Curvature Weighted Decimation: A Novel, Curvature-Based Approach to Improved Lidar Point Decimation of Terrain Surfaces

Round 1

Reviewer 1 Report

Line 98-99 What is the "Reference Source not found..." for?
Line 131 how did you determine 15-50% and what does it mean?
line 144 "downloaded"
line 150 define "more accurate" as you have no comparison to external measurments
line 166 what is an "inaccurate" model
line 246 which improves accuracy is a function of the data in addtion to the algorithm
Las does not mean Lidar, it could be derived from photogrammetry
line 279 3 meters - why?  You have not described the quality of the data you are using or
its density
Line 304 "reference source not found" again???
line 330 Why is 0.5 used?
Conceptually there is nothing wrong with this paper.  But why thin data is the
question that is not truly addressed.  It needs to be tested against a data
set of higher accuracy.  It does not address the success of classification
which is an issue before the issue of the paper is addressed.  The accuracy
and density of the Lidar data will change results and is not really addressed.
Why is not human based break line addressed as an alternative.
While interesting it is not really changing the major issues of classification,
data quality (accuracy against data of higher quality), and why do we need to
decimate which nether any of my colleagues or I ever do, but we test against
data of higher accuracy.
Lastly, what the data is being used for is a function of "success" and should
be addressed.
Thus good work but it is not solving the issue of how to model.
It needs to address better the limits of what this is being used for as it
does not solve many applications.

Author Response

Authors' responses to Reviewer 1.

Thank you for reviewing our paper, "Curvature Weighted Decimation: A novel, curvature-based approach to improved Lidar point decimation of terrain surfaces". We have reviewed and responded to your comments. Further, we have implemented changes you recommend. We believe your comments have made our submission to Geomatics a much better publication.

 

> Line 98-99 What is the "Reference Source not found..." for?

Thank you for pointing this out. This is an inadvertent error in cross referencing, for which we apologize. The error has been corrected. It should be "Section 4.2.5". (New Line 98)

 

> Line 131 how did you determine 15-50% and what does it mean?
This line indicates the findings we make in the results section as well as comments about it we make in the discussion section at Lines 652 - 661 (new Lines 670 - 679). We feel your comment highlights the need to improve this linkage to make it clearer. So at Line 131 (new Line 134) we have added the following text to improve the clarity of this connection.

 

"See Section 3 and Section 4."

 

Note the study considered decimation rates from 0.5% to 50%, and did not investigate higher decimation percentages. Thus we have no data with which to make a statement at rates higher than 50%. We anticipate the improvement continues above 50%, but we can not make that claim based on the study.

 

 

> line 144 "downloaded"
The use of the present participle, "downloading", is in error, and your suggestion, "downloaded" is correct. We have implemented this revision at new Line 147.

 

> line 150 define "more accurate" as you have no comparison to external measurments
Section 2.4 Efficacy Assessment (Line 548 f., new Line 552 f.) goes into great detail on how we considered the accuracy improvement. The various ways in which the improvement in accuracy were measured is somewhat complex, and may not be well-suited to describe both in Section 2.4 and at Line 150 (new Line 153). Keep in mind that the accuracy comparison is comparing two processes as they modify a baseline dataset. "More accurate" at Line 150 is a question of whether one process reducing accuracy (CWD) introduces less error than another process reducing accuracy (random decimation). Both processes derive from the original, undecimated .las file, and both are being compared to that.

 

> line 166 what is an "inaccurate" model
The context for this is modelling of flow in small streams. For example, HEC-RAS models stream flow using cross sections of the terrain. If these cross sections are taken from raster DEMs of, say, 2-meter resolution, then a 2 meter wide stream may be represented in cross section in a way that does not represent the actual geometry. The side slopes will be altered, and the bottom of the stream may be missed altogether. By using most or all available points from the point cloud in the vicinity of the stream, the cross-sectional geometry will be preserved in as much accuracy as is available from the original, undecimated point cloud.

