A Lossless Watermarking Algorithm Based on Line Pairs for Vector Data

With the increasing demand for copyright protection of high-precision and sensitive vector data in Geographical Information System (GIS), research on lossless watermarking has attracted more and more attention. In this paper, a new lossless watermarking method based on line pairs is proposed. Firstly, the points and polygons are unified into the polylines, and then every two adjacent polylines are combined into a line pair. Besides, the storage direction and the interior angle of the line pairs are analyzed. Secondly, the watermark bit is determined by the interior angle of each line pair. Then, the watermark information is embedded by judging whether the storage direction of each line pair and the watermark bit is the same. Finally, experimental results verify that the proposed method works effectively for the data of the points, polylines and polygons, and has good invisibility without damaging the vector data. In addition, compared with the existing algorithm, the proposed method achieves higher robustness against geometric attacks, such as translating, rotating, and scaling the vector data.


I. INTRODUCTION
With the increasingly widespread use of vector data for applications such as smart city, urban planning, navigation, and other industries, the copyright protection of vector data in GIS has become increasingly urgent. The watermarking is considered as an efficient technique to protect copyright and ownership of vector data [1]. As we know, the traditional watermarking techniques embed the watermarking information in the host data by modifying the coordinate values in the space domain [2]- [6] or the frequency domain [7]- [10]. However, these watermarking techniques may cause some damages to the sensitive information presented in the cover-vector data. Additionally, it is clear that even minor changes in the original vector data are also unacceptable for vector data used in surveying, mapping and military fields, which require extremely high data precision [11]- [13]. In such cases, the lossless watermarking instead of traditional watermarking is in urgent need, because The associate editor coordinating the review of this manuscript and approving it for publication was Kuo-Hui Yeh . the lossless watermarking can realize the copyright protection without causing damage to the vector data [14]. However, it is an important issue for the lossless watermarking to achieve the robustness of the watermark algorithm while ensuring that the data undamaged simultaneously. Therefore, it has become a research hotspot in the field of copyright protection research for high-precision vector data.
The existing research of lossless watermarking technology for vector data can be mainly divided into three types. The first one is the reversible watermarking that protects the copyright by embedding watermark information in the original data, and also can recover the original data from the watermarked data by extraction [15]- [17]. Unfortunately, the reversible watermarking technique has an evident defect that the watermarking can be used only once because the reversible watermark information has to be removed after extraction [18]- [20]. Therefore, the method does not satisfy the requirement of permanent watermarking for users. Besides, to fulfill the requirements of the reversibility and watermark embedding, most reversible watermarking needs more storage space by means of destroying the precisions of VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ original data [21], [22]. Thus, it is not real lossless to some degree from this perspective. The second lossless watermarking technology is the zero watermarking [23] that generates a watermark from the characteristics of vector data without any modification on the host vector data. The generated watermark will be stored in an IPR (Intellectual Property Right) repository to facilitate future watermark detection [24]. The key of the method is to extract stable features of the host vector data, which is helpful to resist several attacks. There are two methods to extract the features, which are based on statistical features and geometric features, respectively [25]- [27]. For example, in literature [28], the map was divided into rings by using concentric circles. Then, the number of vertices in each ring is counted, which is utilized as the information of the statistical feature. The information of the feature is further combined with a watermark to generate the zero watermark. Compared with reversible watermarking, zero watermarking achieves completely lossless. However, it constructs watermark but not embed watermark, so there is a risk of misjudgment when extracting and claiming the copyright. For example, everyone can build a watermark from one data and register to an IPR agency that they trust. It should also be pointed out that such a method stores the watermark information in a third-party copyright agency, which has many restrictions in practical applications.
The third one is storage feature-based watermarking. Recently, one lossless watermarking technique based on storage feature has been found in the literature [29]. This method embeds the watermark information by modifying the storage order of the polyline data without modifying the coordinate values, thus avoids the defect of the reversible watermarking in copyright protection only once and the limitation of the zero watermarking in reliance on third-party agencies. With this method, the storage direction of the polyline is quantized by 0 and 1 according to the storage feature of the polyline. To embed the watermark information, it is judged whether the embedded watermark information is consistent with the quantization value of the storage direction. If they are the same, the storage order of the polyline remains unchanged. Otherwise, the storage order of polyline is reversed. Compared with zero watermarking, this method indeed embeds the watermark into the data without the participation of any IPR agency. However, this method is only useful to achieve the lossless watermarking of polyline features but it is not suitable for embedding the watermark into point features and polygon features.
As aforementioned, the reversible watermarking method can remove the watermark and recover the data by extraction. But it can only realize the copyright protection of the vector data only once. Besides, some algorithms of the reversible watermarking method still have some damages to the vector data. Although the zero watermarking method does not cause any damage to the vector data, its implementation relies on third-party copyright agencies, which is not conducive to practical applications. The storage feature-based lossless watermarking method can not only guarantee data accuracy but also has good robustness and practicability. However, it can only be applied to polyline vector data and cannot be used for point and polygon data.
Motivated by the storage feature-based method mentioned above, a novel lossless watermarking method is proposed in this paper, which introduces the concept of the line pair. Point features, polyline features, and polygon features are finally abstracted as line pairs, and the line pair is used as the minimum operation unit for watermark embedding and extraction. Thus, the proposed method can be applicable for the data of points and polygons in addition to the vector data of polylines.
The key is to transform and represent points and polygons in forms of polylines, and select the most representative features of polylines for watermark embedding. Therefore, the procedure of the proposed method in this paper includes two steps: The first one is to unify points and polygons into the form of polylines. Then, the characteristics of polylines are then extracted to realize lossless watermarking embedding.
The rest of the paper is organized as follows. First, Section 2 presents the storage features of the vector data which is the basis of the proposed algorithm. Then, the details of the proposed algorithm, including the embedding and the extraction processes, are described and analyzed in Section 3. Experimental setup is given in Section 4. Experimental results are provided in Sections 5. Finally, discussions and conclusions are drawn in Section 6 and Section 7.

