Robust and Efficient Corner Detector Using Non-Corners Exclusion
Round 1
Reviewer 1 Report
The authors propose a method to detect corners in computer vision using an algorithm based on the Harris corner algorithm. The authors improve the implementation of this method using ideas from the Fast algorithm. The presentation is clear, however the paper has some concerns.
The first phrase of the abstract is at least misleading. There are simply too many computer vision algorithms that do not rely on corner detection. In fact current research is moving away from this concept due to, as the authors mention, low reliability.
Regarding, the method itself, the authors should consider whether the performance gain is simply due to the firts heuristic they apply in step A. Non-corners Exclusion. By eliminating those corners without intensity change in pixels 1, 5, 9 and 13 they are effectively considering a lower number of possible corners (for example an acute corner ocuppying pixels 6, 7 and 8 of the Bresenham circle). Authors should clarify how much this affects the quality of detection.
Regarding evaluation, the authors use one small sample of images where tests are applied. Why those particular images? They also apply various transformations to the images, in order to evaluate the stability of the detection. However, a most natural way to test it would be on a video stream, where additional artifacts appear such as luminosity changes.
Author Response
Dear Editors and Reviewers:
Thank you very much for your valuable comments. We have carefully revised the submitted manuscript (applsci-654049) to address each of your critiques. The major revisions have been marked in red in the revised manuscript. We also have updated some grayscale statistical charts with color ones. For our convenience, our point-by-point responses are as follows.
Yours Sincerely
Zaifeng Shi
Tao Luo
12/24/2019
Reviewer #1: The authors propose a method to detect corners in computer vision using an algorithm based on the Harris corner algorithm. The authors improve the implementation of this method using ideas from the Fast algorithm. The presentation is clear, however the paper has some concerns.
The first phrase of the abstract is at least misleading. There are simply too many computer vision algorithms that do not rely on corner detection. In fact current research is moving away from this concept due to, as the authors mention, low reliability.Answer: Thank you for your valuable comments. In fact, SIFT and other feature descriptor detection methods have better accuracy and robustness, and are more widely used in computer vision nowadays. However, corner detection is still a feature extraction type that cannot be ignored in computer vision. When the accuracy requirements are not very high, corner detection can still be applied due to its simplicity and good performance. For example, it has been used in object detection, 3D reconstruction and other fields in recent years [R1.1- R1.3].
Per your comments, we have modified the expression in abstract and introduction, and added the references in the introduction part. The modified sections are highlighted in red.
[R1.1] Y. Pang, J. Cao and X. Li. Learning sampling distributions for efficient object detection. IEEE Trans. Cybern, 47(1): 117-129, 2017.
[R1.2] 2. Yan.C et al. A fast Uyghur text detector for complex background images. IEEE Trans. Multimed. 20(12): 3389–3398, 2018.
[R1.3] 3. Zhang, S and Liu, W: Single image 3D reconstruction based on control point grid. Multimedia Tools and Applications, 77(3): 1–19, 2018.
Regarding, the method itself, the authors should consider whether the performance gain is simply due to the firts heuristic they apply in step A. Non-corners Exclusion. By eliminating those corners without intensity change in pixels 1, 5, 9 and 13 they are effectively considering a lower number of possible corners (for example an acute corner ocuppying pixels 6, 7 and 8 of the Bresenham circle). Authors should clarify how much this affects the quality of detection.
Answer: Thank you for your helpful comments. In the introduction section, we mentioned that our method has two key ideas for reducing the complexity of Harris detector: one is to exclude a very large number of non-corners before detection, and the other is using an improved efficient NMS. In the last paragraph of Sec3, we showed that the total time complexity of Harris and RECD is O (9n2+ n2+9n2) and O (n2+9m +9m+10m) respectively. It is obvious that both of our keypoints have contributed to the improvement of our algorithm's efficiency.
In the principle of FAST algorithm, the minimum number of consecutive pixels N is actually a scale to determine the corners. Too large N can lead to several missed corners and the small N bring about too many weak corners. In other words, if we set N to a smaller value, we can indeed detect some acute corners, but at the same time will be disturbed by noise. After testing, the corner point detection performance is the most stable, faster, and effective when N = 12. That’s why we examine three of the four pixels 1,5,9 and 13.
Following your advice, we have added the explanation to the step A in Sec 3, in order to clarify how much it affect the quality of detection.
Regarding evaluation, the authors use one small sample of images where tests are applied. Why those particular images? They also apply various transformations to the images, in order to evaluate the stability of the detection. However, a most natural way to test it would be on a video stream, where additional artifacts appear such as luminosity changes.
Answer: Thank you for your kindly comments. The images we use are dedicated test sets for corner detection, which can objectively reflect the performance of the algorithm.