We have added text to the manuscript to clarify this at Line 171 (new Line 174):

"This reduction in model accuracy is illustrated in Figure 9 and articulated in Section 4.2.8."

 

> line 246 which improves accuracy is a function of the data in addtion to the algorithm

We agree with your observation. We studied six panels in three different types of terrain. By having two study panels in mountainous terrain, two in piedmont (foothills), and two in the coastal plain, we feel we have enabled the data to preliminarily reveal how trends in the terrain may impact the relative performance of DARO and SWCS. If identifying broader trends in this pattern becomes warranted, further study will be welcomed. However, our scope for this study was limited to six panels for initial development and publication.

We have added the following statement at Line 249 (new Line 254):

 

"This process is explained in greater detail in Section 2.4."

 

> Las does not mean Lidar, it could be derived from photogrammetry
Thank you for this important clarification. We believe you are referring to the mention of LAS files on Line 256. We realized that by simply removing the word "Lidar" from the sentence, it still reads correctly while not incorrectly limiting the source of the data to Lidar. This is now at new Line 261.

 

> line 279 3 meters - why?  You have not described the quality of the data you are using or its density
The grid spacing of 3 meters was a judgement call, seeking to strike a balance between how informative the grid analysis was and how long it takes to run an analysis of 258,064 points (for the 232 hectare panels). The lower the grid spacing, the better the estimation of introduced error, but also the higher the number of points to compute. We felt that 3 meters was sufficient given that each scenario was run 30 times to assure statistical significance.

This is the sample-point pitch for computing then comparing elevation values from the original TIN model and the TIN model created from the decimated points. Both of these TIN models are in-memory only, used for stochastic generation of error statistics, and are not themselves data products.

The quality of the source data may be found in Table 4, between Line 595 and 596. However, as another reviewer has mentioned, we raise QL1/QL2 in the Abstract, then do not refer to it in that acronym in the body of the paper. We have added clarification for this in the paper at Line 553 and 596.

After Line 553 (new Line 566), we also added text to clarify that the grid is an in-memory-only temporary object, and is not intended to be a data source or product. It is in this paragraph:

"It must be emphasized here that the research deals primarily with points in point clouds and the TIN models tessellated from them. The grid used for the efficacy assessment is a temporary, in-memory-only grid. It is neither a data source nor a data product."

 

> Line 304 "reference source not found" again???
Thank you for pointing this out. This is an inadvertent error in cross referencing, for which we apologize. The error has been corrected. See new Line 309.

 

> line 330 Why is 0.5 used?
We use 0.5m^-1 here so as to relate the example computation in Figure 1 to the unit circle. We seek to show that by having a having a higher curvature, the unit circle sampled at a 1m chord length has a higher middle ordinate than the circle of smaller curvature. This is to provide an intuitive understanding of the general premise of the research of the paper. Conveniently, it also illustrates how radius and curvature are mathematically inverses of each other, but when using curvature as the control variable, sampling over lower curvature results in lower error between neighboring samples.

It should also be noted that the middle ordinate is being used in Figure 1 to show the maximum possible measurement error when two sampled points happen to fall exactly 1.0 meters from each other when this measurement is projected to the x-axis. We selected these values as the sample width of 1.0 m and the curvature range of 1m^-1 – 2m^-1 are in the range of many real world situations. Further, by using radius values of 1 and 2, we reduce the reader's cognitive load in grasping the essential concept relating curvature and introduced error.

 

> Conceptually there is nothing wrong with this paper.  But why thin data is the question that is not truly addressed. 

We concur that establishing the utility of point cloud decimation strengthens the paper. In view of this, we have added the following at Line 32.

"Petras, et al. (2023) point out that there are advantages to decimating point clouds in some applications. For example, they point out that a Geiger-mode scanner returns 25 pulses per square meter, and this high density increases storage requirements and processing time."

(Ref = Petras, V., Petrasova, A., McCarter, J. B., Mitasova, H., & Meentemeyer, R. K. (2023). Point Density Variations in Airborne Lidar Point Clouds. Sensors, 23(3), 1593.)

