Application of Fractal Dimension of Terrestrial Laser Point Cloud in Classification of Independent Trees

Round 1

Reviewer 1 Report

Peer-review report: Application of Fractal Dimension of Terrestrial Laser Point Cloud in Classification of Independent Trees

The authors provide a terrestrial point cloud -based method to classify tree species using fractal dimensions. They show that the developed method provides ‘fractal characteristics’ of trees, enabling them to separate the three tree species from each other based on these features. In general, the manuscript is well written. Background for the proposed study is provided, the methods are clearly established and supported by graphics. The results are presented concisely and followed by a short discussion and conclusions. However, there are some shortcomings I would like to point out to provide the authors an opportunity to further improve the readability and impact of the study.

The first concern is related to terminology, which should be consistent throughout the manuscript. I assume that by ‘tree classification’ you mean tree species classification. This does become clear at some points, but sometimes the reader might feel it confusing while guessing on what grounds are the trees just ‘classified’. Another terminology-related comment deals with the point cloud data. In the first two pages several different terms for a TLS point cloud are given: Terrestrial laser point cloud, 3D laser point cloud, LiDAR point cloud, laser point cloud, 3D point cloud, dense canopy point cloud. I would say that ‘terrestrial laser point cloud’, ‘dense terrestrial point cloud’, or just ‘TLS point cloud’ is relevant for this context. 

Another concern is related to properly describing the background of the proposed study to bind it into the current state-of-the-art of this context. The introduction has potential to introduce the topic and lead the reader to the knowledge gap that is to be filled by this study. Now the fractal theory and its relationship with point clouds and 3D modelling of trees remains somewhat unexplained. Also, the novelty of this work needs to be highlighted even more, to convince the readers that this paper really contributes to the science. The aim of the study is presented in one single sentence at the end of introduction without presenting any hypotheses or assumptions about the outcome of the study. There is a clear structure in the results of this study, so why not formulate the objects to guide the reader. I do not know whether it is an opinion or not, but I feel that I would also like to add some short description (a sentence or two) about the methods used to achieve the objectives. 

The last major comment is related to the discussion and conclusions section that is relatively short yet concise and lacks a proper comparison of the study outcomes with previous work related to this topic. I encourage the authors to think about the impact of the proposed study and how the results reflect it. How the outcomes of this study compare with some pre-existing outcomes of similar topics. Compare the methodology, have someone used a similar approach earlier or is this one of a kind? Compare different tree species classification approaches and their feasibility and applicability in practice. How robust do you think your method is? Is it applicable with another dataset, or another forest environment?

Line-specific comments:

L28-33 Please use a citation to bind this into context.

L29 Plant classification?

L36-38 Identification and classification of plant species using what methods? 2D or 3D imaging, point clouds, …

L47-51 Although these statements are rather general, it would be feasible to use appropriate citations here. By ‘high density LiDAR point cloud data’ you probably mean terrestrial laser scanning, not airborne laser scanning. I think this detail should be mentioned here, as there is a difference in scanning geometry and the achieved level of detail between these two techniques. Terrestrial point clouds characterize well the horizontal forest structure, while vertical forest structure might be better captured with aerial point clouds.

L57 Please enlighten the reader a bit more about the principles behind ‘fractal theory’, and how e.g. ‘L-system’ and ‘IFS’ are related to it.

L59 ‘fractal has been widely used…’. Do you mean that fractal dimensions have been widely used, or did I now understand it correctly?

L68-73 Objectives of this study could be presented in more detail. I think it would be worth mentioning in short, with a few words, what kind of point clouds and point cloud processing methods are used.

L87 ‘Field survey’. A rather small detail though, but I think this refers more to conventional field inventory of measuring trees by manual means. Please consider reformulating this sentence so that it becomes clear that you are collecting a hemispherical point cloud to capture the 3D reconstruction of the surrounding environment.

L99 A suitable citation considering the multi-scan setup should be used here.

L110 If the box-counting method is widely used, please provide a reference citation(s) for readers that are unfamiliar with the proposed approach.

L130 A nice description of the workflow. For enhanced readability, please consider numbering the phases into the image and referring to them in the related text description. This way the figure is more bound into the text. 

L286- In the first paragraph of discussion, please be careful with terms and definition. Use a consistent terminology throughout the work. For example, ‘3D canopy laser point cloud’ does make sense in this context, but is not generally used. A point cloud has (almost) always three dimensional properties, so it is not a necessity to point out this feature. Then, if the point cloud is acquired with TLS, why not stating that you have ‘terrestrial point clouds’ or ‘TLS point clouds’, or ‘point clouds from terrestrial laser scanning’. Another thing to consider is ‘tree classification’. By what properties are the trees classified? I assume by tree species, but now it does not become clear at each point. 

