Round 1

Reviewer 1 Report

Dear Authors,

thank you very much for your interesting article. However, I have several remarks and recommendations:

1. The manuscript in general would benefit a lot from writting it more detailed and clear. For instance in the figure presenting the methodology (figure 1), it is clear that you set up a threshold first and then at a later stage you optimize its value. However, from the description it was not entirely clear what is the order of these two steps.

2. In the abstract you state that: "Second, in  order to make the experimental results more objective and reasonable, the Douglas-Peucker algorithm is used to simplify the information changing curve, and the optimal angle threshold range for generating stroke is obtained for different road network structures". Please explain in which sense it is more objective.

3. Also, in the abstract you mention only Monaco case study, while in the paper there are two more case studies. It would be good to refer to them as well.

4. What do you exaclty mean by: "Then the strokes in the two road networks are selected in the same proportion"?

5. Row 60, page 2. In the sentence: "Therefore, accurately describing...", after therefore, I would add "we argue that...".

6. Row 75, page 2 - spelling mistake "Douglas-Puck".

7. In the manuscript once you state: "element level" and "neighborhood level" and later "road elements" and "neighborhood level". Is road elements and element level the same?

8. How is neighborhood level defined?

9. Row 218, page 8 You state: "Similarly, the topological relationships between strokes are 218 different under different angle thresholds. And the greater the difference in topological relationships, the greater the difference in the amount of information produced". How is the difference in topological relationships defined/calculated/expressed?

10. Row 271, page 10. Please add the explanation about the curve simplification. It is not clear to me if you simplify the curve or the road network?

11. Please add the information where the experiments where implemented, with the use of which software, tools or programming language.

12. What is the detail level your solution is applicable for?

Thank you

Author Response

To Reviewer 1

Thank you very much for reviewing this article and thank you for your valuable comments and suggestions. We have made one-by-one revisions in the text based on your comments. The details of the changes are as follows.

Point 1: The manuscript in general would benefit a lot from writing it more detailed and clearer. For instance, in the figure presenting the methodology (figure 1), it is clear that you set up a threshold first and then at a later stage you optimize its value. However, from the description it was not entirely clear what is the order of these two steps.

Response 1:

Thanks for the comments.

In Line 104 – 113, we have redescribed the methodology. And the update process of threshold is highlighted in step (2) - (3). The specific methodology are as follows:

“

(1)    Set the initial angle threshold, threshold = 1°.

(2)    According to the angle threshold, merge segments into strokes and the new road network will be generated.

(3)    Select indicators of information volume and, under the new road network, calculate the information volume of both road network elements and neighborhood levels.

(4)    If the threshold is greater than 90°, perform the step (5). Otherwise, set threshold = threshold + 1°, and repeat the step (2) – (4).

(5)    Draw the road network’s information volume curve under different angle thresholds and simplify the curve using the Douglas-Peucker algorithm, to determine the optimal angle threshold range for generating strokes in a specific road network.

”

Thank you very much for your comments and valuable suggestions.

Point 2: In the abstract you state that: "Second, in order to make the experimental results more objective and reasonable, the Douglas-Peucker algorithm is used to simplify the information changing curve, and the optimal angle threshold range for generating stroke is obtained for different road network structures". Please explain in which sense it is more objective.

Response 2:

Thanks for the comments.

In determining the optimal threshold range, literature [31] has tried to use the slope of the curve. However, when the interval between angle thresholds is too small (e.g. 1°), it usually occurs that multiple slopes are equal, and then the optimal range of the angle threshold can’t be screened out.

Therefore, in literature [31], it is proposed to extend the interval to 5° and to use the above method to determine the optimal range of angle threshold. However, if this problem is solved only by enlarging the threshold interval, there will be some limitations:

First, how to determine the interval threshold is more reasonable.

Second, when the interval is determined (e.g. 5°), the results from 1° may be different from those from 2°.

Therefore, it is reasonable to simplify the information change curve by using the Douglas-Peucker algorithm, and then find out the optimal range of angle threshold.

Thank you very much for your comments and valuable suggestions.

Point 3: Also, in the abstract you mention only Monaco case study, while in the paper there are two more case studies. It would be good to refer to them as well.

Response 3:

Thanks for the comments.

In this paper, the threshold range of road network construction in Chicago and Moscow are consistent with the commonly used threshold (60°), which proves the rationality of the proposed method. However, in the process of stroke selection, the calculated angle threshold is consistent with the common threshold, it is not comparable. Therefore, this paper only determines the threshold range of stroke construction in Chicago and Moscow, but does not select stroke.

