[2-01]Jungyeop Kim, Robust Vector Digital Watermarking Using Angles and a Random Table

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Advances in Information Sciences and Service SciencesVolume 2, Number 4, December 2010

Robust Vector Digital Watermarking Using Angles and a Random Table

Jungyeop Kim1,Department of Computer Science, Universit of Missouri, Columbia, USA, [email protected]

doi:10.4156/aiss.vol2. issue4.9

AbstractIn this paper I propose a new digital watermarking method using angles. Angles like distance are

not changed easily in vector data. Because of this, the proposed method is robust to scaling. Inprevious methods there are distortion and topology change. However, this proposed method doesnt

have distortion and topology change because I used intersection test. Therefore, the proposed methodcould be used in various fields to protect the copyright of vector map.

Keywords: Digital Watermarking, Vector Map Data, GIS, Angles, A Random Table

1. Introduction

The Internet and web growth is proceeding very rapidly and many digital contents are distributed byInternet. Although it has the pros that new information is created, pirate copies are generated at the

same time [24, 28]. Thus, many people have looked to data embedding methods identifying digital dataowners in order to protect copyright [8]. It is difficult to distinguish the pirate copies from the original

because there is no difference between the original and the copies. Finally, it causes to violate an ownerright of data. Therefore, copyright protection is essential in knowledge based societies [6]. There areencryption and security firewalls to protect copyright. However, if someone deciphers the code or gets

through the firewall, it can be useless [8].Although a digital watermarking adds watermarks which show copyright into the original data, the

method doesnt damage the original data. Thus, it is a good method to protect copyright when anownership dispute generates. Digital watermarking is the method of embedding information into a

digital content to protect copyright [1, 4, 5, 10, 15, 18, 23, 25, 31]. Digital watermarking has severalfeatures. First, the embedding effectiveness is the probability of detection after embedding. Second, the

fidelity is the similarity between the original and the watermarked data. Third, a false positive is thedetection of watermarks in data that does not contain any watermarks. Fourth, the robustness is the

ability to detect the watermarks in watermarked data after several operations [8].We can classify digital watermarking methods according to several criteria. First, there are non-blind watermarking and blind watermarking method according to using the original data. Non-blind

watermarking is the method that does not require original data for watermark extraction, while blindwatermarking method does. Figures 1 and 2 show the blind watermarking method briefly.

Figure 1. Watermark embedding process

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Robust Vector Digital Watermarking Using Angles and a Random TableJungyeop Kim

Figure 2. Watermark extraction process

Second, there is frequency domain method and spatial domain method by embedding watermarkmethod. Frequency domain method is to embed watermarks into frequency domain after changing theoriginal data to frequency. This method is known to guarantee robustness. However, it happens not to

extract watermark after geometrical attacks like rotation, scaling, and translation [31]. Moreover, it isnot easy to control the distortion after embedding watermarks [9].

Third, spatial domain method is to embed watermarks into the original data directly. Although thismethod is known to be weaker than the frequency domain method in the robustness aspect, it has the

advantage of controlling the distortion after embedding watermarks. Particularly, it can be a goodmethod in vector map data because the distortion and position accuracy are very important in map field.

Therefore, I proposed vector map digital watermarking in spatial domain.Vector map data are frequently used in GIS (Geographic Information Systems), navigation, and webmap services [15]. Because coordinates are acquired only with expensive instruments, aerial

photographs, vectorizing or other such means, the accumulation and management of vector map dataare both costly and time-consuming processes [9, 19, 20]. GIS entails hardware, software, data, and

human resources, among which data acquisition is the major cost. Indeed, this can account for 80% ofan overall budget [16]. Vector data are used in several fields including government. And I expect that

the value of the vector data is increased. However, illegally distribution and sale dont make a profitand cause distorted market system [17]. Therefore, as already stated, vector map copyright requires

effective protection [9, 13, 19, 20, 21, 22]. Vector map data is various compared with other multimediadata such as image, video and audio file formats. Since the vector map data have a floating point data

sequence with a precision, it is difficult to apply general multimedia watermarking methods to thevector map data directly [9]. In this paper, a new blind watermarking method for vector maps is

proposed using interior angles. Because the angles are not changed easily, the proposed method can be

robust and guarantees fidelity.

