Low-Overlap Bullet Point Cloud Registration Algorithm Based on Line Feature Detection

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

- This paper proposes a low-overlap bullet pointcloud registration method using line feature detection.

- from my point of view, the paper's topic is relevant and interesting

- please place title 2 on page 3

- please enhance the quality of the images

- please add the scale notation in the point cloud images (and also other information such as the number of points could be interesting)

Comments on the Quality of English Language

- English can be improved 

Author Response

Dear Reviewer,

We would like to thank you for your efforts in reviewing our manuscript titled " Low overlap bullet point cloud registration algorithm based on line feature detection", and providing many helpful comments and suggestions, which will all prove invaluable in the revision and improvement of our paper, as well as in guiding our research in the future.

Point 1: please place title 2 on page 3

Response 1:

         Thank you for your suggestion. Considering the aesthetic and readability aspects, we have moved title 2 to the next page (Page 3, line 116).      

Point 2: please enhance the quality of the images

Response 2:

         We've improved the clarity of all the images to make sure they're visible. 

Point 3: please add the scale notation in the point cloud images (and also other information such as the number of points could be interesting)

Response 3:

Thank you for your suggestions. Due to the subtle nature of bullet markings, which are difficult to discern with the naked eye, we have continued to use the original coloring method to display the matching of bullet markings in the simulation section. However, in the experimental section with actual bullet point cloud data, we have adopted a different presentation method and annotated the scale and quantity of the experimental point cloud. For detailed information, please refer to Figure 12 in the paper (Page 18, line 408).

Thank you again for your valuable comments and suggestions.

Yours sincerely,

Qiwen Zhang

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors, 

Thanks for sharing the excellent research work done. 

I enjoyed reading the paper. The only comment I have is to improve the resolution for the figures. I suggest saving the figures as .SVG format, followed by copying into the manuscript. 

Comments on the Quality of English Language

English is generally ok. No major concerns. 

Author Response

Dear Reviewer,

We would like to thank you for your efforts in reviewing our manuscript titled " Low overlap bullet point cloud registration algorithm based on line feature detection", and providing many helpful comments and suggestions, which will all prove invaluable in the revision and improvement of our paper, as well as in guiding our research in the future.

Point 1: The only comment I have is to improve the resolution for the figures. I suggest saving the figures as .SVG format, followed by copying into the manuscript.

Response 1:

         Thank you for your recognition and advice. We've improved the clarity of all the images to make sure they're visible.

Thank you again for your valuable comments and suggestions.

Yours sincerely,

Qiwen Zhang

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The presented work is of great interest, although the experimental part is limited to the presentation of a single case. Therefore, it is unclear how effective the proposed algorithm might be in scenarios where the point clouds are acquired using different systems and/or under different conditions.

 

The introduction is very concise but adequately introduces the topic. In the description of the voxelization of the point cloud, there is a reference to the large number of points acquired. Is it possible to approximately indicate how many points each point cloud consists of? Also, in paragraph 2.2, the necessary steps to perform a rough registration of the point clouds by aligning the central axes of the bullets are described. In step 1, the process starts by stratifying the cloud into layers along the y-axis. The authors do not explain whether the choice of the y-axis is arbitrary or if the scans are acquired in such a way that the choice of the y-axis is mandatory. Still in the same paragraph, lines 141-143, it is not clear how the four points on which the sphere is constructed are taken.

 

In lines 166-167, the meaning of the sentence is unclear. In line 173, there is a reference to publication [26] without clarifying what similar idea it concerns (the reader would have to read the referenced publication, and even then, it is not certain that the similarity would be evident). In line 215, the term NTH is introduced without being described. In lines 237-240, the text is unclear.

Author Response

Dear Reviewer,

We would like to thank you for your efforts in reviewing our manuscript titled " Low overlap bullet point cloud registration algorithm based on line feature detection", and providing many helpful comments and suggestions, which will all prove invaluable in the revision and improvement of our paper, as well as in guiding our research in the future.

