Rethinking Point Cloud Data Augmentation: Topologically Consistent Deformation

Dear Reviewer Agtr:

Thanks for your time and insightful reviews. We appreciate your recognition of our work. We responded in detail as follows:

Q1: Concepts of homeomorphism need further discussion. From mathematical aspects, the 3D surfaces in the mentioned datasets (e.g., ModelNet40) are mostly homeomorphisms across different classes. For example, the plane and guitar are homeomorphisms, while the plane and cup are not.

A1: Thank you for your recognition of our work. Indeed, as you say, when we look at different samples, their shapes and structures can be transformed into each other through a series of continuous deformations without involving holes or tears; then they are homeomorphic, such as a plane and a guitar. A cup with a handle has a hole, and the plane is non-hole, so they are not homeomorphic. This is relative to the different samples.

However, our SinPoint is to consider a single sample. Our aim is to make a single sample produce continuous smooth deformation through homeomorphic mapping, which makes the deformed sample maintain semantic consistency while increasing the geometric diversity of a single sample, so that the model can learn more discriminant features.

Data augmentation based on homeomorphism can enhance the diversity of a single sample, enabling the model to learn more discriminative features and improve model performance (see Tables 1, 2, 6, 9, and 10). The anti-interference ability of the model is further improved (see Table 3).

Since we are not specifically designing machine learning models to learn features of homeomorphisms between different samples, we do not consider homeomorphisms between different samples.

Q2: The proposed method mostly employs the sine-based deform functions and designs the Markov chain data augmentation process, which is more likely to be a stable and continuous deformation process than a topology-consistent transformation.

A2: Thanks for your professional questions. Our data augmentation can be regarded as two processes, as shown in Figure 2. First, a topology-consistent deformation sample is generated through sine transformation based on homeomorphism, and the original sample and the augmented sample are input into the Markov augmentation process based on the basic transformation to further increase the diversity of samples.

From Table 4, we can find that the independent Markov gain is 1.0 and the independent SinPoint gain is 1.2. In this case, only augmented samples are used, and when further mixed samples are used to expand the variance of the data, the performance is improved again. In this case, the mixed Markov gain is 1.5, and the mixed SinPoint gain is 1.7. This also shows that SinPoint's performance improvement is always better than the Markov process. When the three work together, the performance gain is 2.0. This also shows that SinPoint and Markov can promote each other. And SinPoint played a crucial role.

We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.

Dear Reviewer 8z5w:

Thanks for your time and insightful reviews. We responded in detail as follows:

Q1: ...for example [1]. Despite this claim, the paper’s analysis ... appears trivial, and it lacks an in-depth discussion on how increasing variance—specifically through the proposed augmentation—enhances model generalization to unseen data.

A1: Thank you for your valuable opinions, especially the one you mentioned [1], which is very valuable to us. This is a work that studies the basic theory of data augmentation, which provides deeper theoretical support for our work. Especially in the process of constructing Markov augmentation, our method is further proved to be correct and effective theoretically.

Compared to [1] which mainly studies the theory of basic transformations, we propose a novel SinPoint to construct augmented samples. Meanwhile, this construction can steadily expand the variance of the data. As shown in Figure 2 (in https://github.com/Anonymous-code-share/ICML2025), the distribution of the augmented samples generated by our method is closer to the real distribution, which enables better coverage of the data distribution in the test set. This increased variance helps to reduce the bias of the model, thereby improving its ability to generalize to unseen data. Other methods can lead to huge biases that are detrimental to model learning. Due to word constraints, we will provide an in-depth analysis in the latest version.

Q2: The contribution … sine functions are homeomorphisms. However, this proof seems too trivial to be …, … it's obvious ….

A2: Thank you for your valuable advice. For a professional scholar like you, understanding is relatively simple. However, in the field of point cloud augmentation, most of the methods in Table 1 lack theoretical basis. Our method is the first one based on homeomorphic theory for point cloud augmentation, and we have to admit that it is indeed a significant contribution in the field of point cloud data augmentation. We hope that more detailed definitions and proofs will help different readers quickly understand the relevant theories of our SinPoint.

Q3: A better way to demonstrate its effectiveness would be to compare it against using each transformation individually to isolate the impact of the Markov chain process itself.

A3: Thank you for your constructive comments. We add ablation experiments to analyze the influence of different transformations on the model. It can be seen from the experiments that the Markov augmentation process has a better stable gain. The results are as follows:

Table R1: Ablation analysis for a single transformation with Markov.