2. Related works

Generally, watermarking algorithms are categorized into two classes. Algorithms in the frequency

domain embed watermarks in the transform coefficient. The main transforms are DFT(Discrete FourierTransform), DWT(Discrete Wavelet Transformation), and DCT(Discrete Cosine Transform). These

watermarking algorithms in the frequency domain are known to be robust to attacks. However, itremains difficult to correct distortions of data after watermarks are embedded. [9], [26] presented anew method by which the 2D (x, y) coordinates of each vertex are combined to construct a complex

value (z=x+iy), after which DFT can be applied to that value. The watermarks embedded in Fourierdescriptors can be extracted. These methods, however, have some defects. For example, after the

embedding of watermarks, the original data is distorted. Also, these methods can extract watermarks

only under specific attacks, not any or all attacks. There are other watermarking algorithms that embedwatermarks by changing the DWT coefficients in the DWT domain [30]. Again, however, thesemethods can extract watermarks only under some attacks. [19] presented a blind watermarking

algorithm that does not require original data to extract watermarks. The method embeds watermarksutilizing the coordinates within a single object that are highly correlated in the DCT domain. However,this method distorts the original map. Moreover, it, too, can extract watermarks only under certain

attacks.

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Additionally, there are other algorithms that operate in the spatial domain. These algorithms embedwatermarks by directly modifying the coordinates. These watermarking methods can, in comparison

with algorithms operating in the frequency domain, more easily control the distortion incurred in theembedding of watermarks. [7] and [22] proposed such spatial-domain watermarking algorithms. The

main idea behind this kind of algorithm is to partition data into several blocks and to embedwatermarks in coordinates within those blocks using PSNR (Peak Signal to Noise Ratio). A

watermarked map thus can be created by the direct alteration of those coordinates. [20] proposed a new

method based on this principle. Their method partitions data into blocks and then embeds watermarksusing the statistics of the coordinates within those blocks. All such methods, however, are limited in

that they cannot extract watermarks under certain operations. [3] designed a novel watermarkingmethod. First, coordinates are extracted by the Douglas-Peuker algorithm. Second, watermarks are

embedded into coordinates as the correlation between them. Although this method shows good resultsunder some operations, other generalization algorithms can easily remove watermarks generated using

this method. Also, rotation and translation could destroy those watermarks. [14] proposed a newmethod using azimuth with the features of the vector map data. After calculating azimuth, it embedded

watermarks into the azimuth. However, this method has the drawback that it requires the original dataand preprocessing before extracting watermarks. In this paper, a novel method which doesnt need the

original data and preprocessing is proposed. And the proposed method is robust to several attacksunlike other methods.

3. The features of the vector map digital watermarking

Vector map data are frequently used in GIS, navigation, and web map services [13, 14]. The

importance of the location information comes to the force recently, and then the vector map is based to

the map fields. Vector map data is various compared with other multimedia data such as image, video,

and audio file formats. Since the vector map data have a floating point data sequence with a precision,it is difficult to apply general multimedia watermarking methods to the vector map data directly [9].Therefore, we need to understand the structure of the vector map data.

The vector data consist of points and lines, which represent objects. The vector data doesnt havethe change of the objects when the data are scaled. And the data are used in mobile fields because the

data has low file volume. However, if the position accuracy is not accurate, the position or shape of theroad and buildings are inaccurate. Finally, the services based on this location information can be

useless. Because of this reason, a vector map watermarking has to have the fidelity. The fidelity and

robustness are the trade-off. That is, if the robustness is enhanced, the fidelity becomes weakened. Onthe contrary, if the fidelity is enhanced, the robustness becomes weakened. So, vector map digitalwatermarking is very difficult, we should consider what is more important.