Please note we also mention the memory burden of "large quantities of redundant points" in the Abstract.

 

> It needs to be tested against a data set of higher accuracy.  It does not address the success of classification which is an issue before the issue of the paper is addressed.  The accuracy and density of the Lidar data will change results and is not really addressed. Why is not human based break line addressed as an alternative. While interesting it is not really changing the major issues of classification, data quality (accuracy against data of higher quality), and why do we need to decimate which nether any of my colleagues or I ever do, but we test against data of higher accuracy.

 

Thank you for these extended remarks. One reason we used the North Carolina Department of Public Safety's (NCDPS) Lidar dataset was because it has already been classified by NCDPS' contractors. (The other reason is that it is free to the public and very easily to download.) Though automated classification is a fascinating and important topic in our field, it is not within the limits of this research effort.

Testing of the algorithm: We feel that the highest quality dataset which is free to us in North Carolina is the dataset provided by NCDPS (sdd.nc.gov). Thus, when we used data from that site, we already were using the most accurate data available. When we assess the introduced elevation error for the resulting decimated point cloud, we assess it against the undecimated terrain point cloud (in which non-ground points are filtered out).

We agree with Reviewer 1 that decimation alters the accuracy and density of the terrain point of the point cloud. We compare CWD's introduced error statistics with random decimation as a proxy for the commonly used sequential decimation. Though it is inevitable that all decimation techniques must introduce some error and reduce the point density, this paper demonstrates that CWD introduces less error than random decimation. Further, steps are taken in the algorithm to preserve more points where the point density is lower for the given input dataset. Though the algorithm tends to homogenize the sparsity (inverse density) of the terrain points, this aspect is not formally studied beyond its cumulative result in the introduced error statistical analysis.

Regarding the alternative of human-based breakline delineation, we did not raise this alternative specifically, but we agree that we should. We have added the following text Line 712 (new Line 730):

"Though the insertion of break lines at features would remedy this shortcoming, such work is labor intensive. Our goal is to provide a tool which does not require intensive human data entry such as introduction of break lines. Automated estimation and insertion of break line locations is a potential area of future research for terrain point clouds."

Lastly, automated classification techniques should be carried out on undecimated point cloud datasets as discrete point curvature and dihedral angle will be important parameters for some algorithm based classification processes. Decimation reduces the data density of these parameters. Our vision for Curvature Weighted Decimation is for decimation of terrain and not point clouds with non-terrain points in them. We have added a statement in the Discussion (after Line 797) to this end so as to clarify our intent and the limits to the potential of the algorithm.

 

> Lastly, what the data is being used for is a function of "success" and should be addressed.
We agree with this statement. We feel this important point is touched on in section 1.3 Decimation Generally (see lines 161-170.) We have added the following statement in the Discussion around Line 759 (new Line 834) to make this idea stand out more clearly.

"The cross sectional clipping plane of Figures 9a and 9b also underscore the loss of accuracy around the microtopography of streams. Were one of these cross sections included in flood modelling software, the hydraulic geometry of the CWD-decimated dataset (image b) is more accurate than that for the randomly decimated dataset (image a). This effect would also be present for other types of microtopography such as roadway break lines and retaining walls. This illustrates the claim in Section 1.3 (Decimation Generally) that random or sequential decimation may result in inaccurate or even unusable models, in this case, for hydraulic modelling of bank full flow or higher."

 

> Thus good work but it is not solving the issue of how to model.

Thank you for your comment. A secondary purpose of the paper is to introduce the CogoDN FOSS package, which includes modelling of terrain and alignments. We wish to let people know of its existence and availability. But mention of the module is incidental with respect to this paper. The focus and main point of the paper is the new way to decimate point clouds in an approach that introduces less error than the most common methods currently in use.

> It needs to address better the limits of what this is being used for as it does not solve many applications.

Thank you for your comment. We have added a statement at Line 32 to seek to address this.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Interesting work. Congratulations. If you consider, I have some suggestion.

1-     QL1/QL2 Lidar data should be mentioned briefly. There is nothing in the text, only in the abstract.

