Feature-Preserved Point Cloud Simplification Based on Natural Quadric Shape Models
Round 1
Reviewer 1 Report
This is worth publishing now! Especially the Fig. 13 is convincing. Included are only few typo corrections. Fix them, no need to review once more.
p27L611: The grid-based created -->
The grid-based approach/simplification created ...
p28L667: programing --> programming
p31L768: zhang --> Zhang
Below is a comment, which is left to the consideration of the editors:
It could be wise to reduce the size of Figs 8,9,12,14,15 and 16 just a bit (e.g. so that the Fig 8 fits on one page). They would remain quite readable with a little more modest size, too. The same comment with Table 1: maybe you could fit the content to 3 columns: rule definition + 2 images? You may gain a reduction of 1 or 2 pages! :)
As asuggestion for your possible future efforts, I would suggest you check also if there are any fast and noise-tolerant methods to approximate some of the following curvature energy modes (expressed with principal curvature k1 and k2):
a) [(k1+k2)/2]^2 : sensitive to deviation from the local (...) saddle points
b) k1*k2: (...) conical surfaces
c) (k1-k2)^2: (...) sphere surface
d) max(|k1|,|k2|)^2: (...) planes
e) (k2/k1)^2 (...) straight 1-dim segments
Some of these could be a part of your library of the simplification rules.
Perhaps there are some specific applications for some of these?
Author Response
Revision Report: Feature Preserved Point Clouds Simplification Based on Natural Quadric Shape Models
First of all, the authors would like to thank the editors and the reviewer for their time and their valuable comments. Your comments give us confidence of our work, and encourage us to continue our research. The suggestions for the future efforts are valuable. The speed of the FPPS is still a pay point in our work. The simplification rules which you provide are very useful for FPPS.
The revisions according to your comments are as follows:
(1) Comment: p27 L611: The grid-based created --> The grid-based approach/simplification created ...
Response: Thank you for your suggestion. The modification details are as follows:
The grid-based simplification created voxels at a specific resolution without geometric feature estimation, and compute the center of each voxel as the simplified point cloud.
(2) Comment: p28 L667: programing --> programming
Response: Thank you for your suggestion. The modification details are as follows:
Parallelized programming is another method to solve the problem of the algorithm’s efficiency. Using OpenMP and GPU, we have tried to introduce parallelization into FPPS.
(3) Comment: p31 L768: zhang --> Zhang
Response: Thank you for your suggestion. The modification details are as follows:
39. Zhang, K.; Qiao, S.; Zhou, W. Point cloud segmentation based on three-dimensional shape matching. Laser & Optoelectronics Progress 2018, 55, 121011-121011.
(4) Comment: As a suggestion for your possible future efforts, I would suggest you check also if there are any fast and noise-tolerant methods to approximate some of the following curvature energy modes (expressed with principal curvature k1 and k2):
a) [(k1+k2)/2]^2 : sensitive to deviation from the local (...) saddle points
b) k1*k2: (...) conical surfaces
c) (k1-k2)^2: (...) sphere surface
d) max(|k1|,|k2|)^2: (...) planes
e) (k2/k1)^2 (...) straight 1-dim segments
Some of these could be a part of your library of the simplification rules.
Perhaps there are some specific applications for some of these?
Response: Thanks for your suggestion. The valuable suggestion is very useful to our work. The curvature energy modes which the suggestion provided inspire us to expand the point cloud matching model (PCMM). We consider that the new simplification rules according to your suggestion will be sure to improve the efficiency of FPPS.
We appreciate your insightful suggestions. We revised the manuscript based on your comments. The suggestion for our future work is very useful. Once again, thank you for all the valuable comments and suggestions.
Reviewer 2 Report
The authors have included a revision report as additional material, as if the paper were a revised submission.
It seems that the reviews in the report have been addressed.
However, I am not one of the original reviewers, and I have further comments.
The paper is badly written, with many confusing passages.
I have listed some of them at the end of the review.
Moreover, I suggest the authors to proofread the whole paper, maybe with the help of someone.
Table 1 (line 357) explains the shape-based simplification algorithm.