4. The scheme of the proposed method

4.1. Calculating angles

Although objects are rotated or translated, the angle is one of the spatial features unchanged valueseasily. Using this feature, I can propose a robust vector map watermarking method. Unlike the azimuth

method used in [14], the proposed method uses interior angles with 3 points. So, a new method doesntthe original data, and then can be a robust method on geometrical attacks.

The interior angle can be calculated using the three consecutive points of the object. Watermarks are

embedded into the angle, which changes the coordinates. We can calculate the angle with the cosinerule. In figure 3, the interior angle is computed from the angle FAB using F, A, and B points. We can

compute the correct interior angle using the cosine rule when the angle is less than 180. However,

when the value is greater than 180, the value is , not angle (figure 3). In this paper, calculating

angle is important. Therefore, it is not a problem to use the cosine rule.

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Figure 3. Interior angle

4.2. The random table

After calculating angles on each object, we generate a random table. We apply the random table tothe vector map data. This random table can be watermark key. Users can use the random table as

different data. It can be prevented to attempt to damage watermark by using a random table. And wedont need a original data when watermarks are extracted because of a random table. That is, even

though the algorithm of the watermarking is known, the extraction of the watermark is impossiblebecause this random table is used as a watermark key. The random table is used when 0 between 9 is

changed a random number and watermarks are generated. Also, because we use the random table as awatermark key, we dont need the original data when watermarks are extracted.

4.3. The intersection test

The change of the coordinates become after watermarks are embedded into the original data.Although the ideal method is that there is no change of the coordinates, it is impossible. So, after

embedding watermarks, if the change is within the allowable error, we can say it is not to damage tothe vector map.

In vector map data, the positional accuracy is very important unlike in general multimedia data.

That is, if the positional accuracy is wrong, the map is useless. And if the topology of the vector map ischanged after embedding watermarks, it makes a big problem. For example, if two lines are detached

or are crossed after embedding watermarks, some problems are generated. Many watermarking onvector map have not considered the topology. In this paper, we return the problem points to the original

points using the intersection test. The intersection test can check if the change of the topology afterembedding watermark. The intersection test returns values of 1 when two lines intersect, -1 when two

lines dont intersect, and 0 when a line includes an end point [12]. Figure 4 shows the state of the two

lines. Comparing returned values before and after embedding watermarks, we preserved the topologyof the vector map data.

There is an important thing that we have to consider. After embedding watermarks, there is a casethat the return value is different. However, if the change is within an allowable error, the watermarks

remain.

Figure 4. The states of lines

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5. The realization of the digital watermarking using angles

5.1. Making a random table

In this paper, we used a random table as a watermark key. After calculating each angle of theobjects, we changed an integer number of the angle into a new value using a random table. The reason

why we use integer number is this proposed method is to embed watermarks in decimal. The new valueis used to generate watermarks, not to change real coordinates. An example of the application of the

random table is as follows. First, the owner fixes the range of the random table as 20. A randomnumber between 0 and 20 is generated. Then, a number between 0 and 9 is changed to a number

between 0 and 20 (Table 1). If the angle is 46.32, it is changed to 167.32. This changed value is usedwhen the calculations are made to generate watermarks.

Table 1. Random tableReal

value0 1 2 3 4 5 6 7 8 9

Changed

value6 13 11 1 16 19 7 5 8 3

5.2. Making angles

Because vector data consist of points, we can calculate the angle with three points. The angle is notchanged easily under general manipulations. The watermarking method using the angles can be good

method because the angle is good information to embed watermarks. The angle is obtained using the

consecutive three points and the cosine rule. In this experiment, we calculated the angle with the

starting point as the center. Therefore, we can get one angle per object. In figure 5, point A is starting

point, and then point E, A, and B are consecutive points. We can calculate angle EAB using cosine

rule.