2-     QL1/QL2 Lidar data mostly used for DTM or DSM. What effect does the proposed sparse method have on this issue? The author should address this issue. Although there is a title called "1.1.2. Terrain modeling", this part should be detailed. You should check the following papers:

a-      Comparison of data reduction algorithms for LiDAR‐derived digital terrain model generalization

b-     An investigation of DEM generation process based on LiDAR data filtering, decimation, and interpolation methods for an urban area

3-     In section 1.1.2.1.3. Discrete Gaussian Curvature (line 99) and 2.2. Random Decimation (line 304).  There is a mistake: “This observation will be reiterated in the discussion in Section Error! Reference source not found..” please check it.

4-     It is not clear how RMS error calculated.

5-     If DSM is produced at different resolutions (for example, 50 cm, 1 m, and 5 m) from the sparse point cloud obtained as a result of the Random method with the proposed CWD method, which method will be more successful. Because a topographic product in which the spatial resolution changes is not affected by which data it uses after a certain point. This issue should be discussed.

6-     As a final suggestion, I can say this: In recent years, photogrammetric point clouds have also been used extensively. This issue should also be studied in terms of data sparseness. Data sparsity can also be examined in terms of 3D object modelling.

 

Author Response

Thank you for reviewing our paper, "Curvature Weighted Decimation: A novel, curvature-based approach to improved Lidar point decimation of terrain surfaces ". We have reviewed and responded to your comments. Further, we have implemented changes you recommend. We believe your comments have made our submission to Geomatics a much better publication.

 

Interesting work. Congratulations. If you consider, I have some suggestion.

Thank you for your kind words.

 

1-     QL1/QL2 Lidar data should be mentioned briefly. There is nothing in the text, only in the abstract.

Thank you. We have added mention of QL1 and QL2 accuracy levels at Line 553 (new Line 558) and 596 (new Line 612). 

 

The text at new Line 558 reads

These questions were assessed by using Lidar .las files from the North Carolina Department of Public Safety's Lidar repository (sdd.nc.gov). In this dataset, the four studied panels east of 80°W longitude are QL2. The two studied panels west of 80°W longitude are QL1.

 

The text at new Line 612 reads

The Coweeta and Tuttle panels are QL1 data quality. The other four panels are QL2 data quality, as reflected in the second column of Table 4.

 

 

2-     QL1/QL2 Lidar data mostly used for DTM or DSM. What effect does the proposed sparse method have on this issue? The author should address this issue. Although there is a title called "1.1.2. Terrain modeling", this part should be detailed. You should check the following papers:

a-    Comparison of data reduction algorithms for LiDAR‐derived digital terrain model generalization

b-    An investigation of DEM generation process based on LiDAR data filtering, decimation, and interpolation methods for an urban area

 

Thank you. Upon your recommendation, we have reviewed these papers.

 

Section 1.1.2 is only discussing the topic of those decimation methods which are restricted to terrain modelling. This is in contrast to the title of Section 1.1.1, Non-Terrain Point Cloud modelling. We now see that it may be unclear to a reader what difference we mean to highlight in between these sections. To make it clearer, we are renaming Section 1.1.1 "Non-Terrain Point Cloud Decimation" (new Line 60), and Section 1.1.2 "Terrain-Related Point Cloud Decimation" (new Line 80).

 

Yet we understand the above minor change does not resolve the important issue raised by Reviewer 2, inclusion of the contribution of these papers. After considering these papers, we have added another paragraph after Line 797 (new Line 848):

Future research could investigate the veracity of this anticipated improvement. For example, the study carried out by Yılmaz and Uysal (2016) decimated the raw Lidar points via sequential decimation. This study could be repeated using Curvature Weighted Decimation as the decimation algorithm to determine whether and by how much this alters the final results. Similar positive impacts may be found if CWD were used in the study carried out by Polat, et al. (2015).

 

3-     In section 1.1.2.1.3. Discrete Gaussian Curvature (line 99) and 2.2. Random Decimation (line 304).  There is a mistake: “This observation will be reiterated in the discussion in Section Error! Reference source not found..” please check it.