L304 Please keep in mind that terrestrial and aerial point clouds provide different 3D reconstruction of trees due to different data acquisition geometry. Therefore, the two techniques cannot be compared as such. It is true that TLS and terrestrial MLS point clouds are comparable in terms of data acquisition geometry, but also these two techniques deliver slightly different point clouds in terms of quality. MLS enables higher temporal resolution in data acquisition and coverage, but geometric accuracy, point density and increased noise need to be considered.

Author Response

The authors would like to express their gratitude to the reviewer 1 for his/her constructive and helpful comments for substantial improvement of this paper. The manuscript has been carefully revised according to your comments and suggestions, which are very valuable to the improvement of this manuscript. We hope our revision has improved the paper to a level of your satisfaction. The replies to your specific comments/suggestions are as follows.

Comment 1: The first concern is related to terminology, which should be consistent throughout the manuscript.

Response: Thank you for your comment. We have standardized the terminology throughout the paper, including "dense terrestrial laser point cloud" and "tree species classification".

Comment 2. Another concern is related to properly describing the background of the proposed study to bind it into the current state-of-the-art of this context.

Response: Thank you for your comment. We have added relevant background in the "Introduction" and "Materials and Methods" sections.

Comment 3. The last major comment is related to the discussion and conclusions section that is relatively short yet concise and lacks a proper comparison of the study outcomes with previous work related to this topic.

Response: Thank you for your comment. We have revised the last section.

Comment 4. L28-33 Please use a citation to bind this into context.

Response: Thank you for your comment. We have added the relevant references in the corresponding positions.

Revision in our paper:

Plants play an important role in the whole ecosystem because of their important impact on the ecological environment[1]–[3]. Tree species classification is the first basic work for correct understanding and research of trees[4]–[6]. It is also the core issue of remote sensing monitoring of forestry resources and ecological effect assessment[7], [8]. Urban ecological construction and greening are important aspects of urban development[9]. This process not only considers the number of trees planted, but also fully considers the allocation of plant species to optimize urban environment from biomass and carbon balance[10]–[12].

Reference:

[1]   P. Lesica and F. W. Allendorf, “Ecological genetics and the restoration of plant communities: mix or match?,” Restoration ecology, vol. 7, no. 1, pp. 42–50, 1999.

[2]   J. Walter, A. Jentsch, C. Beierkuhnlein, and J. Kreyling, “Ecological stress memory and cross stress tolerance in plants in the face of climate extremes,” Environmental and Experimental Botany, vol. 94, pp. 3–8, 2013.

[3]   J. A. Savage et al., “Allocation, stress tolerance and carbon transport in plants: how does phloem physiology affect plant ecology?,” Plant, Cell & Environment, vol. 39, no. 4, pp. 709–725, 2016.

[4]   F. E. Fassnacht et al., “Review of studies on tree species classification from remotely sensed data,” Remote Sensing of Environment, vol. 186, pp. 64–87, 2016.

[5]   M. P. Ferreira, F. H. Wagner, L. E. Aragão, Y. E. Shimabukuro, and C. R. de Souza Filho, “Tree species classification in tropical forests using visible to shortwave infrared WorldView-3 images and texture analysis,” ISPRS journal of photogrammetry and remote sensing, vol. 149, pp. 119–131, 2019.

[6]   D. Cardoso et al., “Amazon plant diversity revealed by a taxonomically verified species list,” Proceedings of the National Academy of Sciences, vol. 114, no. 40, pp. 10695–10700, 2017.

[7]   E. Raczko and B. Zagajewski, “Comparison of support vector machine, random forest and neural network classifiers for tree species classification on airborne hyperspectral APEX images,” European Journal of Remote Sensing, vol. 50, no. 1, pp. 144–154, 2017.

[8]   L. Ballanti, L. Blesius, E. Hines, and B. Kruse, “Tree species classification using hyperspectral imagery: A comparison of two classifiers,” Remote Sensing, vol. 8, no. 6, p. 445, 2016.

[9]   F. Li, R. Wang, J. Paulussen, and X. Liu, “Comprehensive concept planning of urban greening based on ecological principles: a case study in Beijing, China,” Landscape and urban planning, vol. 72, no. 4, pp. 325–336, 2005.