Figure 5. Example of objects

5.3. Making the own value

In this paper, the users own value is used when watermarks are generated. This own value make theproposed method to be secure because the own value is needed when the watermarks are extracted.

And if the users own value is used, the person who distributes the map can be identified. The usersown value becomes G(x) and is used when watermarks are generated. We used the value after

changing to ASCII code value. For example, if the own value is HKD, H: 1001000(71), K:

1001011(74), and D: 1000100(67) are changed. Eventually, G(x) becomes 212(71+74+67). This G(x)becomes essential value when watermarks are embedded and extracted.

5.4. Generalization and embedding watermarks

We can generate watermarks using a random table and an angle. The integer of the calculated angle

is changed to a new value using a random table. The new value becomes P(x). Using a formula (1), wecan get the watermark. For example, if the angle is 113.169546, the integer 113 is changed P(x) 13131

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with table 1. When SIK is used as a own value, the value is G(x) 228). Therefore, the watermark iscalculated 93 through a formula (1), and then the angle is changed as 113.93.

watermark = G(x) - P(x)%G(x) (1)

This changed angle makes the movement of the coordinates as the changed. That is, the difference

between the original angle and the changed angle is bisected, and then the bisected-angle is reflected to

coordinates. We can calculate the changed coordinates using formula (2). Figure 6 is example which isthe part of the object. Figure 7 is to enlarge figure 6. We can the changed coordinates C as the same

formula.The procedure of the embedding watermarks is below.

Step 1. Calculate angles and a random table.Step 2. Calculate P(x) using a random table.

Step 3. Calculate G(x) using the own values.Step 4. Change calculated angles to watermarked angles.

Step 5. Calculate watermarked coordinates.

Figure 6. The original object

Figure 7. Enlarged object

(2)

5.5. Extracting watermarks

The proposed watermarking algorithm is a blind method that does not need original data to extractwatermarks. Only a random table and the users own value are needed as watermark keys. The process

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of extracting watermarks proposed in this paper is similar to the process of embedding watermarks.After calculating the angle in watermarked data, one obtains new values using the random table. The

watermarks are calculated using the users own value, P(x), and G(x). Finally, whether the calculatedwatermark is reflected in the angle between the three points is confirmed. If it is, in fact, reflected, the

data can be regarded as watermarked data. We use CR (Correspondence Ratio) to validate theembedding effectiveness. The number of the objects in the data is the denominator in CR. The

numerator, meanwhile, is set as the number of angles checked for an embedded watermark during the

watermarking process.

objectstheofnumberthe

watermarkextractedtheofnumbertheCR

(3)

The procedure of the extracting watermarks is below.Step 1. Calculate angles in watermarked data.

Step 2. Calculate P(x) and G(x) using a random table and an own value.Step 3. Calculate watermarks using formula (1).Step 4. Check if watermarks are embedded or not.

6. Experimental results

6.1. Experimental data and watermarking attacks

In this paper, we used the vector map file. These data, actually building data, are on the 1/1,000

scale. According to the National Geographic Information Institute of Korea, the maximal error allowedin a 1/1,000 scale map is 0.7m. Therefore, if the change is within this range, the proposed method

preserves the integrity of maps. Because of this reason, we used a large scale map.An attack in watermarking is an intentional or unintentional operation generated when data is

manipulated. Because the structure of the vector data is different from general multimedia data, thecharacter of the attack is different [19]. The attack on vector data in GIS can be classified into three

types: geometrical attacks, vertex attacks, and noise attacks [27]. However, almost no informationwould be lost in geometrical attacks such as rotation, translation, and scaling. On the other hand, vertexattacks make the vector map data unusable [3]. So, it is critical for a watermarking of vector map data

to be able to withstand vertex attacks. In this paper, we experimented on vertex attacks with cropping,

generalization, and adding objects. Noise attacks are to add noise on vector map. It is not frequent togenerate and is not good attacks because these attacks can make loss of the position accuracy [27].However, we examined noise attacks as adding noise separately in this paper.