The authors make use of symbols ("center", "voxel", "alpha_shape") which apparently refer to steps in the algorithm.
However, the symbols should be defined in the text.
The short sentences you added after "//" symbol, as if they were C++ comments (?), are not enough to understand the algorithm.
Furthermore, the reasons behind the steps in the algorithm are not explained.
For example, why is the center of the ellipsoid preserved more than its edges?
The authors propose a point cloud simplification method, but they test it on meshes.
They describe how to remove points from the point cloud, but they do not explain how the mesh is transformed when a point is removed.
For example, did they merge nearby faces when a point is removed? Further explanation is required.
-- Typos and confusing passages --
Line 54: "Especially, when facing huge original point clouds" remove comma.
Lines 101-103: this sentence is unclear. Please clarify.
Line 117: "The simplification rules are built." Please explain this sentence. What does "built" mean?
Line 119: "The simplification rules refer to regular shapes and, are" remove comma.
Lines 129-130: "data set of point clouds" is R a point cloud or a set of point clouds?
Line 130: "p_i is the ith data" What is a "data"? Is p_i a point in a point cloud?
Line 150: "Thus, the data attributes are scatter and simple." If "scatter" is an adjective, it should be "scattered"? Besides, what does "scattered and simple" mean?
Line 179: "executed as shown in eq1:" missing space and period "eq. 1"
Line 203: "multi-layer point cloud voxel grids are created by voxelization, like a pyramid." you mean "multi-resolution"?
Line 226: "Assuming the number of key points for scale keeping is \alpha_sift" Where is \alpha_sift defined?
Line 227: "Then, probability of point_SIFT is limited in the zone [0, \alpha_sift )" Why? Please clarify.
Line 231: Equation 4: is \alpha_sift the same as \alpha_SIFT? If so, please use the same symbol.
Line 239: "In a small area, the local optimum angle and density are picked as the boundary feature data." How do you compute the boundaries? Unclear.
Line 252: Points in Fig. 6b are almost invisible.
Line 253: "Assuming the size of data is \alpha_outlier" Unclear, is \alpha_outlier a parameter?
Line 284: "Using the Kd-tree with threshold \sigma_c," What is the threshold of a Kd-tree? Please clarify.
Line 286: Equation 9: is C_curvature the same as c_curvature? If so, please use the same symbol.
Line 304: "taht"
Line 306: "If point p can satisfy equation (10)" equation 10 is an expression, not an equation, unless I missed the definition of f(x,y,z). Therefore, points cannot "satisfy" it. Please explain.
Line 320: What is \phi? Unclear.
Line 322: equation 12: please check parentheses order in this equation.
Line 346: "h is the average of h_s, h_p, and h_c." Please define h_s, h_p, and h_c.
Line 348: "ellipsoid are shown in Table1" missing space
Line 354: "Or else, if the point" remove "Or"
Line 357: Table 1: Please remove "//" in descriptions.
Line 361: "All the codes were written" -> "The code was written"
Line 382: "This prove that parameter k exists in the upper boundary" Please clarify. What is an "upper boundary" here?
Line 384: please put the caption for Fig. 8 in the same page as Fig. 8.
Line 416: "Figure 11": is the wrong figure cited here?
Line 423: "Fortunately, the inflection point is shown in Figure 10" It is not clear in Fig. 10 where the inflection point is.
Line 493: "Figure13" missing space
Line 602: "In order to measure the stability of experimental result, the simplification algorithms are transplanted to another computer configured as the same compiling environment." Are you talking about numerical stability? How does a different computer with exactly the same compiler let you test numerical stability?
Line 657: "but also used different data sets to, validate the simplification effects of" remove comma
Author Response
We have uploaded a point-by-point response to the reivewer's comments as an attached Word file. Thank you very much.
Author Response File: 
Author Response.doc
Round 2
Reviewer 2 Report
The paper looks better.
I still have a few minor notes:
Line 359: "creating voxels at resolution \alpha": so, you are using voxelization with resolution \alpha to downsample the point cloud. If that is the case, just write it.