[10] S. T. Lovell and J. R. Taylor, “Supplying urban ecosystem services through multifunctional green infrastructure in the United States,” Landscape ecology, vol. 28, no. 8, pp. 1447–1463, 2013.

[11] J. Yang, J. McBride, J. Zhou, and Z. Sun, “The urban forest in Beijing and its role in air pollution reduction,” Urban forestry & urban greening, vol. 3, no. 2, pp. 65–78, 2005.

[12] V. A. Parsa, E. Salehi, A. R. Yavari, and P. M. van Bodegom, “Analyzing temporal changes in urban forest structure and the effect on air quality improvement,” Sustainable Cities and Society, vol. 48, p. 101548, 2019.

Comment 5. L29 Plant classification?

Response: Thank you for your comment. We have changed it to "tree species classification" (L30).

Revision in our paper:

Tree species classification is the first basic work for correct understanding and research of trees.

Comment 6. L36-38 Identification and classification of plant species using what methods? 2D or 3D imaging, point clouds, …

Response: Thank you for your comment. Here we refer to the use of 2D images of trees for tree species classification. We have added a description in the article (L37).

Revision in our paper:

Research on the identification and classification of tree species has focused on the appearance characteristics of plants, especially in the early period, mainly using 2D images of trees to identify tree species by extracting the shape of tree leaves.

Comment 7. L47-51 Although these statements are rather general, it would be feasible to use appropriate citations here. By ‘high density LiDAR point cloud data’ you probably mean terrestrial laser scanning, not airborne laser scanning. I think this detail should be mentioned here, as there is a difference in scanning geometry and the achieved level of detail between these two techniques. Terrestrial point clouds characterize well the horizontal forest structure, while vertical forest structure might be better captured with aerial point clouds.

Response: Thank you for your suggestion. We have added citations. We have changed "laser point cloud" to "terrestrial laser point cloud".

Revision in our paper:

In the past decade, Light Detection and Ranging technology has been widely used in the field of agricultural and forestry vegetation remote sensing [20]–[23] due to its high-precision and high-density 3D spatial information acquisition capability. High density terrestrial laser point clouds data can obtain accurate horizontal and vertical vegetation distribution structure[24]–[27].

Reference:

[20]  M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies: Lidar, an emerging remote sensing technology that directly measures the three-dimensional distribution of plant canopies, can accurately estimate vegetation structural attributes and should be of particular interest to forest, landscape, and global ecologists,” BioScience, vol. 52, no. 1, pp. 19–30, 2002.

[21]  Q. Chen and C. Qi, “Lidar remote sensing of vegetation biomass,” Remote sensing of natural resources, vol. 399, pp. 399–420, 2013.

[22]  M. Castillo, B. Rivard, A. Sánchez-Azofeifa, J. Calvo-Alvarado, and R. Dubayah, “LIDAR remote sensing for secondary Tropical Dry Forest identification,” Remote sensing of environment, vol. 121, pp. 132–143, 2012.

[23]  K. Zhao et al., “Terrestrial lidar remote sensing of forests: Maximum likelihood estimates of canopy profile, leaf area index, and leaf angle distribution,” Agricultural and Forest Meteorology, vol. 209, pp. 100–113, 2015.

[24]  C. Cabo, C. Ordóñez, C. A. López-Sánchez, and J. Armesto, “Automatic dendrometry: Tree detection, tree height and diameter estimation using terrestrial laser scanning,” International journal of applied earth observation and geoinformation, vol. 69, pp. 164–174, 2018.

Comment 8. L57 Please enlighten the reader a bit more about the principles behind ‘fractal theory’, and how e.g. ‘L-system’ and ‘IFS’ are related to it.

Response: We have added an introduction to "fractal theory".

Revision in our paper:

L-system (Lindenmayer system) is an algorithm proposed by Aristid Lindenmayer in 1968 [31], [32]. It can describe processes such as the growth of plants. References [35], [36] used L-system to simulate the basic shape of trees, stochastic L-system to simulate the growth of apical buds, and control the growth direction of branches to simulate the phototaxis and geotaxis of tree growth. IFS theory, introduced by Zadeh [37], is an extension of fuzzy set theory and more suitable for explaining human thinking than fuzzy set theory. IFS theory is a powerful way to deal with uncertainty and vagueness, and was introduced by Atanassov [38].

Comment9. L59 ‘fractal has been widely used…’. Do you mean that fractal dimensions have been widely used, or did I now understand it correctly?

Response: We have changed " fractal " to " fractal dimensions ".