Through these two experiments, the rationality and validity of this method are proved, and at the same time it is also proved that this method is suitable for various road networks with different morphological structures.

We added instructions in Lines 21 and 442, respectively.

“Finally, we apply this model to three different road networks , and the optimal threshold ranges are 54°-63° (Chicago), 61°-63° (Moscow), 45°-48°(Monaco). And taking Monaco as an example, this paper conducts stroke selection experiments. The results demonstrate that our proposed algorithm has better connectivity and wider coverage than those based on a common angle threshold.”

“From the experimental results of this paper, it can be seen that the optimum angle threshold range for road construction in Moscow and Chicago are 61°-63° and 54°-63° respectively, which is consistent with the commonly used angle threshold for road construction, and verifies the rationality of this method.”

Thank you very much for your comments and valuable suggestions.

Point 4: What do you exactly mean by: "Then the strokes in the two road networks are selected in the same proportion"?

Response 4:

Thanks for the comments.

For the same road network, when constructing stroke, the threshold of deflection angle is different, and the number of strokes will be different. The original Monaco road network contains 1549 segments. We generated strokes for Monaco’s road network using both 46° (Road network I) and 60° (Road network II) as angle thresholds. Using thresholds of 46° and 60° resulted in 847 strokes and 806 strokes, respectively. The following table shows the number of strokes screened from the two networks in the same proportion.

Table 1. The number of strokes selected with the same proportion

After determining the number of selections, we then calculated the information volume for each stroke in the two road networks using the methods in Chapter 2.3. Finally, according to the amount of information and the proportion of selection, we selected strokes in Road networks I and II. And the experimental results show that our method is more effective at determining the angle threshold than fixed threshold methods in terms of suspension, connectivity and coverage.

By selecting the same proportion of the two road networks, we can see that the optimal angle thresholds are different for different road networks. If all road networks use a fixed angle threshold in the construction of stroke, the situation in Chapter 3.5 will appear.

Thank you very much for your comments and valuable suggestions.

Point 5: Row 60, page 2. In the sentence: "Therefore, accurately describing...", after therefore, I would add "we argue that...".

Response 5:

Thanks for the comments.

In Line 65, we have made corresponding modifications. The changes are as follows:

 “However, while strokes are widely used in road network research, few scholars have examined the best methods of determining the most accurate angle threshold. Instead, most research directly applies a fixed angle threshold in stroke generation, ignoring the influence of a road network’s geometric and structural properties. This paper attempts to remedy that limitation by arguing that a road network’s geometric and structural properties have an important influence on the determination of the angle threshold.

To this end, in this paper we determine a model for describing changes in road network information under different angle thresholds to reflect the differences in strokes.”

Thank you very much for your comments and valuable suggestions.

Point 6: Row 75, page 2 - spelling mistake "Douglas-Puck".

Response 6:

Thanks for the comments.

I am very sorry for the trouble caused by my carelessness. We have checked the spelling of ‘Douglas-Peucker’ in the full text.

Thank you very much for your comments and valuable suggestions.

Point 7: In the manuscript once you state: "element level" and "neighborhood level" and later "road elements" and "neighborhood level". Is road elements and element level the same?

Response 7:

Thanks for the comments.

In this paper, the road element is the same as element level. To avoid confusion, we have changed the road elements in the manuscript to element level.

Thank you very much for your comments and valuable suggestions.

Point 8: How is neighborhood level defined?

Response 8:

Thanks for the comments.

In road network, the neighborhood level of roads is usually expressed as the relationship of topological connection between roads [1-3]. Therefore, in this paper, we choose the stroke’s degree, between-ness and closeness to represent the topological relationship.

[1] Jiang, B.; Liu, L. Street‐based topological representations and analyses for predicting traffic flow in GIS [J]. International Journal of Geographical Information Science, 2009, 23(9), 1119-1137.

[2] Wenjing, L.; Dan, Hu.; Yi, Liu. An improved measuring method for the information entropy of network topology [J]. Transactions in GIS, 2018, 22, 1632-1648.

[3] Bisheng, Y.; Xuechen, L.; Qingquan, L. Generating hierarchical strokes from urban street networks based on spatial pattern recognition [J]. International Journal of Geographical Information Science, 2011, 25(12), 2025-2050.

Thank you very much for your comments and valuable suggestions.