Q4: However, it would be beneficial to show results where MSF is applied to classification and SSF to segmentation. (Justification for two methods (SSF and MSF))

A4: Thank you and Reviewer SdQc for your constructive comments. This experimental analysis was also considered in an earlier manuscript but was removed due to formatting issues in the submission version. According to your suggestion, we will re-add this part of the experiment and analysis in the latest version, and some results are compared as follows:

Table R2: SSF and MSF on classification and segmentation.

Q5: However, the authors did not specify the percentage of original samples used or explain how the mixup rate was chosen, which is important for reproducibility and understanding its impact.

A5: Thanks for your careful review. We show in Figure 5 that the original sample and the enhanced sample are input together for training, without setting the mixing rate. As can be seen from Table 4, SinPoint alone can improve the performance by 1.2, and the improvement after mixing samples is only 0.5. Mixed samples do not play a dominant role in performance improvement. SinPoint and the Markov augmentation process are the decisive factors.

Q6: Definition 1 is not used anywhere in the paper, as it measures the variance of the prediction but not the data input.

A6: We put Definition 1 in the text to facilitate logical coherence and reader understanding because Definition 1 and Theorem 1 are related. And definition 1 is also used in the proof of Theorem 1 in the supplementary material.

Q7: Algorithm 1 is confusing as it's named SinPoint.

A7: Thanks for reminding me. We will modify the title of algorithm 1 to SinPoint without Markov. The pseudo-code of the Markov process is added in the latest version.

We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.

Dear Reviewer SdQc:

Thanks for your time and insightful reviews. We responded in detail as follows:

Q1: It's possible that large deformations, even if theoretically homeomorphic, could still distort the shape in a way that effectively changes the topology.

A1: Thank you for agreeing with our theory. Homeomorphism is strictly maintained in theory and has been proved by theorem 2. If the topology is inconsistent, holes or tears will be created after deformation, but our continuous deformation based on sine transformations does not create holes or tears and therefore does not change the topology. However, in machine learning, excessive deformation can lead to ambiguity, which we need to avoid. As we have verified in Table 3, too large deformation parameters will be detrimental to model learning. Therefore, we choose the appropriate parameters to generate the enhanced sample.

Q2: A much bigger concern is … limited to … simple … datasets. Without … on complex … datasets.

A2: Your question is very professional. In terms of experiments, we also tested on complex datasets, and Table 10 in the supplementary material shows our experimental results on S3DIS and SemanticKITTI.

Q3: The paper doesn't justify why a sine function is the best choice, compared to other possible deformation methods. a lack of comparison to …, like thin-plate splines or free-form deformation.

A3: Your questions are very professional and very helpful to us. We clarify that we are not saying that the sine function is the best choice. We discussed why the sine function was chosen, and we have a brief introduction in Section 4.3. The reasons are as follows: The sine function is a periodic function, and by controlling the amplitude, the maximum deformation can be easily adjusted. Other functions, such as monotonic functions, parabolic functions, or other types of functions, cause excessive deformation as the diameter of the object increases, which leads to augmented samples deviating from the real ones.

In contrast, thin-plate splines are computationally more complex and may not be suitable for current applications. Free-form deformation (FFD) can provide flexible deformation control, but the process is complicated. Thus, it is simpler and more efficient to use the sine function directly.

This can be our future exploration direction because FFD can generate more controlled deformation samples. We would like to thank the reviewers for their valuable comments, which also guide us to a new exploration direction.

Q4: The Markov Chain Augmentation Process, while adding flexibility, also adds complexity, and it's not entirely clear if the benefits outweigh the costs.

A4: Thank you for affirming our method. We have given a quantitative analysis of your concerns in Table 11 (in supplementary material). Compared to existing methods, such as PointAugment, our method reduces time costs by up to 10 times and improves performance by 11%. We not only save the calculation cost but also improve the accuracy of the model.

Q5: The choice of evaluation criteria, specifically the datasets.

A5: Thanks for your suggestion. To make a fair comparison with other methods, we had to conduct primary experiments on these datasets. However, we have also carried out additional experiments, including S3DIS and SemanticKITTI, in Table 10 of supplementary materials. Moreover, in Table 3, we further investigate the robustness of the SinPoint by simulating complex noises in the real world. We plan to explore SinPoint's performance on more realistic and complex datasets in future work.

Q6: More qualitative analysis, ... showing examples of failure cases

A6: Thanks for reminding me. We added it in the latest version, and you can see more qualitative analysis examples of failure cases in Figure 1 (in https://github.com/Anonymous-code-share/ICML2025). Meanwhile, we also conducted ablation experiments as shown in Table 7. When excessive deformation occurs, the performance will decline.

