{f}$ specifically supervises the RIConv++ module in learning the target features. The filtering mechanism is designed to remove edge responses and suppress false positives. To maintain clarity and conciseness within the paper's space constraints, we focus on the core contributions in the main text. We will expand on these design choices in the main text and direct readers to the supplementary materials for a more detailed analysis and experimental validation.

Question-3: " In the ablation study, Table 3: How come the Coord works fairly well? It does not seem to contain that much information intuitively. "

Response: While point coordinates may seem limited in expressiveness, they are a fundamental geometric property of point clouds, capturing 3D positions and encoding global shape information. In memory bank-based anomaly detection, coordinates are commonly used for patch matching and similarity comparison. The good performance of "Coord." in Table 3 results from our method’s precise registration, ensuring consistent coordinate correspondence across point clouds, which makes coordinate-based comparisons effective even without additional features.

Question-4: " What is the intuition behind using $\mathbf{F}''$ and the $\mathcal{P}^{align}$ coordinates as the features in the coreset? Why not other extracted features? "

Response: In constructing the coreset, we chose to use feature $\mathbf{F}''$ and aligned coordinates $\mathcal{P}^{align}$ for the following reasons: $\mathbf{F}''$ offers strong rotational invariance and high local resolution, effectively capturing local geometric patterns, while $\mathcal{P}^{align}$ provides 3D position and global shape structure, offering both spatial priors and a structural reference. This combination balances local detail and global consistency, enabling the model to detect subtle local anomalies while maintaining robust geometric coherence.

We did not use $\mathbf{F}'$ or $\mathbf{F}$, as they are designed for key point matching to compute the rotation matrix for registration. Their limited receptive fields and weaker semantic representation make them less suitable for capturing the broader geometric context required for effective anomaly detection.

Dear Reviewer BTG1,

Thank you for your thoughtful and constructive feedback, as well as your positive assessment of our approach. We have provided detailed responses to your concerns above. We notice that you have not yet acknowledged the rebuttal, submitted your final recommendation, and engaged in further discussion with us. If there are any remaining or unclear issues, we would greatly appreciate the opportunity to clarify or further improve our work. Your feedback is highly valuable, and we are eager to address any remaining points that could help strengthen the paper.

Sincerely,

The Authors

Point-by-Point Response to Reviewer PScz

We sincerely appreciate your thoughtful and constructive comments, which have greatly enhanced the quality of our manuscript. Below, we provide detailed responses to each of your questions.

Question-1: " Figure 2 is somewhat complex and should be simplified to improve readability. "

Response: Our intention was to align the architectural diagram with the methodology by illustrating the training/inference procedures, as well as the Rotation-Invariant Feature Extractor. We acknowledge the resulting complexity and will simplify Figure 2 by removing unnecessary lines, standardizing dashed styles, and eliminating redundant labels.

Question-2: " Provide the equation for $\mathcal{L}\_{oc}$ in the main text. "

Response: We have provided the equation for $\mathcal{L}\_{oc}$ in the Supplementary Material and will move it to the main text in the revision.

Question-3: " How long does it take to train the proposed method? "

Response: Our method learns features via a registration task that enforces geometric alignment and multi-scale consistency between source and target point clouds. As it does not rely on category-specific supervision, it is inherently category-agnostic and can be trained jointly across the entire dataset. Under our experimental setup (RTX 3090 GPU, batch size 1), full training takes approximately 27 hours on Anomaly-ShapeNet (40 categories) and about 34 hours on Real3D-AD (12 categories). In contrast, methods like R3D-AD and PO3D-AD require ~1 hour and ~7 hours per category, respectively. While our single training run is longer, it eliminates the need for category-wise training, resulting in significantly greater overall efficiency.

Question-4: " What is the inference speed in frames per second (FPS)? "

Response: Thank you for the suggestion. While FPS is less commonly used for point cloud anomaly detection due to variable point counts and the absence of a clear “frame” definition, we report average inference time per sample as a practical alternative. Under our setup (RTX 3090 GPU, batch size 1), our method takes an average of 2.53 seconds to process one sample on the Real3D-AD dataset, outperforming other memory bank-based methods, as shown in Table 1 below.