Point 9: Row 218, page 8 You state: "Similarly, the topological relationships between strokes are 218 different under different angle thresholds. And the greater the difference in topological relationships, the greater the difference in the amount of information produced". How is the difference in topological relationships defined/calculated/expressed?

Response 9:

Thanks for the comments.

In GIS, the topological relationship is defined as the degree of association or proximity between two map elements [1]. And in this paper, the topological relationship is defined as the degree of association between strokes.

The topological relationship of maps is mainly characterized by the connectivity of nodes. In this paper, we first construct the dual graph of the road network, so that the roads in the road network can be transformed into nodes. Then the degree, betweenness and closeness are selected to describe the topological relationship. The indicators are described below.

Table 2. Indicator of topological relationship

Most of the existing information measurement methods are based on Shannon information entropy [1]. But this method has some limitations. In Line 196, we describe the limitations of this method and introduce the computational model used in this paper. It is described as follows:

“Shannon [18] introduced probability to study the measurement of information amount. He believed that information comes from the uncertainty of information, and proposed the concept of information entropy to represent the average information amount contained in information source [11]. Subsequently, Sukhov [19-20] first introduced information theory into cartography and used it to measure the diversity of map symbols. But the information entropy theory is based on the probability of map symbols: if the probability of two map symbols is the same, their information volume will be the same. The traditional information entropy model will not reflect differences between map symbols, meaning that is not suitable for calculating road network information in our study. We therefore adopted a metric model based on spatial characteristics [21] that takes into account differences in strokes’ spatial distribution characteristics. We used each stroke’s corresponding spatial characteristics as the measurement index in order to measure its information volume:

                                  (1)

where  is the measurement index expressing the stroke’s geometric and structural characteristics, such as the length and connectivity of the stroke. And  is the information volume under different angle thresholds.”

[1] Hong Z, Jing H, Jie Y; et al. Quantitative Measurements on Topological Structural Information of Road Networks Based on Complex Network Analyses [J]. Geography and Geo-information Science, 2017, 33 (2):5-10.

[2] Wenjun, O.; Xianlin, Y. Measuring of cartographic information amount the general eigen value measuring method [J]. Map, 1988, (4), 20-24.

Thank you very much for your comments and valuable suggestions.

Point 10: Row 271, page 10. Please add the explanation about the curve simplification. It is not clear to me if you simplify the curve or the road network?

Response 10:

Thanks for the comments.

In Line 281, we have added a shortly explanation about the Douglas-Peucker (D-P) curve simplification algorithm.

“The D-P algorithm includes two simplified methods: fixed point and fixed distance. D-P fixed distance algorithm needs to set a distance threshold, which is used as the basis of whether to retain the current point or not. Similarly, D-P fixed point algorithm needs to determine the number of retained points in advance, and then determine which points will be retained according to the distance from the points to the line.”

Thank you very much for your comments and valuable suggestions.

Point 11: Please add the information where the experiments where implemented, with the use of which software, tools or programming language.

Response 11:

Thanks for the comments.

The operating environment of the system is Windows 10 (Intel(R) Core (TM) i5-7400 CPU @ 3.00 GHz, 8GB). The softwares used in this experiment include Gephi and ArcGIS. And the programming language is Python.

Thank you very much for your comments and valuable suggestions.

Point 12: What is the detail level your solution is applicable for?

Response 12:

Thanks for the comments.

The experimental data in this paper come from OSM. The downloaded road network contains many ranks, such as primary, link, pedestrians, unclassified, etc. When many detail levels of the road (unclassified) into the network, there will be a large number of suspended roads. And in order to ensure the connectivity of the original road network, this paper chooses three levels of roads: primary, secondary and tertiary to carry out experiments. In this paper, the road rank is not used as the index of calculating information volume. Therefore, under the premise of ensuring the connectivity of the original road network, if we choose other ranks or levels of road for experiment, the method in this paper is also applicable in theory.

Thank you very much for your comments and valuable suggestions.

Author Response File: Author Response.pdf

Reviewer 2 Report

Dear authors,

- check all spelling of Douglas-Peucker alg. (p. 2 Puck; p. 19 Poker)

- wrong reference to Fig.3 (page 4, in the text, is the wrong reference to Fig.4b)

- Fig. 3 is original, or it is taken from [9]?

- Table 1- It is not a table. The presented code is not pseudocode. Pseudocode must be written most in words than in commands.

- Fig. 4 If the flowchart contains the END symbol, it must contain also START symbol (according to flowchart symbology - use for both oval). Command i=i+1 in branches put to the rectangle.