Revision in our paper:

In fact, fractal dimension has been widely used

Comment 10. L68-73 Objectives of this study could be presented in more detail. I think it would be worth mentioning in short, with a few words, what kind of point clouds and point cloud processing methods are used.

Response: Thank you for your suggestion. We have made changes to this.

Revision in our paper:

In this study, by using the dense terrestrial laser point cloud data of different types of independent tree species, the fractal algorithm is used to calculate the fractal dimension of terrestrial point clouds data and achieve the classification of independent tree species according to the fractal characteristics of natural tree canopy.

Comment 11. L87 ‘Field survey’. A rather small detail though, but I think this refers more to conventional field inventory of measuring trees by manual means. Please consider reformulating this sentence so that it becomes clear that you are collecting a hemispherical point cloud to capture the 3D reconstruction of the surrounding environment.

Response: Thank you for your suggestion. We have revised this sentence.

Revision in our paper:

We scanned the trees using the RIEGL VZ-400i TLS mounted on a tripod.

Comment 12. L99 A suitable citation considering the multi-scan setup should be used here.

Response: Thank you for your suggestion. We have added the appropriate citations.

Revision in our paper:

Reference:

[46]  V. Kankare et al., “Individual tree biomass estimation using terrestrial laser scanning,” ISPRS Journal of Photogrammetry and Remote Sensing, vol. 75, pp. 64–75, 2013.

Comment 13. L110 If the box-counting method is widely used, please provide a reference citation(s) for readers that are unfamiliar with the proposed approach.

Response: Thank you for your suggestion. We have added the appropriate citations.

Revision in our paper:

Reference:

[48]  T. Ai, R. Zhang, H. Zhou, and J. Pei, “Box-counting methods to directly estimate the fractal dimension of a rock surface,” Applied Surface Science, vol. 314, pp. 610–621, 2014.

[49]  J. Perret, S. Prasher, and A. Kacimov, “Mass fractal dimension of soil macropores using computed tomography: from the box-counting to the cube-counting algorithm,” European Journal of Soil Science, vol. 54, no. 3, pp. 569–579, 2003.

[50]  Z. Yang and Y. Li, “The Box-counting Dimension of Spatial Patterns of Population Distribution of Lilium regale,” 2018.

[51]  D. A. Palanivel, S. Natarajan, S. Gopalakrishnan, and R. Jennane, “Trabecular Bone Texture Characterization Using Regularization Dimension and Box-counting Dimension,” in TENCON 2019-2019 IEEE Region 10 Conference (TENCON), 2019, pp. 1047–1052.

Comment 13. L130 A nice description of the workflow. For enhanced readability, please consider numbering the phases into the image and referring to them in the related text description. This way the figure is more bound into the text.

Response: Thank you for your suggestion. We have revised.

Revision in our paper:

Comment 14. L286- In the first paragraph of discussion, please be careful with terms and definition. Use a consistent terminology throughout the work.

Response: Thank you for your suggestion. We have standardized the terminology throughout the paper.

Revision in our paper:

According to the fractal characteristics of natural tree canopy, this paper proposes an independent tree species classification method based on the fractal expression of terrestrial point clouds. Firstly, dense terrestrial laser point clouds data of different types of independent trees are obtained by multi-station scanning with terrestrial laser scanner. Then, the fractal dimension values of terrestrial point clouds data are calculated by box-counting fractal method using RANSAC gross error elimination. Finally, the fractal dimension is used to classify different tree canopy morphological species. The experimental results show that the fractal dimension can describe the characteristics of different types of independent trees, and can effectively achieve the tree species classification of independent trees. It verified the feasibility and validity of the fractal theory to introduce the dense terrestrial laser point clouds feature expression. It has broad application prospects for the recognition of 3D spatial morphology of  vegetation and dense terrestrial laser point clouds data intelligent processing.

Comment 14. L304 Please keep in mind that terrestrial and aerial point clouds provide different 3D reconstruction of trees due to different data acquisition geometry. Therefore, the two techniques cannot be compared as such. It is true that TLS and terrestrial MLS point clouds are comparable in terms of data acquisition geometry, but also these two techniques deliver slightly different point clouds in terms of quality. MLS enables higher temporal resolution in data acquisition and coverage, but geometric accuracy, point density and increased noise need to be considered.

Response: Thank you for your suggestion. We have abandoned comparing MLS with TLS.