6.2. Embedding watermarks

Position accuracy and topology are very important in vector maps. If the accuracy is reduced ortopology is changed after embedding watermarks, the value of the map is lost. We categorized

topology as falling into three distinct types, as shown in figure 4. A difference in the intersection testresults before and after the embedding of watermarks would indicate a change in the topology due to

the embedding of the watermarks. Through the intersection test, we can check whether fidelity ischanged. In this paper, there was no such difference. We tested RMSE (Root Mean Squared Error).

The result shows that RMSE is 0.0004. We examined whether embedded watermarks were extracted

from the watermarked data to check the embedding effectiveness. In the case of the proposed method,CR was 100%. Therefore, the proposed method preserved the integrity of the map and the topology.

Figure 8 is the original data and the watermarked data.

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Figure 8. Original data(up) and watermarked data(down)

6.3. The robustness tests

We tested the attacks of the three types to check the robustness in this paper. First, geometrical

attacks use a map without changing point numbers, and include translation and scaling attacks. Table 2shows the CR of these attacks. The translation attack moves all objects a certain distance. And the

scaling attack is not changing scale in map field. We enlarged and reduced map data with consideringthe map data as an image. We proved the proposed method doesnt have any problem with geometrical

attacks through the result of the experiment. Next, we extracted watermarks under vertex attacks. We

experimented on the vector data with cropping and generalization. We used generalization based on

Douglas-Peuker algorithm and changed threshold 1m, 10m, and 100m. The experiment proved that thismethod can extract embedded watermarks. Noise attacks are those that add noise into the data. In this

paper, we moved the coordinates in each certain area within the allowable error. And we moved and

rotated the vector map data with minute distance and angle. The experimental result shows theproposed method is robust to the noise attacks.

Figure 9. Adding objects

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Figure 10. Cropping

Generalization 1 Generalization 2 Generalization 3

Figure 11. Generalization

6.4. Experimental analysis

The goal of this work is to develop a new vector watermarking method that is robust to secure acopyright and preserve the fidelity of watermarking data. We embedded and extracted watermarks

using angles which are one of the spatial features. The experimental results show that the fidelity isgood. That is, RMSE is 0.07 with no change in topoogy. We examined several attacks on the vector

map to test the robustness. In geometrical attacks, we extracted every watermark for translation andscaling. However, we couldnt extract every watermark under the vertex attacks because awatermarked coordinate is eliminated under a vertex deletion attack. Also, the CR value was not 100%

since added coordinates dont have any watermark. Under the noise attacks, the CR value was veryhigh. So, we proved that this method is robust digital watermarking. Table 3 shows the estimate of the

proposed method according to the features of the watermarking.

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Table 2. CR Results

Attack range CR

Geometrical attacks

translation

1 100%

10 100%

100 100%

scaling

Scaling factor 0.5 100%




Vertex attacks

generalization

1 85%

5 97%

10 84%

Adding objects 95%

Noise attacks

By rotation

0.1 96%

0.01 99%

0.001 100%

By translation

0.1m 100%

0.01m 100%

0.001m 100%

Adding noise per areaFirst 100%

Second 100%

Table 3. Evaluation based on watermarking features

Watermarking

features

Method

Embedding

effectivenessFidelity Robustness

False

positive

rate

The proposed method

7. Conclusions and future work

We proposed new digital watermarking using angles. To embed watermarks, we calculated anglesand changed the angles. The proposed method is blind watermarking, which extracts watermarks using

a method similar to that used to embed them. The experimental results show that this method hasfidelity that is vital to map data and is robust to attacks. In this paper, we embedded watermarks into a

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spatial domain with reflecting the features of spatial objects. Through the intersection test, we canpreserve the topology of the map data. This is a condition for a vector map digital watermarking

method. However, this method has a weak point that we cannot extract watermarks if the interiorangles are changed. Future work will include improving this weak point using several spatial features.

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