II. THE STORAGE FEATURES OF THE VECTOR DATA
As aforementioned, only the polylines can be embedded the lossless watermarking in Zhou's scheme [29], which limits the practical use of this method. To enable the storage feature-based method for more practical use, this paper proposes a novel watermarking method with three contribution work: (1) Unify the points and polygons into the forms of polylines. (2) Extract and determine special features of all two adjacent polylines, which are called the line pairs, for lossless watermarking embedding. (3) Design the lossless watermarking embedding with the extracted features of polyline data.  There are a series of discrete points in vector point data, each point has a vertex and other property information. For the convenience of description, we assume that points are the same as vertices denoted by, V = v 1 , v 2 , v 3 , . . . , v i , . . . , v np , np means the number of points. v i denotes the i-th number of the vertex v i = (x i , y i ), x means the coordinate of the x-axis, and y refers to the coordinate of the y-axis, respectively.
The process of unifying points into polylines is that two adjacent points are connected into a line segment by means of which the unified polylines are obtained. Figure 2(a) shows the original points, and Figure 2(b) the polylines composed of every two adjacent points. As shown in Figure 2(a) and Figure 2(b), we can get a total of four polylines, denoted here as For example, as for a polyline l 1 , coordinates of two endpoints are v 1 (x 1 , y 1 ) and v 2 (x 2 , y 2 ). Therefore, the polyline unified by the point can be expressed as, . The amount of polylines is np 2 , and the operation of means rounding down.

2) UNIFY POLYGON TO POLYLINE
The process of unifying polygons into polylines is to treat each polygon as a point and then unify the two points as a polyline using the method of 2.1.1. The basic process is shown in Figure 3. According to this basic process, a concrete example is given in Figure 4. Figure 4(a) shows the original polygons, and Figure 4(b) shows the polyline composed of two adjacent polygons.
As shown in Figure 4(a) and Figure 4(b), according to the definition in the previous section, we can get a new polyline l 1 = (v 1 , v 2 ), where P 1 and P 2 are the centers of gravity of be calculated by formulas (1) and (2).
Then, the polyline unified by the points can be expressed as l (m+1) / 2 = (P m , P m+1 ), m ∈ 1, n pg − 1 , n pg is the number of polygons and the number of unified lines is n pg 2 .