Author Response File: Author Response.docx

Reviewer 2 Report

In this paper, the authors carry out an interesting application of fractal dimension to distinguish (and hence, classify and recognize) three species of trees by accurately calculating the 3D box-counting dimensions of their canopies, which are mathematically treated as independent point cloud sets. To deal with, they follow a task flow that has to be addressed before carrying out the calculations. It is also worth pointing out that they use an algorithm allowing the calculation of the box dimension of 3D point clouds combined with a RANSAC gross error elimination approach.

In my opinion, the paper is interesting, well-written, and technically sound. Thus, I recommend it for acceptance in Fractal and Fractional. Also, I suggest the authors to take a look at the following remarks in order to (slightly) enhance the quality of their manuscript.

-Line 66: replace "generation" by "generated".

-Line 110: though the box dimension is the model of fractal dimension that has been applied mostly in empirical applications of fractal dimension (especially in Euclidean contexts), the authors should also comment on the models of fractal dimension for fractal structures that were studied in [SPR19] (see references below), which can be also calculated in non-Euclidean contexts.

-Lines 110-111: rewrite them as follows. Let n\in N , F be a non-empty bounded subset of R^n, and N_L(F) be the smallest number of cubes (in R^n) of side L that cover F (which coincides with the number of cubes of side L that intersect F by Definition 3.1 in [FAL90]).

-In Eq. (1), please, replace the "ln" notation by the "log" notation. Also, note that such a limit does not have to exist necessarily (though in empirical applications of fractal dimension, as it is the case, that limit is effectively calculated as the slope of a regression line in a log-log plot).

-Line 124: remove "an".

-Line 125: remove the dot after the word "sequence" and state clearly that the number of iterations is denoted as "Iterator", hereafter.

-The quality of Fig. 4 is not optimal.

-Line 151: Is it necessary to state Eq. (4) (the equation of a straight line) in a separate line in the text?

-Line 179: The title of that subsection should begin by a capital letter.

-Line 218: I think that the acronym "RANSAC" should be removed.

-In page 12, Fig. 10, the authors show how the fractal dimension of each tree species is distributed. While it is true that the fractal dimension of the ginkgo species seems to behave differently compared to the fractal dimension of either the photinia or the cypress species, it is not so clear that the fractal dimension of the photinia species is different (in median or mean) than the one of the cypress species. In this way, maybe a hypothesis test could be conducted to determine if there are significant differences between the (median or mean of their) fractal dimensions. However, the small size of the samples (only three trees from each species were considered in this work) makes that comparison unfeasible from a statistical viewpoint. I recommend the authors to comment on it as a future research.

--

References:

\bibitem{FAL90}
K.~Falconer, \emph{{Fractal geometry. Mathematical Foundations and
Applications}}, 1st ed., John Wiley {\&} Sons, Ltd., Chichester, 1990.

\bibitem{Fernandez-Martinez2019a}
Manuel Fern{\'{a}}ndez-Mart{\'{i}}nez, Juan Luis~Garc{\'{i}}a Guirao,
Miguel~{\'{A}}ngel S{\'{a}}nchez-Granero, and Juan Evangelista~Trinidad
Segovia, \emph{{Fractal dimension for fractal structures: With applications
to finance}}, vol.~19, 2019.

Author Response

Thank you for your comments concerning our manuscript. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper.

Comment 1:

-Line 66: replace "generation" by "generated".

Response: Thank you for your comment. We have revised.

Revision in our paper:

the branch and leaf model was generated by particle system method

Comment 2: -Line 110: though the box dimension is the model of fractal dimension that has been applied mostly in empirical applications of fractal dimension (especially in Euclidean contexts), the authors should also comment on the models of fractal dimension for fractal structures that were studied in [SPR19] (see references below), which can be also calculated in non-Euclidean contexts.

Response: Thank you for your comment. We have revised.

Revision in our paper:

The box-counting dimension is one of the most popular fractal dimensions, which is applicable to simple fractals as well as complex fractals. The essence of box-counting dimension is to change the degree of coarse visualization to measure the figure, usually starting from counting large boxes, and then decreasing the scale of boxes, only counting those "non-empty" boxes[52].

Comment 3: -Lines 110-111: rewrite them as follows. Let n\in N, F be a non-empty bounded subset of R^n, and N_L(F) be the smallest number of cubes (in R^n) of side L that cover F (which coincides with the number of cubes of side L that intersect F by Definition 3.1 in [FAL90]).

Response: Thank you for your comment. We have revised.