Point 1:：It is unclear how effective the proposed algorithm might be in scenarios where the point clouds are acquired using different systems and/or under different conditions.

Response 1:

         Thank you for raising the concern that it is not clear how effective the proposed algorithms are in scenarios where point clouds are obtained using different systems and/or under different conditions. We have taken your comments into account and have included a section 4 dedicated to the evaluation of the algorithm, in the hope of providing a more balanced perspective on the research and making recommendations for further improvements (Page 19, line 415-448).

Point 2: In the description of the voxelization of the point cloud, there is a reference to the large number of points acquired. Is it possible to approximately indicate how many points each point cloud consists of?

Response 2:

         Thank you for pointing out semantic ambiguities in the text. A description of the number of point clouds is available in the subsequent experimental session Table 1 (Page 11, line 301)as well as in Figure 12 (Page 18, line 408), and we have added an approximate description of the number of point clouds in 2.1 of this paper as well (Page 4, line 143-145).

Point 3: In step 1, the process starts by stratifying the cloud into layers along the y-axis. The authors do not explain whether the choice of the y-axis is arbitrary or if the scans are acquired in such a way that the choice of the y-axis is mandatory. Still in the same paragraph, lines 141-143, it is not clear how the four points on which the sphere is constructed are taken.

Response 3:

We recognize your question about the singularity of the point cloud format to which the algorithm in this text applies. Because the acquisition device is an auto-zoom 3D measuring instrument, which has a hardware structure that scans on a fixed test bench (as shown in Fig. 8 (Page 15, line 379)), the surface undulation of the data obtained defaults to the z-axis, and the direction of the bullet traces defaults to the y-axis. If other data inputs do not match the default axis positions, simply flip the data during the preprocessing stage. Lines 141-143 of the same paragraph, according to the geometric theorem, four points in any non-coplanar space can find an external ball, and this theorem shows that four points in any non-coplanar space can uniquely determine a ball in 3D space, i.e., these four points are on the surface of this ball. So the four points in this paper are taken arbitrarily by the arbitrary function rand.

         Apologies for our lack of clarity in the article, it has been corrected in the article (Page 5, line 162 and 164-166).

Point 4: In lines 166-167, the meaning of the sentence is unclear.

Response 4:

         Sorry we didn't describe it clearly, the original description is " The strong dependence on the initial position and the resulting error due to the large number of non-overlapping regions resulting in many spurious key point matches." we originally meant "Many existing alignment algorithms, such as the ICP algorithm, have high requirements for the initial position of the point cloud alignment, and many incorrect feature point matches can occur with small overlap rates, both of which can result in excessive error in the results", we’re very sorry for the reading difficulty, and we have corrected the expression in the original text (Page6, line 189-192).

Point 5: In line 173, there is a reference to publication [26] without clarifying what similar idea it concerns (the reader would have to read the referenced publication, and even then, it is not certain that the similarity would be evident).

Response 5:

Thank you for your valuable advice. In literature 26, authors Theiler, P. and Schindler, K. provide such a coarse registration in a fully automatic fashion, and without placing any target objects in the scene. The basic idea is to use virtual tie points generated by intersecting planar surfaces in the scene. Such planes are detected in the data with RANSAC and optimally fitted using least squares estimation. Due to the huge amount of recorded points, planes can be determined very accurately, resulting in well-defined tie points. Given two sets of potential tie points recovered in two different scans, registration is performed by searching for the assignment which preserves the geometric configuration of the largest possible subset of all tie points.

This is because binding point matching based on geometric constraints is very reliable, but the combinatorial complexity of the binding points makes it difficult to determine the effective number of binding points. In contrast, matching points individually using local descriptors is effective, but error-prone and often ambiguous. Therefore, the authors of this literature chose to combine these two steps to get the best of both worlds. The combined set of hypothetical correspondences is first filtered with a new geometric descriptor, discarding most of the correspondences with very different descriptors. Then, instead of making a final decision based on the descriptors, the matching is done by searching for the largest subset of the reduced set of candidate matches.We have borrowed this idea and filtered the overall set of bullet points by the most linear feature of the bullet scars, discarding correspondences that are very different, and extracting the bullet scars as a linear feature. The extracted bullet marks are shown in Figure 4 (Page 7, line 202).