B. FEATURES OF LINE PAIR
Before introducing algorithms in detail, we make the following definitions and related features.

1) THE CONCEPT OF LINE PAIR
This is defined as combining two adjacent polylines into a line pair. In other words, a line pair is a combination of two adjacent polylines.
A set of line pairs are denoted by PairL = {(l 1 , l 2 ) , (l 3 , l 4 ) , . . . , (l N −1 , l N )}, N means the number of the polylines, so one single line pair is denoted by PairL (q+1) / 2 = l q , l q+1 , q is odd and q ∈ [1, N − 1]. As we can see, a line pair consists of two polylines and N polylines can form N 2 line pairs. Besides, the line pairs will be used as the minimum operation unit for embedding and extracting watermark information.

2) STORAGE DIRECTION OF A LINE PAIR
Firstly, we introduce the length calculation method of a polyline, which still uses the method introduced in Zhou's paper, which will not be described here. In this paper, we use Len to indicate the length of polyline.
Then, we define that if the length of the pre-sequence polyline in storage is larger than the length of another, the storage direction of a line pair is 1. Otherwise, the storage direction is 0. It can be calculated by formula (3).
From the definition and the formula, we can see that the storage direction of a line pair is only related to the length of two adjacent polylines. We know that the length of two adjacent polylines will not be changed when translating or rotating the vector data. Therefore, the storage direction of a line pair will be kept after translating or rotating the data. In addition, after the data is scaled, the scale ratio of two adjacent polylines is the same and the size relationship between the two adjacent polylines will not be changed, that is, the storage direction of a line pairs after scaling will not be changed. Therefore, in this paper, we have decided to use the storage direction of the line pair to embed the watermark information because the storage direction of a line pair has a geometrically invariant feature of translation, rotation and scaling.

3) THE INTERIOR ANGLE OF A LINE PAIR
A line pair has two polylines and the interior angle of a line pair is the angle of two mathematical vectors that can be formed by taking the first and last points of its two polylines, respectively. Figure 5 is an example of showing an interior angle of a line pair, and the interior angle is denoted by θ, θ ∈ [−π, π]. As shown in Figure 5, the interior angle of a line pair (l 1 , l 2 ) is θ, which is the angle between vectors Vector (l 1 ) and Vector (l 2 ). According to the formula of the angle based on two vectors, we can get the interior angle of each line pair by formula (4).
As seen from the above definition and formula, the interior angle of each line pair will not be changed after the vector data is translated, rotated or scaled. Therefore, it is well-known that the interior angle of each line pair is tolerant to geometric transformation, e.g., translation, rotation, scale, etc. This feature of the interior angle is useful for calculating the bit of the watermark information, which can ensure the synchronization relationship of watermark information after the geometric transformation.

4) REVERSE A LINE PAIR
Reversing a line pair means changing its storage order, namely swapping the storage position of its two polylines, which can be expressed by formula (5).
Rev PairL l q , l q+1 = PairL l q+1 , l q (5) As seen from the formula (5), the coordinate values and the topological relationship of the vector data will not be changed after reversing a line pair.

III. PROPOSED WATERMARKING ALGORITHM
This section may be divided by subheadings. It should provide a concise and precise description of the experimental results, their interpretation, as well as the experimental conclusions that can be drawn.

A. BASIC IDEA
According to the analysis of Section 2, all storage features can be abstracted into a line pair. Therefore, the lossless watermarking algorithm will be described based on a line pair that is the minimum operation unit. There are two key points, the first one is the fact that the bit of watermark information is determined by the interior angle of a line pair and the second one is that the watermark information is embedded in the storage direction of a line pair.
The proposed method mainly includes the watermark embedding process and the watermark extraction process.