Since video contains multiple image transformations, using video for detection seems to be a better idea. But actually, this does not make more sense for our research. First, in practical applications, if corner detection is applied to a video, it will not detect every frame. Taking video mosaicing as an example, in order to ensure real-time performance, corner detection is generally performed only in the first few frames. In other words, many transformations in the video will not be encountered in the application of corner detection. Secondly, video is actually composed of many frames of images. There is no essential difference between detecting on video and detecting on image. Therefore, our experiments are sufficient to assess the consistency of the method.
Author Response File: 
Author Response.doc
Reviewer 2 Report
I like the mathematical foundation of the work done. I think the Computational Time Performance section needs more details.
The paper is well written and researched.
Author Response
Dear Editors and Reviewers:
Thank you very much for your valuable comments. We have carefully revised the submitted manuscript (applsci-654049) to address each of your critiques. The major revisions have been marked in red in the revised manuscript. We also have updated some grayscale statistical charts with color ones. For our convenience, our point-by-point responses are as follows.
Yours Sincerely
Zaifeng Shi
Tao Luo
12/24/2019
Reviewer #2: I like the mathematical foundation of the work done. I think the Computational Time Performance section needs more details.
Answer: Thanks for your detailed comment. All time experiments are performed on a 3.20GHz Pentium (R) Dual-Core CPU platform with 2GB random access memory. We execute these five corner detectors in Matlab R2014a a hundred times for each type of test image, then the mean execution times are measured and calculated through the timing function in Matlab (tic/toc).
We admit that this method is not the most accurate: because corner detection time is affected by the computing power of the hardware platform. In fact, the most accurate time measurement method is to measure the complexity of each algorithm. However, this method cannot be implemented due to experimental conditions. Therefore, we choose to measure the mean time of each corner detector and calculate the speedup to measure the speed improvement of our method: the relative comparison under the same conditions is convincing.
Based on your suggestions, we found that in Sec 4.3, our interpretation of the metric of time performance, which is speedup, is not complete, and the analysis of experimental data is not sufficient. Therefore, we have made detailed additions to these aspects in revision. The revised sections are highlighted in red.
Author Response File: Author Response.doc
Reviewer 3 Report
Abstract
“First, the principle of FAST algorithm…”
It is an algorithm proposed by the authors of the paper? It is confusing that it same to be the proposal. Must be indicated the long name of the “FAST” algorithm.
“The detection time of the proposed detector is only approximately 8.2% that of the original Harris detector.”
It is compared with the Harris detector only from the running time point of view? From other points of view, it performs exactly the same. It is not presented in the abstract the name of the proposal.
Keywords
“Harris”
It must be extended to be more illustrative. Same for "FAST", include the long name.
Page 1, line 35
“Canny edge detector ….”
Canny edge detector [?] ….
Page 2, line 85
“In this paper, a robust and efficient corner detector improved from the Harris corner detector, named RECD, is proposed.”
It is not presented the long name of the proposal just the acronym.
Page 3, line 100
“Harris and Stephens [?] …..”
Indicate the publication.
Page 10, 313
Misspelling
“Fig .10” -> “Fig. 10”
Page 10, 317-318
“Fig .12” -> “Fig. 12”
Conclusions
“In this paper, a robust and computationally efficient corner detector is proposed based on the Harris algorithm.”
What kind of algorithm is the “Harris algorithm”? Indicate the reference [?] where it is proposed.
“FAST corner detector…”
Indicate the reference [?]. Indicate the long name for “FAST”
“CRF”
Include the long name.
“NMS”
Include the long name.
“CCN and ACU”
Include the long name.
“The experimental results show that the RECD is more accurate with respect to ACU criterion and more robust with respect to CCN criterion under all the five transformations except compression. Moreover, the RECD shows the fastest computation time among the five corner detectors.”
Please give quantitative values to the improvements.
The latest reference is from 2013. This rise the question regarding the novelty of the proposal.
Author Response
Dear Editors and Reviewers:
Thank you very much for your valuable comments. We have carefully revised the submitted manuscript (applsci-654049) to address each of your critiques. The major revisions have been marked in red in the revised manuscript. We also have updated some grayscale statistical charts with color ones. For our convenience, our point-by-point responses are as follows.
Yours Sincerely
Zaifeng Shi
Tao Luo
12/24/2019
Reviewer #3:
Abstract“First, the principle of FAST algorithm…”
It is an algorithm proposed by the authors of the paper? It is confusing that it same to be the proposal. Must be indicated the long name of the “FAST” algorithm.
Answer: Thanks for your comment. Feature from Accelerated Segment Test (FAST) algorithm is not proposed by us, it is proposed by Rosten and Drummond in 2005, which has been referred in the introduction part with [9]. Our key idea is to exclude a very large number of non-corners before detection. FAST just uses the 16 pixels in the Bresenham circle to decide whether a point is actually a corner, which requires very low computation time. This method is perfectly consistent with our keypoint. Thus we introduced the principle of FAST corner detector to our first step.