In the original article, we did not describe the idea clearly, and In the original article we did not describe the idea very clearly and have made it clear in the specific formulation in the text. (Page 6, line 198-200).

Point 6: In line 215, the term NTH is introduced without being described. In lines 237-240, the text is unclear. In lines 237-240, the text is unclear.

Response 6:

         Thank you for your careful correction. NTH is the phrase to the nth meaning two random positions in the nth generation population, which has been re-swapped in the text to describe it because of semantic ambiguity. We have made revised changes (Page 8, line 242).

Lines 237-240 are a description of some of the parameter values set in the improved cuckoo algorithm for finding the optimal rotation angle, which we have clearly expressed in the original text (Page 9, line 264).

Thank you again for your valuable comments and suggestions.

Yours sincerely,

Qiwen Zhang

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This paper proposes a new algorithm for low-overlap point cloud registration based on linear feature detection, which uses a voxel reduction method to remove noise and outliers and reduce computational costs. The sphere point cloud is transformed to the best initial position using geometric features and the central axis of the sphere, and a discrete Hough transform with icosahedral fitting is used to simplify the parameters of the transformation search space and obtain the direction vectors of linear features. The optimal rotation angle is determined using an improved cuckoo algorithm, which allows for accurate registration of ball point clouds with a low degree of overlap. Experimental results have shown that the proposed method significantly reduces the registration error compared to existing algorithms such as ICP, GICP, and TRICP.

However, some revisions need to be completed.

1. The title, abstract, and introduction were found appropriate. But in the introduction, it would be appropriate to provide a general organization of the article.

2. The introduction provides extensive information about the background and significance of the problem. However, it does not identify any gaps in the current literature that this research aims to fill. Explicitly stating these gaps would strengthen the introduction and highlight the novelty of the research.

3. For a better understanding and analysis of the numerical experiments, it would be good to present the pseudo-code of the proposed algorithm.

4. The readability and quality of Figure 7 should be improved.

5. The computational complexity of the proposed approach is not considered.

6. The paper should include a Discussion section, which should include a thorough analysis of the limitations of the proposed method. Taking these limitations into account will provide a more balanced view of the study and suggest areas for further improvement.

Comments for author File: Comments.pdf

Author Response

Dear Reviewer,

We would like to thank you for your efforts in reviewing our manuscript titled " Low overlap bullet point cloud registration algorithm based on line feature detection", and providing many helpful comments and suggestions, which will all prove invaluable in the revision and improvement of our paper, as well as in guiding our research in the future.

Point 1: In the introduction, it would be appropriate to provide a general organization of the article.

Response 1:

Sorry we have not expressed my writing enough, and I have added the general structure of the article in the original text (Page 3, line 102-115).

The structure of the paper is as follows. Section 1 describes the research background and related work. Section 2 is devoted to our methodology.Section 2.1 introduces automatic cyclic voxel downsampling, Section 2.2 explains the principle of fitting the bullet median.Section 2.3 describes the extraction of linear features of the bullet traces using the discrete Hough transform.Section 2.4 searches for the optimal rotation angle in the parameter space using the improved Cuckoo algorithm to achieve a low overlap rate for the bullet point cloud alignment.In section 2.5, the algorithm is analysed for its the computational complexity of this algorithm is analysed in Section 2.5. In Section 3, we apply the algorithm to some noisy bullet point cloud models and actual bullet point cloud data collected, and compare the results with those of the icp, TRICP, and GOICP algorithms, and the computational error is close to 0, which proves the validity of the algorithm. Suggestions for possible further improvements of the algorithm are made in Section 4. Finally, in Section 5, the methodology and experimental results used in this paper are summarised.

