Rigorous Boresight Self-Calibration of Mobile and UAV LiDAR Scanning Systems by Strip Adjustment
Round 1
Reviewer 1 Report
The paper is very interesting and calibration technique is presented in the framework of Lidars. Introduction is good. The performed work is well explained and reading has the enough mathematical evidences as needed. Reading is very easy and clear. Conclusion are well presented.
Author Response
The authors gratefully acknowledge you for your careful review. According to the comments, we have tried our best to revise the manuscript to make it better. English language and style are minor revised. The other changes from the original manuscript were highlighted in the changed version.
Reviewer 2 Report
The article present a boresight self-calibration method suitable to mobile applications. Overall, the article is well-written. Minor language issues exists, e.g., in line 470, there is no verb in the sentence. Lever arm calibration was left out, which slightly lowers the interest of the paper. However, boresight angle calibration seems to work. The most accurate calibration would include both lever arm and boresight angles in the same adjustment.
In line 142, you set the rotation order to phi, omega, kappa. Maybe you could give some justification why this rotation order is suitable for your case? It would also be beneficial to write the contents of R_I_L(phi, omega, kappa) open.
The color of trajectories in fig 1 is too dark.
In line 327, C_i should probably be (C^j-C^k)_i
In lines from 377 to 382, you repeat all the values that are presented in table 3. I feel this is not necessary.
Author Response
The article present a boresight self-calibration method suitable to mobile applications. Overall, the article is well-written. Minor language issues exists, e.g., in line 470, there is no verb in the sentence. Lever arm calibration was left out, which slightly lowers the interest of the paper. However, boresight angle calibration seems to work. The most accurate calibration would include both lever arm and boresight angles in the same adjustment.
Response:
The authors gratefully acknowledge you for your careful review. The main changes from the original manuscript were highlighted. According to the comments, we have tried our best to revise the manuscript to make it better, and an item-by-item response follows. English language and style are minor revised. The lever-arm offsets are usually accurately measured after the system assembling or obtained from the design drawings. Of course, the calibration model could be easily extended if needed. In general, only boresight angle calibration is needed just as in the existing research. The main reason is that the boresight angles cannot be measured directly and accurately.
Major Comments:
1) In line 142, you set the rotation order to phi, omega, kappa. Maybe you could give some justification why this rotation order is suitable for your case? It would also be beneficial to write the contents of R_I_L(phi, omega, kappa) open.
Response: Right-handed coordinate systems are used in the design. The rotation order depends on the design of the system provider.
2) The color of trajectories in fig 1 is too dark.
Response: The brightness of fig 1 was adjusted to a higher level.
3) In line 327, C_i should probably be (C^j-C^k)_i
Response: This mistake was corrected.
4) In lines from 377 to 382, you repeat all the values that are presented in table 3. I feel this is not necessary.
Response: This issue was revised. Some similar issues were also revised.
Reviewer 3 Report
The paper describes a small correction to point clouds obtained from Lidar platforms, either mounted on a vehicle or on a drone / UAV. The main focus is on the boresight angle correction between the Lidar and the Inertial Measurement Unit, i.e. a purely geometric correction; three angles are iteratively estimated, with the assumption that initial (good) guesses based on the geometry of the mounted setup are available.
The paper starts with an extensive review of existing correction algorithms. It becomes clear that there are so many previous papers dealing with almost the same problem that it is hard to distinguish the novelty of this particular manuscript. In l. 128, the authors admit that their method is similar to the one of Kumari et al.; there are two sentences specifying the differences, but this paragraph could be improved by providing more details and a motivation why the authors expect their modifications of the Kumari et al. paper to be improvements for their data sets. Did they try to apply the Kumari et al. approach and got inferior results?
A positive aspect of the approach is that it is self-calibrating, i.e. no independent data sets or ground control points are needed. The requirement is, however, that the point clouds are sufficiently overlapping, meaning that one has to drive the same path at least twice (in opposite directions, which has been done here) or fly with the UAV with a significant overlap of the strips. If this is respected, the correction can be done by post-processing only. The calculation times on an ordinary PC as they were using are reasonable (a couple of minutes only).
However, the whole algorithm seems to be quite involved and is not explained in sufficient detail in the paper. For example, l. 282 talks about "uniform filtering, and then a distance filtering" to eliminate "too" sparse and noisy points. What does this mean, how is this done in practice? Probably, there are several choices to be made - what it "too sparse" or "too noisy", and the filters for sure come with parameters one has to choose - which ones, how were they chosen? How do these choices impact on the results? Please be more explicit here.
On the other hand, the equations (9) to (13) are almost too explicit; as it is very easy to see how to arrive at equation (14) which then is solvable by matrix inversion, the authors could consider to delete some of the equations and the corresponding text.
The Table 2 shows the changes in the angles, all are smaller than 0.4 degrees. As expected, the misalignments are really hard to see in Figs. 5 to 8. This might in part be due to the limited graphic quality of them, could you improve on that (higher dpi)? You have to look very closely to see that some line structures are actually a little bit blurred prior to the correction.