Thank you for pointing this out. This is an inadvertent error in cross referencing, for which we apologize. The error has been corrected. It now reads "Section 4.2.5". See new Line 309.

 

4-     It is not clear how RMS error calculated.

We have added a brief description of how we computed RMS error at Line 577 (new Line 588).

 

Root Mean Square Error was computed using Equation E5.

         Equation E5 (See the attached word document to view the equation, or Line 588 of the revised paper.)

where Δz is the elevation difference between the undecimated TIN surface and the derived TIN surface, and N is the total number of points in the grid.

 

Reviewer 2 may wish to verify this by looking at the C# source file at

https://github.com/PaulSchrum/CogoDN/blob/Schrum_2023_Curvature_Weighted_Decimation_paper/CogoDN/Surfaces/TIN/TINsurface.cs

In that file, see lines 913, 914, 924, and 930.

 

 

5-     If DSM is produced at different resolutions (for example, 50 cm, 1 m, and 5 m) from the sparse point cloud obtained as a result of the Random method with the proposed CWD method, which method will be more successful. Because a topographic product in which the spatial resolution changes is not affected by which data it uses after a certain point. This issue should be discussed.

 

Thank you for your recommendation. In response we have added the following statement in the Discussion Section starting at Line 797 (new Line 818):

 

Derived DEM Products

If a raster Digital Elevation Model is derived from a randomly decimated point cloud or a Curvature Weighted Decimated point cloud, it is anticipated that the CWD-derived DEM will be more accurate over the decimation range of 15% - 15%. This is because random and sequential decimation, by disregarding, the discrete curvature of the LAS points, will tend to strike chords which undercut or overshoot decimated points in the intermediate in-memory TIN. This undercutting is illustrated in Figure 9a at the stream bank location marked "High Error".

 

In Figure 9a and b, the front clipping plane of the image causes the triangulated mesh to show an example of a cross-section profile for the stream. This illustrates why CWD tends to introduce less elevation error totals than random or sequential decimation. The text labels "High Error" for Figure 9a and "Low Error" for Figure 9b show examples of this. The generation process from a randomly decimated terrain surface point cloud would carry this error forward into the DEM data derived from it.

 

 

6-     As a final suggestion, I can say this: In recent years, photogrammetric point clouds have also been used extensively. This issue should also be studied in terms of data sparseness. Data sparsity can also be examined in terms of 3D object modelling.

 

We agree with this comment. Mr. Schrum feels that the method we use here for computing point sparsity in the projected plane is the most appropriate approach for describing the sparsity of physical points or features. We agree that there is useful research to be done in reducing redundant points and finding edges on 3D objects, including building roofs and sides and similar things. Future automated point classification algorithms may use these parameters (Discrete Point Curvature and dihedral angle) to locate these edges. Once planar surfaces such as inclined roof gables are located, points which are interior to these planar structures may be decimated from the dataset as redundant.

 

The topical coverage of the current paper on Curvature Weighted Decimation is limited to .las files which have already been classified for ground and non-ground by the North Carolina Department of Public Safety (NCDPS). Our group does yet not have strong experience with structure from motion computations. Yet a fertile area of potential research is to use the metrics of curvature (see Table 7), dihedral angle, point sparsity, and face normal vectors to classify points or to provide input dimension to an AI algorithm for point classification. We are excited by such prospects and agree with Reviewer 2's overall observation.

 

In summary, we have added the following statements to the Discussion Section at new Line 852:

 

Other Data Sources

Though the focus of this paper is the decimation of Lidar terrain point clouds, the information available from the temporary in-memory TIN model of the undecimated point cloud is anticipated to be of value in point clouds from photogrammetric inputs. Specifically, the information available from the in-memory TIN model consists of point sparsity, dihedral angle between faces, and discrete Gaussian curvature.

 

Further, these parameters may be used to develop new routines for classifying unclassified datasets. This topic could be undertaken as future research.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Publish as the authors did an outstanding job responding to the first review