B. WATERMARKING EMBEDDING
The proposed embedding process is illustrated in Figure 6. The process of the watermarking embedding can be described as follows: Step 1: Generate the watermark information The generation of the watermark information is used similar to Zhou's method, so the watermark information W is W = {w i |i = 1, 2, ...L w }, w i = {0, 1}, L w is the length of watermark.
Step 2: Unify the data into the polyline Read the vector data and judge the data type first. Then, unify the point into a polyline according to the method in 2.1.1, and finally, unify the polygon into a polyline according to the method in 2.1.2. Step 3: Combine two adjacent polylines into a line pair PairL (q+1) / 2 = l q , l q+1 , and calculate the storage direction of each line pair by formula (3) and get dir (q+1) / 2 .
Step 4: Calculate the interior angle of each line pair Calculate interior angle of each line pair by formula (4) and get θ (q+1) / 2 .
Step 5: Calculate the watermark bit of each line pair Calculate the watermark bit Index by formula (6).
where, rand( ) is a random function that can obtain random numbers with a range of values (0, 1). Then, the watermark embedded for each line pair is w Index (q+1)/2 .
Step 6: Embed the watermark for each line pair For each pair, embed the watermark according to formula (7), As we can see, if the storage direction of each line pair is the same as the watermark information, the storage order of a line pair can be kept. Otherwise, the storage order of a line pair should be reversed by formula (5).
Step 7: Get the watermarked vector data After embedding the watermark in all the line pairs, the watermarked vector data is obtained.

C. WATERMARKING EXTRACTION
Watermarking extraction is the reverse process of watermarking embedding. Since the extraction is performed without a knowledge of the original data, the proposed scheme is a blind one. The overall flowchart of the watermark extraction processes is shown in Figure 7. The watermarking extraction process can be described as follows.
Step 4: Detect the watermark information according to the storage direction of each line pair by formula (8), Step 5: Extract the copyright information We use the normalized correlation (NC) to extract the copyright information by formula (9), where the range of NC is [0,1]. If NC is larger than a given threshold value, the copyright is the extraction result, and the closer NC is toward 1, the greater the confidence of the extracted result is; otherwise, copyright extraction failed.

IV. EXPERIMENTAL SETUP
This section is devoted to set up the experiments for the analysis of the results of the proposed lossless watermarking scheme. We use ESRI shapefile type of vector data, which is a core vector storage format for storing geometry location and associated attribute information. Three main types of vector VOLUME 8, 2020 data are chosen as test data, i.e., point, polyline and polygon. As shown in Figure 8, they represent transport, waterway and land use from three different areas, respectively, and Table 1 lists the basic information of original data. The data after unifying are shown in Figure 9, where Figure 9(a) is the transport after unifying and Figure 9(b) is the land use after unifying. The simulations that are applied here are coded in MAT-LAB and executed on a PC with Core 2 Duo processor, 8GB RAM and Windows 7.
A meaningless binary watermark of size 100 is given to verify the copyright of ''GEOMARK COPYRIGHT''. NC is calculated between original watermark information and extracted one to determine whether a watermark can be extracted successfully. The threshold of NC is an empirical value. Due to the proposed method is compared with Zhou's algorithm in robustness, so the threshold of NC is set the same For more precision showing the invisibility of watermark, we employ the change rate of coordinate value r c , which is used to evaluate whether the coordinates of vector data have been changed [29].

V. EXPERIMENTAL RESULTS AND DISCUSSION
In order to evaluate the performance of the proposed method, we also compare its performance with Zhou's method using the same data in this section.

A. IMPERCEPTIBILITY
An imperceptibility test is performed to check whether there are some changes compared to the host data after embedding the watermark. In addition, NC is calculated between original watermark information and extracted watermark information. Figure 10 shows the results of the proposed method when testing on the vector data. Results include the watermarked data, which is overlapping with the original data, with the NC value. Besides, the corresponding part is enlarged. The color of the original data is blue and the color of the watermarked data is yellow. For better visualization, the symbols of the original and watermarked transport data are shown with circle and cross, respectively. The width of the original waterway data is slightly larger than that of the watermarked data. The outline of the original land use is colored with blue, and the fill color is none. The outline of the corresponding watermarked data is colored with none, and the fill color is yellow.  From Figure 10, we note that the NC values are 1, and we cannot find any difference between the original data and the watermarked data by naked eyes.
It can be seen from Table 2 that the proposed scheme has not changed any coordinate value after embedding watermark information, which is a good testimony to the excellent invisibility of the proposed scheme.