- Tab. 3 The last equation is divided into two rows.

- Page 12. There is mentioned that the merge operation was based only on the name of the streets. Did you use the category of a street (highway, class 1, class 2)?

- Page 7 - Explanation of Shannon entropy is more common, not only about map symbols (it is not correct explanation).

Author Response

To Reviewer 2

Thank you very much for reviewing this article and thank you for your valuable comments and suggestions. We have made one-by-one revisions in the text based on your comments. The details of the changes are as follows.

Point 1: check all spelling of Douglas-Peucker alg. (p. 2 Puck; p. 19 Poker).

Response 1:

Thanks for the comments.

I am very sorry for the trouble caused by my carelessness. I have checked all spelling of Douglas-Peucker in the text.

Thank you very much for your comments and valuable suggestions.

Point 2: wrong reference to Fig.3 (page 4, in the text, is the wrong reference to Fig.4b).

Response 2:

Thanks for the comments.

I have modified the reference to Figure 3 in Line 138. I am very sorry for the trouble caused by my carelessness.

“There are three commonly used connection strategies: self-fit, self-best-fit, and every-best-fit [9] (Figure 3)”

Thank you very much for your comments and valuable suggestions.

Point 3: Fig. 3 is original, or it is taken from [9]?

Response 3:

Thanks for the comments.

Figure 3 is drawn by me according to the description of literature 9. And similar expressions are used in many literatures [1-3].

[1] Xun W. Stroke selection based on geometric and structural properties of roads; Southwest Jiaotong University: Chengdu, China, 2017.

[2] Zhongliang, F.; Baofeng, W.; Yulong, H. A schematic method based on the integration of stroke construction and displacement for road network [J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(9), 1115-1121.

[3] Qi, Z.; Zhilin, L. A comparative study of various strategies to concatenate road segments into strokes for map generalization [J]. International Journal of Geographical Information Science, 2012, 26(4), 691-715.

Thank you very much for your comments and valuable suggestions.

Point 4: Table 1- It is not a table. The presented code is not pseudocode. Pseudocode must be written most in words than in commands.

Response 4:

Thanks for the comments.

By referring to relevant literature [1] and some information on the Internet, in Line 172, we have made the following modifications to pseudocode. Because formatting errors occur when this table is inserted directly into this article. So we turn the form to TIF format and insert it.

Table 1. Pseudo-code for the stroke generation algorithm

[1] Zhang, J.; Wang, Y.; Zhao, W. An improved hybrid method for enhanced road feature selection in map generalization [J]. International Journal of Geo-Information, 2017, 6(7), 196-217.

Thank you very much for your comments and valuable suggestions

Point 5: Fig. 4 If the flowchart contains the END symbol, it must contain also START symbol (according to flowchart symbology - use for both oval). Command i=i+1 in branches put to the rectangle.

Response 5:

Thanks for the comments.

I've added a START symbol and a rectangle for i=i+1 in Fig.4.

Thank you very much for your comments and valuable suggestions.

Point 6: Tab. 3 The last equation is divided into two rows.

Response 6:

Thanks for the comments.

I am very sorry for the trouble caused by my carelessness. I have modified Equation 3.

Thank you very much for your comments and valuable suggestions.

Point 7: Page 12. There is mentioned that the merge operation was based only on the name of the streets. Did you use the category of a street (highway, class 1, class 2)?

Response 7:

Thanks for the comments.

Since the data we use comes from OSM, the downloaded roads contain multiple category. In this paper, we mainly use three categories: primary, secondary and tertiary.

In Line 319, we added a description of the categories of roads used.

“The rank of roads includes primary, secondary and tertiary. Data preprocessing is carried out for each road network, including merging of segments with the same name and rank, reconstructing topology and checking topology (removing isolated segments).”

Thank you very much for your comments and valuable suggestions.

Point 8: Page 7 - Explanation of Shannon entropy is more common, not only about map symbols (it is not correct explanation).

Response 8:

Thanks for the comments.

In Line 196, we have made some modifications to Shannon Entropy. Indeed, Shannon Entropy is not only about map symbols. It was Sukhov who first introduced information theory into cartography and used it to measure the diversity of map symbol types.

Our modifications are as follows:

“Shannon [18] introduced probability to study the measurement of information amount. He believed that information comes from the uncertainty of information, and proposed the concept of information entropy to represent the average information amount contained in information source [11]. Subsequently, Sukhov [19-20] first introduced information theory into cartography and used it to measure the diversity of map symbol types. But the information entropy theory is based on the probability of map symbols: if the probability of two map symbols is the same, their information volume will be the same.”