Revision in our paper:

Let  in ,  be a non-empty bounded subset in , and  be the smallest number of cubes (in ) of side  that cover  [53]. The box-counting dimension of  was defined by Equation (1):

Comment 4. -In Eq. (1), please, replace the "ln" notation by the "log" notation. Also, note that such a limit does not have to exist necessarily (though in empirical applications of fractal dimension, as it is the case, that limit is effectively calculated as the slope of a regression line in a log-log plot).

Response: Thank you for your comment. We have revised.

Revision in our paper:

Let  in ,  be a non-empty bounded subset in , and  be the smallest number of cubes (in ) of side  that cover  [53]. The box-counting dimension of  was defined by Equation (1):

Comment 5. -Line 124: remove "an".

Response: Thank you for your comment. We have revised.

Revision in our paper:

the bounding rectangle of an the terrestrial point cloud

Comment 6. -Line 125: remove the dot after the word "sequence" and state clearly that the number of iterations is denoted as "Iterator", hereafter.

Response: Thank you for your comment. We have revised.

Revision in our paper:

Using the simplest linear sequence, the number of iterations  was determined by Equation (2):

Comment 7. -The quality of Fig. 4 is not optimal.

Response: Thank you very much for your suggestion. We have revised.

Revision in our paper:

Comment 8. -Line 151: Is it necessary to state Eq. (4) (the equation of a straight line) in a separate line in the text?

Response: Thank you very much for your suggestion. We have revised this sentence according to the Reviewer’s comments.

Revision in our paper:

 was used to obtain the equation of the fitted straight line.

Comment 9. -Line 179: The title of that subsection should begin by a capital letter.

Response: Thank you very much for your suggestion. We have revised.

Revision in our paper:

2.4. Evaluating indicator

Comment 10. -Line 218: I think that the acronym "RANSAC" should be removed.

Response: Thank you very much for your suggestion. We have revised.

Revision in our paper:

The data usage ratio is not less than 50% of the original double logarithmic points.

Comment 11. -In page 12, Fig. 10, the authors show how the fractal dimension of each tree species is distributed. While it is true that the fractal dimension of the ginkgo species seems to behave differently compared to the fractal dimension of either the photinia or the cypress species, it is not so clear that the fractal dimension of the photinia species is different (in median or mean) than the one of the cypress species. In this way, maybe a hypothesis test could be conducted to determine if there are significant differences between the (median or mean of their) fractal dimensions. However, the small size of the samples (only three trees from each species were considered in this work) makes that comparison unfeasible from a statistical viewpoint. I recommend the authors to comment on it as a future research.

Response: We have placed this part in " Discussion ".

Round 2

Reviewer 1 Report

I would like to thank the authors for providing detailed responses to my comments. I am pleased to see that the message of this study has improved since the last review round. However, my concerns are related on the discussion and conclusions section that still lacks a proper comparison to the previous studies. It is now hard for a reader to judge how this study contributed to the existing knowledge of this field of science. The authors have well summarized the most important findings of the study as well as their applicability, but I would like to see a more elaborate discussion on how these findings reflect to the current knowledge. If fractal dimensions have not used in tree species classification before this study, the novelty of this research must be highlighted more. But there are several earlier attempts to classify tree species with terrestrial laser scanning (probably not by using fractal dimensions, but other approaches), so comparison to those studies must be included in the discussion section of this study.

Author Response

Response:

The authors would like to express their gratitude to the reviewer 1 for his/her constructive and helpful comments for substantial improvement of this paper. The “Discussion and Conclusions” section has been revised according to your comments and suggestions. We hope our revision has improved the paper to a level of your satisfaction. Revised portion are marked in red in the paper. The revision in our paper is as follows.

Revision in our paper:

Unlike the tree species classification research based on 2D image [14]–[16], [19], this paper collects terrestrial point clouds data, which has richer morphological structure information compared with image data and can better reflect the structural characteristics of independent trees. This paper classifies tree species based on fractal dimensional features of tree crowns, which is simpler and ensures accuracy compared with other tree species classification methods that extract features such as tree trunk skeleton and leaf shape [55], [56]. Compared with random forest, support vector machines, decision tree and other methods [55], [57]–[59] that need to collect a large amount of sample data for pre-training, this paper does not have a training process, the preliminary workload is small, does not require a large amount of sample data, and costs less in labor and time. In addition, the tree species classification by using Bayes classifier or linear discriminant analysis is not effective when the number of trees is small [60], [61]. From Table 1 and Table 2, it can be seen that the box-counting dimension fitting based on RANSAC gross error elimination method used in this paper has stronger robustness and is less affected by the number of trees.