B. TRANSLATION ATTACKS
Translation attacks involve moving the whole vector data with a specific distance in a specific direction. In this test, we translate the x and y coordinates of the watermarked data at the same time. The comparisons of results of translation attacks between the proposed method and that of Zhou's algorithm are shown in Figure 11.
The experimental results from Figure 11 show that the NC values are always 1, regardless of the translating ratio. It is because the interior angles and the storage directions of a line pair do not be changed when translating the vertices of the data. Furthermore, it can also be seen that the proposed algorithm has a good level of performance in terms of translation attacks, which is the same as that of Zhou's algorithm.

C. ROTATING ATTACKS
Rotation attacks mean that some specific angles are used to turn the vector map around its center. In this test, the watermarked data is rotated around the center from 15 • to 360 • . The results of rotating attacks compared with the method proposed here and that of Zhou's algorithm are shown in Table 3. For easier understanding these results are also shown with the help of graph in Figure 12. The graphs of the three data at 60 degrees and 120 degrees of rotation are shown in Figure 13. As shown in Figure 12 and Table 3, the NC values of the proposed method are always 1 regardless of the angle of rotation. This is because the interior angle and the storage direction of a line pair do not be changed when rotating the data. However, Zhou's algorithm cannot detect the watermark information when a rotating range is between 90 • and 270 • . Furthermore, the NC values are 0 in most cases. Based on the results, it can be seen that our method has excellent anti-rotation ability.

D. SCALING ATTACKS
Scaling attacks refer to the use of a specific value, in both axes, to alter the size of the vector data. When the data is scaled by a certain factor from 0.1 to 10 times the size of data, the results are as shown in Table 4.In order to see the experimental results more intuitively, a comparison with the proposed method and that of Zhou's algorithms with a line chart, as shown in Figure 13.
As seen from Table 4 and Figure 13, the NC value of the proposed method remains 1 whatever the scaling factor changes. However, it cannot resist scaling attacks in Zhou's method. It needs to be pointed out that the scaling operation has no effect on the interior angle and storage direction of a line pair in this scheme. Therefore, the embedded watermarks are not disturbed, and the scheme has a satisfactory performance in resisting scaling attacks.

E. ADDING ATTACKS
Adding attacks often happen when the data is updated. We carried out some experiments to verify whether our algorithm can effectively resist adding attacks. In this experiment, we add approximately from 10% to 200% features into the selected data. The comparison of experimental results is shown in Table 5. The graphs of the three data at the adding ratio of 30% and 60% are shown in Figure 14.
From Table 5, we can see that the proposed algorithm's robustness is lower than that of Zhou's when the adding ratio is up to 110%. It is because the proposed algorithm embeds one bit in a line pair which consists of two polylines, and Zhou's algorithm embeds one bit in one polyline. In theory, a conclusion can be drawn that the watermark capacity of the proposed algorithm is half of that of Zhou's. In addition, it is not difficult to deduce that as the number of adding features increases, the NC values become less than 1, but still more than the threshold. Therefore, the proposed method and Zhou's algorithms can all resist adding attacks. More specifically, the results also demonstrate that the proposed scheme has strong robustness to adding attacks.

F. CROPPING ATTACKS
Cropping attacks refer to the removal of some features from the vector data. It has been reported as one of the most important attacks that need resist. The minimum cropping count is 10% of the number of the features of the data and then gradually increases the cropping ratio in the step of 10%. The results are as shown in Table 6. The graphs of the three data at the cropping ratio of 30% and 60% are shown in Figure 15.  It can be seen from Table 6 that, as the number of deleting features increases, some NC values become less than 1, but all still more than the threshold and even 90% of features are deleted. Thus, the proposed method and Zhou's algorithms all can resist cropping attacks. Moreover, we can see that the NC value between the proposed algorithm and that of Zhou's algorithm is the same when the deletion ratio is less than 60%, and the NC values of the proposed algorithm are lower than that of Zhou's after the deleting ratio is up to 60% and above. However, when the deletion rate is as high as 90%, the NC value of the proposed algorithm is still higher than the threshold. Therefore, it can be seen that the algorithm is slightly worse than Zhou's algorithm in anti-delete attacks, but still has good robustness in anti-cropping.