Line 241: "limited in the zone" and line 271: "is in the zone": zone --> interval
Line 380: "which respectively are computed by the Equations (4), (5) and (9), respectively" double respectively
Line 447: "This phoneme reveals the maximum value of k should be found" phoneme --> phenomenon. Also, I would add a "that" after "reveals".
Author Response
We appreciate your comments and suggestions. We have uploaded a point-by-point response to the reivewer's comments as an attached Word file. Thank you very much.
Author Response File: 
Author Response.pdf
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
This manuscript presents an approach for point cloud data simplification. The topic is of great interesting and also closely related to the theme. However, there are some parts have to be improved.
1: English has to be improved extensively. There are a number of typos as well.
2: The knowledge gap is not clearly described. Some existing papers on the topic are not discussed.
3: The complexity of the presented algorithm is not analyzed.
4: For the figures, HD images are needed and the caption should be self-explanatory.
For specific comments, please refer to the attached PDF file.
The topic is of great interest and the authors are highly encouraged to improve the manuscript.
Comments for author File: Comments.pdf
Author Response
We have uploaded a point-by-point response to the reivewer's comments as an attached Word file. Thank you very much.
Author Response File: Author Response.docx
Reviewer 2 Report
A word document is attached containing my comments.
Comments for author File: Comments.docx
Author Response
We have uploaded a point-by-point response to the reivewer's comments as an attached Word file. Thank you very much.Author Response File: Author Response.docx
Reviewer 3 Report
*General comments*
This is a very welcomed contribution to the point cloud filtering genre in cases, where the surface noise is symmetrical. The value of the paper is in the usage of the expressive polynomial batch of Eq. 10 to not only to match the surface bu to classify it locally. There is a natural problem of controlling the subdivision, and this is done by a recursive addition of new keypoints (or so it seems to). The process resembles neighborhood voting common in the PC and image processing.
Some things are not clear e.g.:
-how the initialization of the key points has been done?
-some details, e.g. can planes merge with possible neighboring planes (like cones extend to neighbors), how spherical part is limited from the border (if not a closed sphere),
-the actual maximum memory usage and computation time on a relatively similar environments and with a relatively equivalent set of tasks. Include a new table.
-In the conclusions, outline some of the potentials for the future algorithm
optimizations.
*Typos and grammatical errors*:
Between lines 169 and 170: Add a sentence explaining your point notation, e.g.:
Points are addressed with a constructor notation P(x,y,z) to simplify the presentation.
122 {p_i(x,y,z)}(1<=i<=n) --> {p_i(x,y,z)}_{1<=i<=n} (set to index, or add a ', ' in between...
194: voxelition --> voxelization
204: Form --> From
219: As we all known, --> It is generally known, that
222-223: angel --> angle
231: We create ... --> complete and clarify the sentence
253: k -- the range --> all these variable introductions (starting from line 198) could be a bit more standard, e.g.:
where k is the range of the local area and \bar{p] the centroid of the points p_i
(when concerning the stuff introduced in an equation).
275: And Then combined --> When combined ...
293: Clarify the sentence, maybe it should be: Conicoids are clearly described and their shape can be completely controlled. We create a CM (Or something like that)
294: equation10 --> add a blanco.
346: Adjust the labels of the first column to the top of the 8invisible) box. Now the table 1 is a bit hard to read. Change rule names from rule_{plane] to plane (and so on).
371: )and --> add a blanco
499: produces unsatisfied --> produces an unsatisfied
499: Fig. 14 is either unnecessary (describe phenomena by words) or zoom into the middle area (two corners of the middle surface), where the most changes are. Now the details are hard to be distinguished.
Tables 4 and 5 should have an extra column about the computing costs.
it could be simply a time over similar tasks, or you could add a new table
with memory and time costs.
565: --> for the selection of the simplification algorithm.
570: make sure you have some time comparison somewhere in the text,
one possibility would be to have the s.t.d. time and memory analysis
at a new table.
572: You should mention (in a general way) where are the potential future
efficiency improvements to the FPPS.
Author Response
We have uploaded a point-by-point response to the reivewer's comments as an attached Word file. Thank you very much.Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
All the comments are addressed sufficiently. Make sure that all the answers are reflected in the text.