Q7: It misses a key connection to the extensive research on non-rigid deformation in computer graphics.

A7: Your question is good, especially your proposed FFD method for computer graphics, which encourages us to develop controlled deformation augmentation in the future. We plan to discuss the feasibility of these methods (like TPS or FFD) as part of our related work.

Q8: Justification for two methods (SSF and MSF).

A8: Due to the word limit, we jointly replied to the same questions in Q4 of Reviewer 8z5w.

Q9: code publicly available upon publication.

A9: Yes, we must do it.

We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.

Dear Reviewer MuAY:

Thanks for your time and insightful reviews. We responded in detail as follows:

Q1: ...such transformations may generate unrealistic data.

A1: Your opinion is very professional. Indeed, when the deformation parameter is too large, it will produce unrealistic data. Therefore, we chose smaller parameters to avoid such results, and ablation experiments were also conducted in Table 7. When the deformation is too large, it will also reduce the performance of the model. Our SinPoint aim is to increase the geometric diversity of the augmented samples while maintaining topological consistency to understand the nature of the data from more viewpoints and conditions, which can effectively avoid the overfitting of the model to the training data.

Q2: ...it dues to confusing part boundaries ... which leads to incorrect training signals. Even though the authors tried to show in Table 10 that their method can work well in scene segmentation ..., the chosen method, MinkNet, is pretty old (2019).

A2: Your observations were sharp and your reviews were professional. To avoid boundary confusion, we introduce more conservative parameters to ensure that the transformed part boundaries remain as accurate as possible and avoid extreme distortions. In addition, as can be seen from Table 7, the appropriate deformation can maximize model performance.

In the experiment, we also found that the performance improvement in the part segmentation was not significant and conducted a series of experimental verifications, as shown in Table 9 and Table 10. We find that most of the data augmentation methods in Table 1 are not suitable for segmentation tasks. As shown in Table 2, only four works reported the result of part segmentation. But our SinPoint is best.

However, to confirm whether the method has limitations, we further verify it on multiple backbones, as shown in Table 9, and it can be found that our method can achieve certain performance improvement.

Further, we test on scene segmentation; in Table 10, the performance improvement is still limited when performing semantic segmentation of S3DIS, while the performance improvement is significant when performing instance segmentation on SemanticKITTI.

We analyzed that ShapeNetPart and S3DIS are fine-grained semantic segmentation datasets, which are more challenging, while SemanticKITTI is a coarse-grained instance segmentation dataset. As shown in Table 1, our method is better suited for object tasks, which explains its superior performance on SemanticKITTI. Our main goal was to use MinkNet to test the limitations of our approach to segmentation tasks, which has been demonstrated in experiments. So we didn't add more scene-level backbone to test.

Q3: the proposed method shows effectiveness with older ... (Table 1) but is less effective ... with recent methods (Table 6).

A3: Your question is valuable. This issue is largely influenced by the dataset and model capabilities. The older backbone design is simple and prone to overfitting due to insufficient data, and data augmentation is to avoid this problem by increasing the diversity of data. Therefore, data augmentation can greatly improve its performance. However, in the recent backbone, due to its more powerful network design and strong representation ability, the backbone is close to the theoretical limit, and the marginal revenue is reduced.

Therefore, all current point cloud augmentation efforts are based on the old backbone to test the performance of the method, which can highlight the advantages of these methods.

Q4: Detailed analysis the impacts part boundaries and label consistency

A4: Your question is very professional and valuable. We have carried out relevant analysis in the first draft, but this part has been deleted from the submission version due to the structural adjustment. For the boundary analysis, we deeply discuss the relationship between the determinant of the Jacobian and the parameter of sine transformation. Regarding label consistency, we analyze it from the property of one-to-one mapping of homeomorphism. Due to the rebuttal word limit, we will re-add these in the latest version.

Q5: The authors should report additional details on model size, number of parameters, and throughput.

A5: Our SinPoint is a plug-and-play, non-parameter method and is only used during the training phase. It is removed during the testing phase. Therefore, our SinPoint does not change the size, number of parameters, and throughput of the baseline. However, to show them more clearly to readers in the future, we plan to report these details and add them to the latest version.

We thank you again for your careful review, which helped us a lot. We have addressed all your concerns in detail. If you have other questions, we can discuss them again, and we look forward to your feedback.