Efficient Calculation of Distance Transform on Discrete Global Grid Systems
Round 1
Reviewer 1 Report
This is a great study and should be published without any changes. I am curious for the 3D applications.
Author Response
Dear Reviewer 1,
We want to thank you for your positive feedback. To tempt your curiosity, we expect that a 3D distance transform would be useful for assessing proximity to obstacles in drone flight-path planning.
Regards,
Faramarz Samavati
Reviewer 2 Report
The authors introduced a distance transform algorithm for Discrete Global Grid Systems. Computing distance transform on traditional Geographic Information Systems (GIS) is usually adopted from image processing methods and prone to distortions resulting from flat maps. The evaluation was done by comparing its speed and distortion with the distance transform methods used in traditional GIS and general 3D meshes. The authors demonstrated that the method is efficient and has minimal distortion.
It would be useful to demonstrate some more real-world examples and compare it with traditional GIS measures. Also, it would be useful to provide measured distance differences and show comparison of calculated differences of distance to features using traditional methods and the proposed method. Comparison Section quantifies the efficiency of the proposed method but not the actual lengths in order to see the quantity of distortion and error. It would be good to provide implementation details of the proposed algorithm and in what environment it was tested.
There are some typos such as in line 39 (semi-regular. which) and line 258 (missing sentence).
Figure 13 is missing explanation in the text.
Author Response
Dear Reviewer 2,
We want to thank you for your positive evaluation and helpful comments. Based on the feedback provided, we have incorporated some revisions in this version of the manuscript listed below.
Reviewer2: It would be useful to demonstrate some more real-world examples and compare it with traditional GIS measures.
Response: In addition to the real-world examples of DT that were already present, we have included another example from precision agriculture (Section 2.1, last paragraph). Additionally, the data from this newly added example is used in our comparison of the distance calculations between our algorithms and the distances calculated in a traditional GIS setting (Section 6).
Reviewer 2: Also, it would be useful to provide measured distance differences and show a comparison of calculated differences of distance to features using traditional methods and the proposed method. The comparison Section quantifies the efficiency of the proposed method but not the actual lengths in order to see the quantity of distortion and error
Response: We now include the amount of the distortion when compared to traditional GIS (planar distance calculations) in Section 6. Additionally, we include a comparison of the geodesic distances calculated by ArcGIS within the “Generate Near Table” tool within the “proximity tools” and our geodesic distance calculations.
Reviewer 2: It would be good to provide implementation details of the proposed algorithm and in what environment it was tested.
Response: In addition to our detailed description of the implementation of Algorithms 1, 2, 3 and 4 and our usage of the Disdyakis Triacontahedron DGGS, we have also included further information about our usage of the ArcGIS Pro “Generate Near Table” tool and have further explained some of the subroutines used (e.g., Algorithm A.1).
Regards,
Faramarz Samavati
Reviewer 3 Report
The manuscript presents an algorithm to efficiently calculate distance transform on a Discrete Global Grid System. This is an interesting use case for a DGGS, and as far as I know, it has not been properly addressed before. The manuscript is well written and structured.
However, I have one major concern, and I think that it needs to be solved before this manuscript can be published in a journal. This concern is about the correctness of the algorithms.
Algs. 1, 2, 3 and 4 depend on the correction of the computeDistance function (well-known) and on the validity of Theorem 1 (that I do not question). But even given that those two are correct, the algorithms themselves remain untested as far as the manuscript presents them. Only a "visual validation" of some examples is provided (Figs 12, 13 and indirectly Fig. 17. The manuscript also says that MMP is "less accurate than the spherical distance calculations", but again without clear evidence beyond some figures.
The readers will be needing to see some evidence, not necessarily formal proofs, that the algorithms are correct. I would do some tests that:
- show that Alg. 1 and Alg. 4 produce the same results when applying them to a number of different features;
- show that Alg. 1 produces correct results. You will be needing some ground truth to show this. Maybe you could try calculating some **geodesic** buffers (I understand that, for instance, ArcGIS can calculate them, though I have not tried it myself) with negative distances on some features and comparing somehow the results with those provided by Alg.1. The results should be closer and closer as the maximum resolution increases. This strategy might not work, or you may prefer some alternative. If it has been shown that Alg. 1 and Alg. 4 are equivalent, this would also be showing that Alg. 4 produces correct results. This, or some other similar testing, is essential. The readers will not trust that the results of this manuscript are correct if it is not shown that these results have been tested against some ground truth and found to be the right ones.
You could also test Alg. 2 and Alg. 3 separately. However, if Alg. 4 is shown to produce correct results, and if it is shown to be equivalent to Alg. 1, I think this would not be really necessary.
Alg. A.1 is also given without much explanations; I would suppose that the math is well-known and a citation can be provided instead of those explanations, but one or the other would be necessary. I suppose that a similar algorithm has not been published before (because in that case a citation would have been provided instead of Alg. A.1). In that case the readers would like to see that some tests have been done comparing the results of this algorithm with some correct distances to validate it.
Besides this major concern, there are some minor issues:
- Line 231 -> "course" should be "coarse".
- Line 247 -> "gird" should be "grid".
