Accurate and Efficient Calculation of Three-Dimensional Cost Distance

Round 1

Reviewer 1 Report

The paper presents the method for cost distance evaluation based on Dijkstra’s algorithm. Paper has a lot of figures, this simplifies the text understanding.

The authors analyze the algorithm complexity for different data structures. But, on my mind, it is very important to analyze the time complexity for huge graphs too. Can this algorithm be used for matrix 1000x1000 in real-time? How the time complexity can be reduced?

Author Response

Dear Reviewer:

 

Thanks a lot for your comments concerning our manuscript entitled “Accurate and efficient calculation of three-dimensional cost distance”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections. We hope it can meet with your approval. The main corrections in the paper and the responds to the reviewer’s comments are detailed below.

 

In the revised manuscript, the changes are highlighted by using red colour. Our point-to-point responses are uploaded in the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper presents an adaptation of Tomlin’s heuristics to the least-cost path problem in 3D raster space. I’m not fully convinced of the innovativeness of the proposed algorithm. It seems that it mostly just replicates the existing methods, i.e., Dijkstra’s algorithm and Tomlin’s heuristics, without a significantly new contribution to raster-based path finding.

 

The proposed algorithm was designed to solve a 3D raster version of the weighted region problem, which has a long history. More than 20 years ago, Szczerba et al. (1998) actually proposed an O(n2longm) algorithm to solve the problem in a n*n*n raster using a heap of a size of m. Is the proposed algorithm better in terms of either accuracy or efficiency? This algorithm is not among “most of these studies only focused on calculating the ‘single-source-to-single-destination’ shortest path without considering the calculation of least accumulative cost from each location to a set of sources.” (page 2)

 

The presentation of the algorithm is too informal and ambiguous. Does Step 4 cover all cases? What if the straight-line between the min-cost voxel and the adjacent voxel intersects a cell with a different (or higher or lower) value? Is it guaranteed that this won’t happen? If not, does the proposed algorithm have a procedure for checking and responding to this? What is the complexity of the proposed algorithm? It should be assessed and presented formally. It seems that the authors attempt to do it in Sec. 3.3 using the O() notation (which is goo), but stopped prematurely. In any case, write pseudocode in a standard format so that the reader can see what exactly is done at each step, and implement and test it in his/her computing environment.

 

Experiments should be conducted (and results should reported) in a more organized and systematic manner. Description of the sample data or sample size is poor. A comparison with other distortion-reducing least-cost algorithms including Szczerba et al (1998) is essential for yet another algorithm to be justified

 

Discuss the characteristics of the proposed algorithm more accurately. It is true that “the proposed algorithm can generate true Euclidean distance in homogeneous frictions,” but this alone doesn’t demonstrate its advantage because (it’s almost silly to say this, but) exact distances can be easily calculated geometrically in homogeneous cost space. It is expected that the algorithm “can provide more accurate least cost in heterogeneous frictions than that provided by most of the existing methods,” but it should be said that this is not guaranteed. After all, it is a heuristics. There is nothing wrong about being a heuristics. But the authors need to inform the reader of when it performs well and more importantly when it doesn’t. Suppose that every voxel is assigned a value of almost 1 (almost 1 meaning 1 plus a significantly small random value). Then a least cost path between two locations should remain on the straight line between them, but the proposed algorithm will deviate from it because there will be no chance of performing Step 4(b). I’m NOT saying that the extended adjacency approach (Figure 2) is better, but such an inefficient method is at least in theory effective to eliminate this problem.

 

The text must be significantly improved, if the manuscript is to be resubmitted. Figures, too.

 

Author Response

Dear Reviewer:

 

Thanks a lot for your comments concerning our manuscript entitled “Accurate and efficient calculation of three-dimensional cost distance”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections. We hope it can meet with your approval. The main corrections in the paper and the responds to the reviewer’s comments are detailed below.

 

In the revised manuscript, the changes are highlighted by using red colour. Our point-to-point responses are uploaded in the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper proposed an algorithm and data structures to calculate the cost distance in discrete 3D space, and Dijkstra’s algorithm is used to calculate the least cost between initial voxels and all the other voxels in 3D space. The idea is fine and the research makes sense. Some suggestions and comments are as follows:

1. Studies on shortest path planning incorporating 3D cost distance are listed, but it seems there is not much research in this field. Please give the reason, or give a more comprehensive review of the literature.
2. Several applications are chosen to verify the algorithm and data structure, including planning the shortest drone delivery path in an urban environment, generating volumetric viewshed, and calculating the minimum hydraulic resistance, why are them?
3. It’s better to give Pseudocode to describe the algorithm.
4. Some references are many years ago, which are not very suitable.

 

Author Response

Dear Reviewer:

 

Thanks a lot for your comments concerning our manuscript entitled “Accurate and efficient calculation of three-dimensional cost distance”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections. We hope it can meet with your approval. The main corrections in the paper and the responds to the reviewer’s comments are detailed below.

 

In the revised manuscript, the changes are highlighted by using red colour. Our point-to-point responses are uploaded in the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The manuscript has been significantly
improved

Author Response

Dear Reviewer:

 

Thanks for reviewing the manuscript. We deeply appreciate your recognition of our research work.

Reviewer 2 Report

My earlier comments still stand, although I appreciate the authors' effort to include the pseudocode.

If the authors plan to revise this manuscript, check the following. The for-loop starting at 35 does not have a comparison between the current value of CostDistance(n) and CostDistance(m) + cost(m,n). It is not part of "calculate n.costdistance based on Equations ..."

In the description of the algorithm's complexity, the authors seem to mix up N and n. See Sec. 3.3. in which "N is the number of voxels in the list" and "a voxter of nxnxn voxels. In any case, there is no reason to use the number of row/col/lay as the indicator of the problem size.

Author Response

Dear Reviewer:

 

Thanks a lot for your comments concerning our manuscript entitled “Accurate and efficient calculation of three-dimensional cost distance”. Those comments are all valuable and very helpful for revising and improving our paper. We have studied comments carefully and have made corrections. We hope it can meet with your approval. The main corrections in the paper and the responds to the reviewer’s comments are detailed below.

 

In the revised manuscript, the changes are highlighted by using red colour. Our point-to-point responses are uploaded in the attachment.

Author Response File: Author Response.pdf