VI. DISCUSSIONS
The results above have verified that the proposed method achieves the robust and lossless watermarking for vector data. For better understanding, this section will compare the performance among different lossless watermarking methods after discussing characteristics of the proposed method.

A. DISCUSSION OF CHARACTERISTICS FOR PROPOSED METHOD
(1) One of the important characteristics of the proposed method is that it offers the ability to unify the vector data in points and polygons into the forms of polylines. Therefore, it can use the features of the polylines to achieve lossless watermarking for three forms of vector data.
(2) The second characteristic of the method is that the concept of a line pair is proposed for the first time, and the features of a line pair are analyzed accordingly. Based on the features of the storage direction and the interior angle of a line pair, the watermark is embedded without changing any coordinates. Additionally, the robustness of watermarking is improved since these two features of the line pairs are invariant to the translation, rotation and scaling of vector data. However, in terms of random vertex deletion attacks, the proposed method is still insufficient. This is because deleting vertices randomly may affect the calculation of the interior angle and the storage direction of the line pair, thereby destroying the watermark. A more reasonable solution is to distribute the watermark evenly in the data as much as possible to reduce the loss of the watermark. This is the focus of our future research work.
(3) The watermarking capacity is the maximum amount of information embedded in the host vector data. The watermarking capacity of the proposed method depends on the number of line pairs for vector data. The number of line pairs is larger, and the watermarking capacity is larger. On the contrary, the watermarking capacity is smaller. The number of line pairs is a quarter of the number of polygon features. Therefore, 400 polygon features are needed for embedding of watermarking information at least, whose length is 100 in experiments of this paper. There are still some issues left for improving the watermarking capacity of the proposed method. For example, are there any strategies to embed multiple watermarking information in one single line pair of vector data? If yes, how to embed multiple watermarking information in a line pair? How to development of novel algorithms to improve the watermarking capacity with some emerging techniques, e.g., Quick Response Code. These questions are worthy of further exploration, because they are the key issue to be solved when the proposed method is applied.

B. COMPARISON AGAINST OTHER METHODS
As mentioned in Section I, the existing lossless watermarking for vector data can be mainly divided into three types: reversible watermarking, zero watermarking and storage feature-based watermarking. Therefore, the following discussion will focus on these three types.

1) COMPARED WITH REVERSIBLE WATERMARKING
Take the reversible watermarking algorithm [21] as an example. It embeds the watermark in the angles at the polar system and eliminates the changes of number length by the conversion of decimal and hexadecimal numbers. Apply this algorithm to the data waterway, and evaluate the results through qualitative and quantitative methods. Figure 16(a) shows that the blue recovered data overlays the red original data, where Figure 16(b) is the partially enlarged view. Table 7 shows the change rate of coordinate values.
As can be seen from Figure 16(a), the recovered data and original data seem to overlap each other. But as Figure 16(b) shows, there is an obvious deviation between the blue recovered data and the red original data. Besides, Table 7 shows the r c of the paper [21] is 2.27%, and that of the proposed  method is 0. It shows the reversible watermarking loses some information of the original data during the watermark embedding process, but the proposed method is lossless indeed. Besides, after the watermark extraction, there is no longer watermark in the data for revisable watermarking, which means its watermark is not permanent.
In words, the proposed method in this paper can present copyright protection without deteriorating accuracy of vector data, while reversible watermarking techniques achieve the copyright protection only once and have an effect on the accuracy of the data.