Thank you very much for your comments and valuable suggestions.

Author Response File: Author Response.pdf

Reviewer 3 Report

Please see attachment.

Comments for author File: Comments.pdf

Author Response

To Reviewer 3

Thank you very much for reviewing this article and thank you for your valuable comments and suggestions. We have made one-by-one revisions in the text based on your comments. The details of the changes are as follows.

Point 1: The idea of using the changes of information to determine the optimal angle is okay. In nature, the purpose of stroke generate is to create another topological representation of road network. To evaluate the new stroke-based representation, case study-based justification needs to be provided. That is, how is relationship between the structure of the new stroke with the human flow (pedestrian flow or traffic flow)? Can the new stroke can better predict human flow than the traditional ones? The comparison is essential to evaluate the effectiveness of this proposed methodology.

Response 1:

Thanks for the comments.

Originally proposed by Thomson and Richardson, stroke refers to the merging of segments according to certain criteria. In this paper, the method of constructing stroke is based on a geometric approach, and its principle is ‘Elements that appear to follow in the same direction tend to be grouped together’, which follows the ‘goodness of continuity’ theme in visual perception. In the construction of stroke, like many other scholars, this paper only focuses on the attributes of the road, but has not yet considered the external factors such as human flow and traffic flow.

However, human flow or traffic flow does have a certain impact on the construction of stroke. On the one hand, drivers prefer to drive on a straighter road, which is consistent with the idea of constructing stroke based on the deflection angle between segments. Therefore, the constructed stroke according to the method in this paper can predict the traffic flow to a certain extent. On the other hand, when a segment is connected with several segments and the connecting angle of all the connected segments is less than the angle threshold, the segment with the smallest deflection angle is selected for merging in this paper. At this time, if considering the traffic flow, the merged segment can be selected according to the traffic flow, which will make the research results more meaningful.

Road is closely related to people's life. In the future research, we will gradually take into account external factors, such as human flow and traffic flow.

Thank you very much for your comments and valuable suggestions.

Point 2: In Figure 9, the threshold degrees for three cities Monaco, Chicago and Moscow are around 37, 9 and 6. Empirically, the common sense of good continuity should be around 30 or 45 degree. If the angles among different roads are all around 10 degree, then we would say the road network is pretty much straight. We will not say the threshold degree for stroke will decrease to 10 degree. Instead, people may still think the degree will be around 30 or 45. In what sense the authors claim that the threshold degree of the stroke should change in different road networks? This concern may relate to the first question: how we may justify the changing degree?

Response 2:

Thanks for the comments.

In Fig. 9, the information volume of road networks in Monaco, Chicago and Moscow changed abruptly when the thresholds were about 37, 9 and 6, respectively. This is mainly because under this threshold, a large number of segments in the road network begin to merge, resulting in a changing number of strokes and their connections and sharp decrease in the amount of information. At this time, the corresponding threshold is not the optimal angle threshold of this road network for stroke construction. Only when the amount of road network information tends to be stable within a certain threshold range, the corresponding threshold range is the optimal threshold range of this road network for stroke construction. To avoid the subjectivity of visual method, we use the Douglas-Peucker algorithm to simplify the information change curve, so as to determine the optimum threshold range for stroke construction. And the optimal threshold ranges of three road networks are 54°-63° (Chicago), 61°-63° (Moscow), 45°-48°(Monaco). From the experimental results, it can be seen that the optimum angle threshold range for road construction in Moscow and Chicago are 61°-63° and 54°-63° respectively, which is consistent with the commonly used angle threshold (60°) for road construction, and verifies the rationality of this method. At the same time, in order to verify the effectiveness of the proposed algorithm, taking Monaco as an example, this paper conducts stroke selection experiments. The results demonstrate that our proposed algorithm has better connectivity and wider coverage than those based on a common angle threshold (60°).

Thank you very much for your comments and valuable suggestions.

Point 3: Another concern is the geographic scale in generating strokes of road network. When generating strokes of road network in a small town at a scale of 1:1000, and when generating strokes of a road network in a nation at a scale of 1:100,000, are there any difference in choosing threshold in addition to the information change?

Response 3:

Thanks for the comments.