Per your advice, we have modified the description in the abstract part in the revision to clarify that the FAST algorithm was not proposed by us. And the long name of the “FAST” algorithm has been added too.
Keywords
“Harris” It must be extended to be more illustrative. Same for "FAST", include the long name.
Answer: Thanks for your meticulous inspection. Following your advice, we have changed “Harris” to “Harris corner detector” and “FAST” to “Features From Accelerated Segment Test” in Keywords part in the revision, to make sure that they are more illustrative.
Page 1, line 35 “Canny edge detector ….” Canny edge detector [?] ….
Answer: Thank you for pointing this out. Canny edge detector is a multi-level edge detection algorithm developed by John F. Canny in 1986. In general, the purpose of edge detection is to significantly reduce the data size of the image while retaining the original image attributes. There are a variety of algorithms for edge detection. Although Canny's algorithm is old, it can be said that it is a standard algorithm for edge detection, and it is still widely used in research.
Following your advice, the reference of Canny edge detector has been added in introduction part in the revision.
[R1.4] Canny J. A Computational Approach To Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):679-698, 1986.
Page 2, line 85 “In this paper, a robust and efficient corner detector improved from the Harris corner detector, named RECD, is proposed.” It is not presented the long name of the proposal just the acronym.
Answer: Thanks for your comments. Upon inspection, we found that the long name of RECD have appeared in the abstract part for the first time, so we did not make any changes here in the revision. Correspondingly, we added an acronym in the corresponding position of the abstract section.
Page 3, line 100 “Harris and Stephens [?] …..” Indicate the publication.
Answer: Thank you for your careful examination. This section introduces a simple method to calculate the response function in Harris corner detector theory.
Following your advice, We have added the reference in the corresponding places.
[R1.5] C. Harris and M.Stephens. A combined corner and edge detector. Proceedings Alvey Conefernce, 147-151, 1988.
Page 10, 313 Misspelling “Fig .10” -> “Fig. 10”
Page 10, 317-318 “Fig .12” -> “Fig. 12”
Answer: Thank you for your meticulous inspection. We feel deeply sorry for the existence of such a careless problem. We examined the full manuscript in detail and did find another error like this. Following your comments and after detailed inspection, we have revised all the problems we can find.
7.Conclusions
“In this paper, a robust and computationally efficient corner detector is proposed based on the Harris algorithm.”
What kind of algorithm is the “Harris algorithm”? Indicate the reference [?] where it is proposed.
“FAST corner detector…”
Indicate the reference [?]. Indicate the long name for “FAST”
“CRF”
Include the long name.
“NMS”
Include the long name.
“CCN and ACU”
Include the long name.
“The experimental results show that the RECD is more accurate with respect to ACU criterion and more robust with respect to CCN criterion under all the five transformations except compression. Moreover, the RECD shows the fastest computation time among the five corner detectors.”
Please give quantitative values to the improvements.
Answer: Thank you for your careful examination. The “Harris algorithm” is the “Harris corner detector” mentioned in abstract and introduction, and the “FAST corner detector” is the same as “FAST algorithm”. We are sorry for these inconsistencies in the manuscript.
Per your advice, the algorithm names in our manuscript have been thoroughly checked and modified to be consistent, in order to ensure that there is no ambiguity. We have added all the long names of these acronyms and the references you pointed out to the conclusion section. The quantitative values to the improvements of our proposed method has also been given at the end of the conclusion. All the modifications are marked red in revision.
The latest reference is from 2013. This rise the question regarding the novelty of the proposal.Answer: Thank you for your instructive advice. After a comprehensive review and summary of the relevant literature, we have added some references for the last five years into the manuscript to ensure the novelty of our proposed method.
[1] Y. Pang, J. Cao and X. Li. Learning sampling distributions for efficient object detection. IEEE Trans. Cybern, 47(1): 117-129, 2017.
[2] Yan.C et al. A fast Uyghur text detector for complex background images. IEEE Trans. Multimed. 20(12): 3389–3398, 2018.
[3] Zhang, S and Liu, W: Single image 3D reconstruction based on control point grid. Multimedia Tools and Applications, 77(3): 1–19, 2018.
[16] Zhang W C and Shui P L. Contour-based corner detection via angle difference of principal directions of anisotropic Gaussian directional derivatives. Pattern Recognition, 48(9):2785-2797, 2015.
[17] Zhang X, Qu Y, Yang D, et al. Laplacian Scale Space Behavior of Planar Curve Corners. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(11):1-1, 2015.
[22] Xiong. W, Tian. W, Yang. Z, Niu. X, and Nie. X. Improved FAST corner-detection method. The Journal of Engineering, 2019(19), 5493-5497, 2019.