Table 1: Comparison of Inference Speed.

Method	average inference time per sample (seconds)
RegAD	7.71
M3DM	6.43
ISMP	4.37
Ours	2.53

Question-5: " Does the proposed method involve hyperparameters, and has a sensitivity analysis been conducted to assess their robustness? "

Response: Yes, our method involves a key hyperparameter: the neighborhood size in RIConv++. To assess its impact, we conducted a sensitivity analysis on the Real3D-AD dataset, as shown in Figure 1 of the supplementary material. The results indicate that smaller neighborhood sizes limit contextual information, while larger sizes may weaken local feature discrimination by aggregating dissimilar points. Despite these effects, our method performs consistently well across a range of values, demonstrating robustness to this hyperparameter.

Question-6: " How does the proposed method perform on noisy point clouds? "

Response: We appreciate the reviewer’s insightful comment. Like most models, ours is sensitive to unexpected noise during testing. To assess robustness, we conducted experiments on the Real3D-AD dataset under two settings. In Setting 1, Gaussian noise (SD = 0.005) was added during training, with various noise levels applied during testing. In Setting 2, noise was added only during testing. As shown in Tables 2 and 3 below, the model without noise augmentation (Setting 2) shows a noticeable performance drop at higher noise levels (SD ≥ 0.003), indicating sensitivity to input perturbations. However, with noise-based augmentation during training (Setting 1), the model maintains stable performance across different noise levels. These results suggest that, with minor fine-tuning, our method can effectively handle noisy point clouds.

Table 2: Results of Setting-1

noise	O-AUROC	P-AUROC
clean	78.0	87.8
SD=0.001	76.7	87.5
SD=0.003	77.7	86.4
SD=0.005	76.8	83.1

Table 3: Results of Setting-2

noise	O-AUROC	P-AUROC
clean	78.0	87.8
SD=0.001	76.9	86.5
SD=0.003	63.0	69.1
SD=0.005	56.6	56.5

Question-7: " Do "Coord." and "Feat." correspond to $\mathcal{L}\_{p}$, $\mathcal{L}\_{oc}$, and $\mathcal{L}\_{f}$, respectively? If not, an ablation study explicitly analyzing the contributions of these three losses is recommended. "

Response: Thank you for the question. "Coord." and "Feat." refer to the registered point coordinates and the learned local features, respectively, but they do not directly correspond to $\mathcal{L}\_{p}$, $\mathcal{L}\_{oc}$, and $\mathcal{L}\_{f}$. To clarify their contributions, we conducted an ablation study on these three loss terms using the Real3D-AD dataset, with results shown in Table 4 below.

The analysis shows that each loss serves a distinct role:

1. $\mathcal{L}\_{oc}$ is the most critical for accurate registration, enabling the model to align structurally consistent local patches even under partial overlap or sparsity. Removing it severely degrades performance.

2. $\mathcal{L}\_{f}$ enhances the rotation invariance and local discriminability of features, directly improving anomaly localization accuracy.

3. $\mathcal{L}\_{p}$ has a smaller impact on detection accuracy but is important for efficient point matching. Without it, inference time increases significantly due to many spurious matches.

In summary, $\mathcal{L}\_{oc}$ and $\mathcal{L}\_{f}$ primarily support accurate feature learning and detection, while $\mathcal{L}\_{p}$ improves inference efficiency. All three contribute to balancing performance and computational cost. We will include these discussions in the revision.

Table 4: Ablation study on loss components.

loss components	O-AUROC	P-AUROC
w/o $\mathcal{L}\_{oc}$	58.1	68.1
w/o $\mathcal{L}\_{p}$	76.9	87.0
w/o $\mathcal{L}\_{f}$	73.4	86.0
$\mathcal{L}\_{oc}$ + $\mathcal{L}\_{p}$ + $\mathcal{L}\_{f}$	78.0	87.8

Dear Reviewer PScz,

We sincerely thank you once again for your constructive feedback and positive evaluation of our work. As the review process nears completion, we would greatly appreciate it if you could kindly submit your final rating at your earliest convenience.

Sincerely,

The Authors