Due to the limitation of data sources (our data comes from OSM), in this paper, we only consider the Geometric and Structural Properties of road network, and have not yet considered the impact of scale on stroke construction. In this paper, we determine the optimum threshold of different road networks according to the change of information. And for different scales of road network, the road network contains different levels of road details, resulting in different amounts of information. In theory, through the method of this paper, the optimum angle threshold range for stroke construction can also be calculated under different scales of the same area.

Thank you very much for your comments and valuable suggestions.

Point 4: The English presentation needs to be significantly improved, for example, in line 23: which calculated in this paper and the commonly used? A professional English service is necessary.

Response 4:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English. We have sent the paper to the professional English editing service for polishing.

In Line 20, we have modified this sentence.

“Finally, we apply this model to three different road networks, and the optimal threshold ranges are 54°-63° (Chicago), 61°-63° (Moscow), 45°-48°(Monaco). And taking Monaco as an example, this paper conducts stroke selection experiments. The results demonstrate that our proposed algorithm has better connectivity and wider coverage than those based on a common angle threshold (60°).”

Thank you very much for your comments and valuable suggestions.

Author Response File: Author Response.pdf

Reviewer 4 Report

My general impression is that the proposed method is very case/data dependent. I suggest adding more effort to somehow increase the viability of the proposed method on different data-sets.

some comments:

Please define "stroke", clearly.

How does your approach manage different types of intersections in experiments?

Page 4 line 129: whose "connection" angle

Page 4 line 114: Gestalt is a German word which means "shape" or "form"

Please define "FID" at the first use

English writing must be improved. There are many issues like line 149: "Add" is imperative but then you used "sorting" 

Page 7 Line 165-168: Please rewrite this sentences. It is not clear what do you mean by them.

Page 9 line 190: please define Vi more clearly. Is it same as Eq. 2?

Page 10 line 262: please rewrite this sentence: The existing algorithm of the simplifying curve has been very mature ....

Page 10 line 264: It is better to write "DP is a classic algorithm" not "is one of the most classical algorithms"

Equation 6 is not necessary. You can skip it.

Please describe D-P fixed point and D-P fixed distance, shortly (at page 10 line 268)

Please define w in eq. 5. How it is computed in your experiments?

Author Response

To Reviewer 4

Thank you very much for reviewing this article and thank you for your valuable comments and suggestions. We have made one-by-one revisions in the text based on your comments. The details of the changes are as follows.

Point 1: Please define "stroke", clearly.

Response 1:

Thanks for the comments.

In Line 44, we have added the following definition to ‘stroke’ at the first use.

“A feasible solution is to concatenate road segments into long lines based on some criteria. It is hoped that these concatenated lines are the original roads. The concatenated line is called a ‘stroke’ in geographical information science [3]. The term ‘stroke’ is prompted by the idea of a curvilinear segment that can be drawn in one smooth movement and without a dramatic change in style. The original idea of building road segments into strokes, proposed by Thomson and Richardson [3], was based on a geometric approach. The basic principle was very simple. ‘Elements that appear to follow in the same direction tend to be grouped together’, which follows the ‘goodness of continuity’ theme in visual perception. Specifically, their method does not rely directly on fragmented segments, but rather constructs a larger selection unit based on perceptual grouping—i.e., strokes—and selects a road according to the length of the stroke [3].”

Thank you very much for your comments and valuable suggestions.

Point 2: How does your approach manage different types of intersections in experiments?

Response 2:

Thanks for the comments.

In this paper, the main types of intersections are as follows:

(1) The intersection only connects two segments.

(2) The intersection connects three or more segments.

As shown in the following figure:

Figure 1. Diagram of different types of intersections

In the construction of stroke, this paper takes the road segment of the road network as the objective. The whole calculation process is as follows:

(1)    Add attribute FID (a randomly generated, continuous natural number) to road network data and sort in descending order. FID is then used to determine the base segment. The deflection angle for a given segment is only calculated when its FID is smaller than that of the base segment in order to avoid repeat calculation of connected segments.

(2)    Calculate each segment’s connectivity and judge the connected mode (only calculate the deflection angle of end-to-end connected modes). This method effectively avoids traversing the whole road network when calculating the deflection angle of each segment.

(3)    Obtain the list of connected segments and select the qualified segments to calculate the deflection angle.

(4)    Choose the minimum deflection angle. If the value is less than the angle threshold, generate a new stroke.

From the above steps, it can be seen that the method in this paper is applicable to all the types of intersections mentioned above, because this paper takes the road segment as the objective.