2) COMPARED WITH ZERO WATERMARKING
Take the literature [27] as an example. The zero watermarking algorithm described in this method takes each polyline as the operation unit. It uses the feature vertex distance ratio (FVDR) of each polyline to realize watermark bit mapping and employs a certain position value of FVDR to generate watermark bits. Apply this method to the data waterway, where the preset watermark length is 32. Three users, A, B, and C, respectively, used the method and registered their corresponding copyrights in IPR 1, IPR 2, and IPR 3, as shown in Table 8.  Table 8 shows that the constructed watermark generated by different users using the same algorithm for the same data is exactly the same. However, they can register different copyrights in different IPR institutions. Therefore, once a data copyright dispute occurs, different users may extract different copyright information for the same data, making it difficult to determine the copyright owner of the data. This also shows that zero watermarking employing the third-party IPR agency has certain defects.
In conclusion, compared with zero watermarking, the proposed method makes full use of the data's own characteristics without the third-party IPR agency and is more practical.

3) COMPARED WITH STORAGE FEATURE-BASED WATERMARKING
As shown in Figure 9, the proposed method can achieve lossless watermarking embedding of geography data in forms of points, polygons and polylines, while the conventional storage feature-based methods can only handle the data in polylines. Besides, the storage direction and the interior angle of a line pair used in this proposed method are invariant in translation, rotation, and scaling of data, and thus offers more robustness than conventional methods (Figure 11 and Figure 12). It should be mentioned that the proposed method suffers from slightly less robustness in addition and deletion compared to conventional storage feature-based methods, as shown in Table 5 and Table 6. But the proposed method can still extract the watermarking information accurately because the NC value is above the defined threshold under the high-intensity addition and deletion of data in experiments.

VII. CONCLUSION
Lossless watermark is a powerful tool to protect the copyright protection of high-precision vector data. However, the conventional storage feature-based lossless watermarking method can only ensure the lossless embedding of watermarks for the vector data in polylines, and are not effective for other types of data. To solve this issue, a novel lossless watermarking method based on line pairs is proposed in this paper, where the data in points and polygons are unified into the form of polylines, and then two adjacent polylines are merged into a line pair. Based on the features of storage direction and interior angle of a line pair, the watermark bit and embedding rule of lossless watermarking are realized in the proposed method. The experimental results have verified that the proposed method can complete lossless watermarking for various types of vector data including points, polylines and polygons. In addition, we prove the better robustness of the proposed method than the storage feature-based method. This research also demonstrates the lossless and robustness of the feature-based method in embedding lossless watermarking and achieves a better performance than traditional storage feature-based methods. Moreover, it is noted that the watermark capacity of the proposed method depends on the number of line pairs, which has distinct effects on watermarking capacity of polygons. How to improve the watermark capacity is planned for our future work.
NA REN received the B.S. and M.S. degrees from Shaanxi Normal University, in 2004 and 2008, respectively, and the Ph.D. degree from Nanjing Normal University, in 2011. She is currently an Associate Professor with the School of Geography, Nanjing Normal University. Her research interests include digital watermarking, data security, and GIS.
QIFEI ZHOU received the B.S. degree in geographic information system from Nanjing Normal University, in 2015, where he is currently pursuing the Ph.D. degree in cartography and geographic information system with the School of Geography. His research interests include digital watermarking and transparent encryption.
CHANGQING ZHU received the B.S. degree in mathematics from the Zhengzhou Institute of Surveying and Mapping, in 1982, the M.S. degree in mathematics from Zhengzhou University, in 1990, and the Ph.D. degree in cartography from the Zhengzhou Institute of Surveying and Mapping, in 1997. He was a Professor with the Zhengzhou Institute of Surveying and Mapping. He is currently a Professor with the School of Geography, Nanjing Normal University. His research interests include digital watermarking, data security, and GIS.
A-XING ZHU received the Ph.D. degree from the University of Toronto, in 1994. He is currently a Professor with the School of Geography, Nanjing Normal University, and a Professor with the Department of Geography, University of Wisconsin-Madison. His research interests include GIS/RS techniques, artificial intelligence, fuzzy logic, and intelligent geo-computing.
WEITONG CHEN received the B.S. degree in geography and the M.S. degree in marine geography from Nanjing Normal University, in 2014 and 2017, respectively. He is currently pursuing the Ph.D. degree in cartography and geography information system with the School of Geography, Nanjing Normal University. His research interests include digital watermarking, geo-data security, and GIS. VOLUME 8, 2020