One of the RMSEs plots (Figure 9d) shows a striking "periodic" pattern for the not-calibrated version of ULS2. Surely there is a trivial explanation for the regular ups and downs (alternating between 40 and 100 cm), could you provide it please to the reader?
In l. 414f, the authors require that the data for MLS systems "should be collected in areas as open as possible" - well, this indicates more a limitation of the method rather than a demand for the data acquisition: we don't always have the luxury to stay away from trees and buildings, in particular not when measuring in forests or in residential areas - trees and buildings are simply there! This should be rephrased accordingly, indicating what you would expect as an error (or in which sense your method would fail in these situations).
Equation (8) replaces the proper trigonometric functions of the rotation matrix by the first term of their Taylor expansion. Looking at the results in Table 2, this seems to be justified, and you can thus solve a simple linear error equation (13). You should mention that also in the more general case, you can solve the original problem by using sin(kappa) instead of kappa, etc., it is only slightly more complicated and still leads to a unique solution provided the correction is not excessively large (>90 degrees).
The paper is repetitive occasionally, saying almost the same things in different phrases several times. The text in l. 374-383 provides all the numbers in all detail as are then written in Table 3. What is the point of displaying the Table then?
Having seen all the distribution of RMSEs across the overlapping regions (Fig. 9), who needs the histograms shown in Fig. 10 in addition to that?
The annotated pdf contains some corrections, mostly on language, although generally, the English is fine. Some other comments are also to be found there.
The paper makes a rather obvious points which is easy to comprehend. The suggested corrections and deletions sum up to minor revisions only and should easily be accomodated.
Comments for author File: 
Comments.pdf
Author Response
The authors gratefully acknowledge you for your careful review. The main changes from the original manuscript were highlighted. According to the comments, we have tried our best to revise the manuscript to make it better, and an item-by-item response follows.
Major Comments:
1) The paper starts with an extensive review of existing correction algorithms. It becomes clear that there are so many previous papers dealing with almost the same problem that it is hard to distinguish the novelty of this particular manuscript. In l. 128, the authors admit that their method is similar to the one of Kumari et al.; there are two sentences specifying the differences, but this paragraph could be improved by providing more details and a motivation why the authors expect their modifications of the Kumari et al. paper to be improvements for their data sets. Did they try to apply the Kumari et al. approach and got inferior results?
Response: Two different aspects between the Kumari’s method and the proposed method were added in the new manuscript from line 128 to line 137.
2) However, the whole algorithm seems to be quite involved and is not explained in sufficient detail in the paper. For example, l. 282 talks about "uniform filtering, and then a distance filtering" to eliminate "too" sparse and noisy points. What does this mean, how is this done in practice? Probably, there are several choices to be made - what it "too sparse" or "too noisy", and the filters for sure come with parameters one has to choose - which ones, how were they chosen? How do these choices impact on the results? Please be more explicit here.
Response: More details about uniform filtering and distance filtering including the algorithm parameter settings were added in the new version from line 284 to line 289.
3) On the other hand, the equations (9) to (13) are almost too explicit; as it is very easy to see how to arrive at equation (14) which then is solvable by matrix inversion, the authors could consider to delete some of the equations and the corresponding text.
Response: The equations (8), (9) and (12) in the previous manuscript was deleted.
4) The Table 2 shows the changes in the angles, all are smaller than 0.4 degrees. As expected, the misalignments are really hard to see in Figs. 5 to 8. This might in part be due to the limited graphic quality of them, could you improve on that (higher dpi)? You have to look very closely to see that some line structures are actually a little bit blurred prior to the correction.
Response: The figures 5 to 8 were redrawn to make them clearer.
5) One of the RMSEs plots (Figure 9d) shows a striking "periodic" pattern for the not-calibrated version of ULS2. Surely there is a trivial explanation for the regular ups and downs (alternating between 40 and 100 cm), could you provide it please to the reader?
Response: The figure 9 was deleted because the figure 10 also shows the error distribution results. The alternating ups and downs in figure 9 may cause by the different overlapping areas in different strips of the same section. The RMSEs are not always regularly changed.
6) In l. 414f, the authors require that the data for MLS systems "should be collected in areas as open as possible" - well, this indicates more a limitation of the method rather than a demand for the data acquisition: we don't always have the luxury to stay away from trees and buildings, in particular not when measuring in forests or in residential areas - trees and buildings are simply there! This should be rephrased accordingly, indicating what you would expect as an error (or in which sense your method would fail in these situations).
Response: The description was rephrased in the new manuscript from line 400 to line 406.
7) The paper is repetitive occasionally, saying almost the same things in different phrases several times. The text in l. 374-383 provides all the numbers in all detail as are then written in Table 3. What is the point of displaying the Table then?
Response: This issue was revised. Some similar issues were also revised.
8) Having seen all the distribution of RMSEs across the overlapping regions (Fig. 9), who needs the histograms shown in Fig. 10 in addition to that?
Response: The figure 9 was deleted because the figure 10 also shows the error distribution results.