Thank you very much for your comments and valuable suggestions.

Point 3: Page 4 line 129: whose "connection" angle.

Response 3:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English. We have sent the paper to the professional English editing service for polishing.

This refers to a segment connected to the initial Segment 1. Its connected angle with Segment 1 is less than the angle threshold.

In Line 138, we added the following instructions:

“In self-fit, the researchers first identified the initial Segment 1. Then, the connected angles of all segments connected with Segment 1 are calculated. Finally, from these connected angles, a segment whose connected angle is less than the angle threshold is randomly selected for merging.”

Thank you very much for your comments and valuable suggestions.

Point 4: Page 4 line 114: Gestalt is a German word which means "shape" or "form".

Response 4:

Thanks for the comments.

In this paper, Gestalt is a theory that describes the overall characteristics. Thomson believes that this theory is also applicable in the field of roads. Therefore, scholars put forward the stroke based on this theory.

Thank you very much for your comments and valuable suggestions.

Point 5: Please define "FID" at the first use.

Response 5:

Thanks for the comments.

In Line 160, we have added the following definition to FID at the first use.

“Add attribute FID (a randomly generated, continuous natural number) to road network data and sort in descending order. FID is then used to determine the base segment.”

Thank you very much for your comments and valuable suggestions.

Point 6: English writing must be improved. There are many issues like line 149: "Add" is imperative but then you used "sorting".

Response 6:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English. We have sent the paper to the professional English editing service for polishing.

In Line 160, we have modified this sentence.

“Add attribute FID (a randomly generated, continuous natural number) to road network data and sort in descending order.”

Thank you very much for your comments and valuable suggestions.

Point 7: Page 7 Line 165-168: Please rewrite this sentences. It is not clear what do you mean by them.

Response 7:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English.

In Line 178, we have rewritten this sentence.

“As stated earlier, map information comes from the diversity of elements and their distribution characteristics. Similarly, road network information comes from the difference in strokes’ number, shape, and structure under different angle thresholds, an example of which is shown in Figure 5.”

Thank you very much for your comments and valuable suggestions.

Point 8: Page 9 line 190: please define Vi more clearly. Is it same as Eq. 2?

Response 8:

Thanks for the comments.

Vi in Eq.1 is different from Eq.2.

We have made the following changes:

In Line 209, we added the following definition of Vi in Eq.1:

“where  is the measurement index expressing the stroke’s geometric and structural characteristics, such as the length and connectivity of the stroke.”

In Line 256, to avoid confusion, we have modified the variables in Eq. 2 as follows:

“                                         (2)

                                       (3)

where  is the weight of indicator i,  is the coefficient of variation of indicator i, is the standard deviation of indicator i, and  is the average of indicator i.”

Thank you very much for your comments and valuable suggestions.

Point 9: Page 10 line 262: please rewrite this sentence: The existing algorithm of the simplifying curve has been very mature.

Response 9:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English.

In Line 276, we have modified this sentence.

“There currently exist several algorithms for simplifying curves, including the interval point method [26], angle limit method [27], vertical distance limit method [28], and Douglas-Peucker method [29].”

Thank you very much for your comments and valuable suggestions.

Point 10: Page 10 line 264: It is better to write "DP is a classic algorithm" not "is one of the most classical algorithms".

Response 10:

Thanks for the comments.

I am very sorry for the trouble caused by my poor English.

In Line 278, according to your suggestion, we have modified this sentence.

“In this study we rely on the latter; the Douglas-Peucker (D-P) algorithm is a classic strategy for simplifying line elements in cartography that can maintain the shape of line elements very well [30].”

Thank you very much for your comments and valuable suggestions.

Point 11: Equation 6 is not necessary. You can skip it.

Response 11:

Thanks for the comments.

We have skipped equation 6.

Thank you very much for your comments and valuable suggestions.

Point 12: Please describe D-P fixed point and D-P fixed distance, shortly (at page 10 line 268).

Response 12:

Thanks for the comments.

In Line 281, we have added a brief description to the D-P fixed-distance and the D-P fixed-point algorithm as follows:

“D-P fixed distance algorithm needs to set a distance threshold, which is used as the basis of whether to retain the current point or not. Similarly, D-P fixed point algorithm needs to determine the number of retained points in advance, and then determine which points will be retained according to the distance from the points to the line.”

Thank you very much for your comments and valuable suggestions.

Point 13: Please define w in eq. 5. How it is computed in your experiments?