- Line 282 -> As the Disdyakis Triacontahedron DGGS is used to illustrate the results of the paper, it would be good to have a brief description of it, and not just the citation. In particular it would be handy to know the approximate sizes of the cells at the different resolutions used to graph your results (as, for instance, in Figure 14) because I think that something like "Resolution 10" is not as illustrative as "Resolution 10 (avg. cell size X meters)" unles you know well that particular DGGS.
Author Response
Dear Reviewer 3,
We want to thank you for your positive evaluation and helpful comments. Based on the feedback provided, we have incorporated some revisions in this version of the manuscript listed below.
Reviewer 3: Algs. 1, 2, 3 and 4 depend on the correction of the computeDistance function (well-known) and on the validity of Theorem 1 (that I do not question). But even given that those two are correct, the algorithms themselves remain untested as far as the manuscript presents them. Only a "visual validation" of some examples is provided (Figs 12, 13 and indirectly Fig. 17. The manuscript also says that MMP is "less accurate than the spherical distance calculations", but again without clear evidence beyond some figures.
Response: Thank you for this feedback. We have added new tests for our algorithms to ensure that they are correct in comparison to each other and to ArcGIS. These tests are detailed in our next response.
Regarding the MMP algorithm, it is a mesh-based algorithm which operates along with the planar faces of the polyhedron and does not consider the projection scheme for the given DGGS. We feel that these two reasons are clear enough evidence that it will not produce accurate distances between two projected points. We included more explanation of this in paragraph 3 of Section 6 in this revision.
Reviewer 3: The readers will be needing to see some evidence, not necessarily formal proofs, that the algorithms are correct. I would do some tests that:
  - show that Alg. 1 and Alg. 4 produce the same results when applying them to a number of different features;
  - show that Alg. 1 produces correct results. You will be needing some ground truth to show this. Maybe you could try calculating some **geodesic** buffers (I understand that, for instance, ArcGIS can calculate them, though I have not tried it myself) with negative distances on some features and comparing somehow the results with those provided by Alg.1. The results should be closer and closer as the maximum resolution increases. This strategy might not work, or you may prefer some alternative. If it has been shown that Alg. 1 and Alg. 4 are equivalent, this would also be showing that Alg. 4 produces correct results. This, or some other similar testing, is essential. The readers will not trust that the results of this manuscript are correct if it is not shown that these results have been tested against some ground truth and found to be the right ones.
  
You could also test Alg. 2 and Alg. 3 separately. However, if Alg. 4 is shown to produce correct results, and if it is shown to be equivalent to Alg. 1, I think this would not be really necessary.
Response: Thank you for your suggestion to use the ArcGIS geodesic buffers. Although we did not use this specific tool, we were able to find a similar tool within ArcGIS Pro. In Section 5.1 of this revision, we included some new tests. The “Generate Near Table” functionality is very close to our distance transform, and we used it to test our distance calculations against those of ArcGIS pro. The additional tests clearly demonstrate that Algorithm 1 produces correct results when compared with the ArcGIS Pro geodesic distance calculations. Algorithms 1 and 4 produce identical results when compared to each other, thus we can conclude that Algorithms 1 through 4 are working as intended.
Reviewer 3: Alg. A.1 is also given without much explanations; I would suppose that the math is well-known and a citation can be provided instead of those explanations, but one or the other would be necessary. I suppose that a similar algorithm has not been published before (because in that case a citation would have been provided instead of Alg. A.1). In that case the readers would like to see that some tests have been done comparing the results of this algorithm with some correct distances to validate it.
Response: We have added more explanation of Algorithm A. 1 including a figure explaining the geometric context.
Reviewer 3: Line 282 -> As the Disdyakis Triacontahedron DGGS is used to illustrate the results of the paper, it would be good to have a brief description of it, and not just the citation. In particular it would be handy to know the approximate sizes of the cells at the different resolutions used to graph your results (as, for instance, in Figure 14) because I think that something like "Resolution 10" is not as illustrative as "Resolution 10 (avg. cell size X meters)" unless you know well that particular DGGS
Response: We have added a sentence explaining the range of the cell sizes for this DGGS in Section 2.2.1. Additionally, we have included the size of the cells for the listed figures in Section 5, as requested.
Regards,
Faramarz Samavati
Round 2
Reviewer 3 Report
- Section 5.1 -> I do not see how you have "mathematically proven that Algorithm 1 and Algorithm 4 produce correct results". If by "mathematical proof" you mean the description of the algorithms given in sections 4.1 and 4.2, I would at least make a reference in the text to those sections so the readers can judge if their contents contain a "mathematical proof". I, for one, would prefer that you make a less strong claim, something such as "we have argued in favour of/discussed about the correctness of Algorithm 1 and Algorithm 4 in sections...".
- Section 5.1 -> You can't, in general, use tests to empirically **demonstrate correctness**, at least if you use demonstrate in the sense of proof. I emphatically suggest you to tone this down. You could write something like "...introduce an empirical test to provide further confidence in the correctness of our algorithms".
Author Response
Dear Reviewer 3,
We want to thank you again for your positive feedback. Based on the feedback provided, we have changed the wording of the first few sentences of section 5.1 and provided references to the different sections of the paper to clarify it further.
Regards,
Faramarz Samavati