Author Response File: Author Response.doc
Round 2
Reviewer 1 Report
The author's have addressed most of the concerns on the initial version of the paper. However, there are some minor issues in the paper that need correction. For example, some references are incorrectly presented using the name of the authors instead of the family name (e.g. Pablo et al. [21]). Also, Figure 13 is missing units.
Regarding the test images, is the method only tested in the five images of figure 1? This seems a quite limited number of test images, is there a reason for this? Are other images used in testing?
Author Response
Dear Editors and Reviewers:
Thank you very much for your valuable comments. We have carefully revised the submitted manuscript (applsci-654049) to address each of your critiques. The major revisions have been marked in red in the revised manuscript. We also have updated some grayscale statistical charts with color ones. For our convenience, our point-by-point responses are as follows.
Yours Sincerely
Zaifeng Shi
Tao Luo
01/02/2020
Reviewer #1: The author's have addressed most of the concerns on the initial version of the paper. However, there are some minor issues in the paper that need correction.
For example, some references are incorrectly presented using the name of the authors instead of the family name (e.g. Pablo et al. [21]). Also, Figure 13 is missing units.Answer: Thank you for your careful examination. We carefully examined the full manuscript in detail and did find another error like this. Following your comments and after detailed inspection, we have revised all the mistakes and typos. We have also added the unit to the ordinate of Fig 13. All modifications are highlighted in the revised manuscript.
Regarding the test images, is the method only tested in the five images of figure 1? This seems a quite limited number of test images, is there a reason for this? Are other images used in testing?Answer: Thank you for your valuable comments. We performed experiments on a large number of test images from Petitcolas and Usc-Sipi images set [R1.1], [R1.2] et al. By summarizing the literature in recent decades, we find that these five images are the most widely and frequently used [R1.3-R1.5]. In order to make the experimental results persuasive and convenient to compare with other methods, we selected the test results of these five test images to present in the paper.
Per your comment, we have added the supplement explanation about choosing test images in Sec 3.
[R1.1]Petitcolas. Photo Database. Available Online: http://www.petitcolas.net/fabien/watermarking/image_data base/ (accessed on 01/02/2020).
[R1.2] The Usc-Sipi Image Database. Accessed: 2019. Available Online: http://sipi.usc.edu/database/ (accessed on 01/02/2020)
[R1.3] F. Mokhtarian and R. Suomela. Robust image corner detection through curvature scale space. IEEE Transactions on Pattern Analysis & Machine Intelligence, 20(12): 1376–1381, 1998.
[R1.4] Performance evaluation of corner detectors using consistency and accuracy measures. Computer Vision and Image Understanding, 102(1): 81–94, 2006.
[R1.5] Zhang, S and Liu, W: Single image 3D reconstruction based on control point grid. Multimedia Tools and Applications, 77(3): 1–19, 2018.
Author Response File: Author Response.doc
Reviewer 3 Report
Conclusions Page 15, Page 398
“Third, we just calculated the corner response function (CRF) of the candidate corners...........”
Delete the word „just”.
In the preparation of the final version of the paper fully respect all the formant requests of the journal. The paper same to be prepared in Word, for instance be careful that the dimension of the text to be the same in the whole paper.
In case of each reference include all the necessary details. For example, in case of reference 21 is not included the page numbers.
Author Response
Dear Editors and Reviewers:
Thank you very much for your valuable comments. We have carefully revised the submitted manuscript (applsci-654049) to address each of your critiques. The major revisions have been marked in red in the revised manuscript. We also have updated some grayscale statistical charts with color ones. For our convenience, our point-by-point responses are as follows.
Yours Sincerely
Zaifeng Shi
Tao Luo
01/02/2020
Reviewer #3: Comments and Suggestions for Authors
Conclusions Page 15, Page 398“Third, we just calculated the corner response function (CRF) of the candidate corners...........”
Delete the word “just”.
Answer: Thank you for your meticulous inspection. In this sentence, “just” expresses “only” meaning, but it seems ambiguous. Following your advice, we have deleted the word “just” in Conclusion part to make the sentence clear. And we revised other grammar solecisms.
In the preparation of the final version of the paper fully respect all the formant requests of the journal. The paper same to be prepared in Word, for instance be careful that the dimension of the text to be the same in the whole paper.
Answer: Thank you for your instructive suggestion. In order to ensure that the paper and journal requirements are the same, we adjusted the manuscript format according to the template provided by the journal, including font, character size, etc. Each section is modified according to its corresponding style, which can be found in the ‘Styles’ menu of Word.
In case of each reference include all the necessary details. For example, in case of reference 21 is not included the page numbers.Answer: Thank you for your valuable comments. After careful inspection, we have supplemented all incomplete references we found.
Author Response File: Author Response.doc