Response 13:

Thanks for the comments.

w is the weight of the measurement index. Where w_i is the weight corresponding to the ith indicator. The value of w is calculated by equation 2(Line 256) and equation 3(Line 257).

Thank you very much for your comments and valuable suggestions.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

If there is not obvious correlation coefficient between the newly designed stroke and traffic flow, what's the purpose to design the new stroke? If you read the paper "Self-organized natural roads for predicting traffic flow: a sensitivity study", as a new topological relationship of road network, the stroke is expected to better predict traffic or pedestrian flow, instead of being able to "predict traffic flow to some extent". If the new stroke in this paper cannot better predict traffic flow than previous work, how do the author judge the advantages of this work?

Author Response

To Reviewer 3

Thank you very much for reviewing this article and thank you for your valuable comments and suggestions. We have read the paper "Self-organized natural roads for predicting traffic flow: a sensitivity study". This paper has a great inspiration for our future research. Thank you again for your advice. And we have responded and revised one by one according to your comments. The details are as follows.

Point 1: If there is not obvious correlation coefficient between the newly designed stroke and traffic flow, what's the purpose to design the new stroke? If you read the paper "Self-organized natural roads for predicting traffic flow: a sensitivity study", as a new topological relationship of road network, the stroke is expected to better predict traffic or pedestrian flow, instead of being able to "predict traffic flow to some extent". If the new stroke in this paper cannot better predict traffic flow than previous work, how do the author judge the advantages of this work?

Response 1:

Thanks for your valuable comments.

At present, in the study of road network, the original segments of road network are usually merged into strokes for the analysis and application of road network. However, in these studies, scholars mainly study the application of road network data (such as road selection, traffic flow analysis), ignoring the process of stroke construction (for different road networks, scholars use a common threshold for stroke construction). As we all know, a reasonable and effective data processing is the basis and key of data use, which will directly affect the results of data analysis. Therefore, a reasonable stroke construction process has an important impact on the analysis and use of road network data. In the process of stroke construction, the selection of angle threshold is the first problem to be considered. Because of the different road network structure, the optimal angle thresholds for constructing stroke are different. The purpose of this paper is to determine the optimal angle threshold for different road networks in stroke construction.

A reasonable method for constructing stroke can better serve the analysis and application of road network data, such as road selection and traffic flow analysis. In order to verify the effectiveness of this method, we design a set of comparative experiments in Chapter 3.2. Because of the privacy of traffic flow data and the difficulty of obtaining it, the comparative experiment designed in this paper is road selection. We take Monaco's road network as an example, generating strokes using both the thresholds calculated in this paper and commonly used(60°) in other studies. Then the same proportion of roads in the two road networks is selected. Our results demonstrate that our proposed algorithm has better connectivity and wider coverage than those based on a commonly used angle threshold.

Compared with other stroke construction algorithms, the proposed algorithm has strong applicability and can be applied to different structures of road networks. And when determining the threshold of deflection angle, some scholars choose visual method or enlarging the threshold interval (5°) to determine the optimal angle threshold [1-2], which lacks certain objectivity and accuracy. The threshold interval chosen in this experiment is 1°, which guarantees the accuracy of the experimental results to a certain extent. At the same time, we introduce Douglas algorithm to simplify the curve, and find the optimal angle threshold range for constructing stroke in different road networks. This ensures the objectivity of the experimental results. In the literature [1], the author sets the angle threshold at 45° to construct the stroke of Sweden's National Highway Network (Road Network I) and Gävle urban street network (Road Network II). And according to the results of stroke construction, the relationship between stroke and traffic flow is studied. However, from the experimental results, it can be seen that the critical points of the relationship between road network I, network II and traffic flow occur at 15° and 30°, respectively. If the author can take into account the differences between the two networks and then select different angle thresholds to construct stroke, the experimental results may be more satisfactory.

Therefore, considering the road network structure characteristics, the stroke construction method has certain research significance for the application of road network data. In the future research, we will continue to analyze the impact of traffic flow and people flow on stroke construction.

[1] Jiang B , Zhao S , Yin J . Self-organized natural roads for predicting traffic flow: a sensitivity study[J]. Journal of Statistical Mechanics: Theory and Experiment, 2008, 2008(07):1-23.

[2] Xun W. Stroke selection based on geometric and structural properties of roads [D]. Southwest Jiaotong University: Chengdu, China, 2017.

Thanks again for your careful work and valuable suggestions.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments are considered and questions are answered.

Author Response

Thanks for your careful work.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.