Point 2: The introduction provides extensive information about the background and significance of the problem. However, it does not identify any gaps in the current literature that this research aims to fill. Explicitly stating these gaps would strengthen the introduction and highlight the novelty of the research.

Response 2:

         We would appreciate your suggestion to clearly identify the gaps in the literature that this paper fills. In our experiments, we found that the bullet as a feature with fine bullet marks is more of a challenge in the low overlap rate alignment process. Compared with tradi-tional images and depth images, the features of bullet point clouds are more difficult to be extracted, so it is difficult for existing point cloud alignment algorithms to accu-rately align bullet point clouds. Especially in cases such as small overlapping areas, these algorithms suffer from poor accuracy, falling into local optimization, or even in-ability to align and mismatch. To address the shortcomings of the existing alignment algorithms ，this paper proposes a low overlap bullet point cloud registration method based on line feature detection.We've corrected it in the manuscript (Page 2, line 88-94).

Point 3: For a better understanding and analysis of the numerical experiments, it would be good to present the pseudo-code of the proposed algorithm.

Response 3:

         Thanks for the reminder, I have added the algorithmic pseudo-code for fitting the central axis and improving the cuckoo algorithm to find the optimal rotation angle to help understand the reading (Page 6, line 187 and Page 9, line 267).

Point 4: The readability and quality of Figure 7 should be improved.

Response 4:

We recognize your concern about the readability of Figure 7 in the article, and to address this, we will describe it. For Fig. 7, it shows the graphs generated by ICP and its variants error values RMS, NNED, HD, and MED at different overlap rates of the bullet point cloud, it is difficult to find an accurate match because the geometric structure and complexity of the overlapping regions of the point cloud can be different, if the overlapping regions contain smaller and more complex geometrical features, it is even more difficult for ICP, TRICP, and GOICP alignment algorithms to match them accurately , resulting in wavy fluctuations in the error value. In contrast, the algorithm in this paper has a stable error value close to 0 when the overlap rate is not less than 20%, which indicates that the alignment algorithm in this paper is very effective in dealing with the current point cloud data, and is able to accurately find the best alignment transform.

We have added the interpretation of the results of Fig. 7 in the paper to help understanding, so that the experimental results are more clear and concise (Page 14, line 354-363).

Point 5: The computational complexity of the proposed approach is not considered.

Response 5:

It is us who is not rigorous enough, we have added section 2.5 to analyse the complexity of the algorithm in this paper (Page 9, line 268-281).

This algorithm mainly consists of the following four steps: voxel downsampling, fitting the central axis, discrete Hough transform to extract line features, and improving the no cuckoo algorithm to find the optimal rotation angle to complete the matching, and the total computational complexity is O(m+k3+n.+T-m+m), where m is the number of points in the point cloud, assuming that there are k voxels on each axis, the number of populations n is set to 20, and the maximal number of iterations is T, then k3≪m and n ≪ m and h ≪ m, then the overall complexity is mainly controlled by O(T-m). The ICP algorithm consists of initialising alignment, iterating nearest-point matching, calculating the transformation matrix and applying it, and iterating until convergence, and the computational complexity is O(T-(mlogm+m)) = O(mlogm). Similarly the computational complexity of TRICP, GOICP is O(T-(mlogm+m)), O(T-(mlogm+m)+ b^d). Where GOICP algorithm branch delimitation by branching factor b =3 and depth of tree d=10.This algorithm has some advantage in complexity.

Point 6: The paper should include a Discussion section, which should include a thorough analysis of the limitations of the proposed method. Taking these limitations into account will provide a more balanced view of the study and suggest areas for further improvement.

Response 6:

Thank you for pointing out the shortcomings of the article structure. We have revised my manuscript according to your suggestions in Section 4 (Page 19, line 415-448).

Thank you again for your valuable comments and suggestions.

Yours sincerely,

Qiwen Zhang

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

The authors addressed all of my concerns, and I think it is ready to publish.