Method for Vector Map Protection based on using of a Watermark

Image as a Secondary Carrier

Yuliya Vybornova

and Vladislav Sergeev

1,2

Department of Geoinformatics and Information Security, Samara National Research University, Moskovskoye Shosse,

Samara, Russia

Image Processing Systems Institute оf RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Samara, Russia

Keywords: Digital Watermarking, Geographic Information Systems, GIS, Vector Map, Raster Image, Discrete Fourier

Transform, Pseudorandom Sequences, Data Protection.

Abstract: In this paper, we present a study of the watermarking method for vector cartographic data based on a cyclic

shift of a polygon vertex list. We propose a method modification to provide an accurate authentication

procedure, as well as to increase the method robustness against map contents modification. The main idea of

the improved method is to use a noise-like image as a secondary carrier for a watermark, represented in the

form of a bit vector. An algorithm for construction of a noise-like image carrying a watermark sequence, as

well as an algorithm for extraction of such a sequence, are given. An experimental study explores the

information capacity of the carrier image and its robustness against quantization and noise adding, i.e.

distortions simulating the embedding into map objects. The efficiency of the method is also demonstrated

on real cartographic data. Conclusions comprise optimal parameters for reliable extraction depending on the

number of polygons on the vector map.

1 INTRODUCTION

The existing methods of active protection (i.e. the

protection by using digital watermarking

technology) of vector map data are mostly

performed by introducing slight (in terms of map

accuracy) distortions into the coordinate information

of vector objects (Abubahia and Cocea, 2017).

Depending on the level of watermark resistance to

distortions, these methods are aimed at solving

various problems of vector map security.

Methods (Abubahia and Cocea, 2015; Lee and

Kwon, 2013; Peng et al., 2015; Wang, Yang and

Zhu, 2017; Yan, Zhang and Yang, 2017; Zope-

Chaudhari, Venkatachalam and Buddhiraj, 2017) are

designed for solving the problem of copyright

protection (protection against unauthorized

distribution) using the technology of robust

watermarks. Methods of protection against

modifications are implemented on the basis of semi-

fragile (Ren, Wang and Zhu, 2014; Da et al., 2018)

and fragile (Wang, Bian and Zhang, 2015)

watermarks, which are used to ensure the

authenticity and integrity of vector data respectively.

Also, one of the common approaches to protect

vector data against changes is the so called "zero-

watermarking" technology (Peng and Yue, 2015)

which implies constructing a watermark on the basis

of the carrier features. Here, the embedding

procedure as such is missing: the watermark is

necessary only for the verification process. The

combined use of different watermarking

technologies, which is called "multiple

watermarking" (Peng et al., 2017), allows to provide

comprehensive protection of vector data from

unauthorized distribution and modification.

There are situations where even minor changes

introduced into the data are unacceptable. For this

reason, another class of vector data protection

methods, "reversible watermarking" (Cao, Men and

Ji, 2015; Peng, Yan and Long, 2017; Wang, Zhao

and Xie, 2016), has emerged, providing the

opportunity to restore the coordinate values after the

watermark extraction. However, these methods do

not demonstrate the required robustness, therefore,

map distortions can negatively affect the correct

restoration of the original coordinate values.

It should be noted that all the above mentioned

methods have the following disadvantages:

284

Vybornova, Y. and Sergeev, V.

Method for Vector Map Protection based on using of a Watermark Image as a Secondary Carrier.

DOI: 10.5220/0007932402840293

In Proceedings of the 16th International Joint Conference on e-Business and Telecommunications (ICETE 2019), pages 284-293

ISBN: 978-989-758-378-0

- Despite the fact that all conversions are performed

with a given accuracy and almost invisible to the

legitimate user, any distortion of the map gives an

attacker the opportunity to detect the presence of the

embedded watermark even without knowing the

watermarking scheme, i.e. by using blind

steganalysis.

- When embedding and extracting the watermark, a

set of map objects must be strictly ordered. Since the

location of objects on the map is quite random, there

is a need to store extra identifiers for objects or

watermark positions.

The embedding approach, we proposed earlier in

(Vybornova and Sergeev, 2019), allows to avoid the

above disadvantages. First, the method does not

imply a change in vertex coordinates: the protective

information is embedded into cartographic data by

cyclically shifting the list of vertices of each

polygon. Secondly, instead of a bit sequence we

consider a raster image superimposed on a vector

map as a digital watermark, so there is no need to fix

the object indexation order when embedding and

extraction procedures. Consequently, this approach

to vector map protection can form the basis for a

whole group of methods, focused on specific tasks,

such as copyright, authenticity and integrity

protection of map data, as well as localization of

unauthorized changes introduced into a vector map.

In this paper, we propose a specific way of using

a noise-like image as a secondary carrier for the

watermark presented in the conventional form of a

bit sequence, and also we explore the issue of the

information capacity of such a carrier.

The rest of the paper is organized as follows. In

Section 2, the basic approach, which we developed

earlier, is presented. Also, this section describes in

detail a new enhanced approach. Section 3

comprises experimental research of the proposed

method for model and real data. Section 4 provides

general conclusions and the main issues of the future

work.

2 METHODS

2.1 Original Watermarking Method

for Vector Maps

The basic watermarking method for vector

cartographic data, that we proposed in (Vybornova

and Sergeev, 2019), is based on the following

features of polygonal map objects:

a) all polygons are closed shapes;

b) the polygon vertices are numbered

consecutively.

These properties provide the ability to cyclically

shift the indices of all vertices in the polygon vertex

list, without changing the coordinate values, that is,

avoiding the introduction of distortions into the

vector map contents.

The first idea of the method (Vybornova and

Sergeev, 2019) is that the digital watermark is

embedded into data by cyclically shifting the list of

vertices of each polygon. For example, to embed one

watermark bit into each polygon, a polygon vertex

list can be shifted in such a way as to change the

first element in the list to either the uppermost

(north) or the lowermost (south) vertex, depending

on the value of the watermark bit. To embed two

watermark bits into the polygon, the leftmost (west)

and rightmost (east) vertices should be also taken

into consideration. In general, an n-bit binary

number can be embedded into each polygon. It

should be noted that for a fixed first vertex of the

list, there is an opportunity to embed an additional

watermark bit into each polygon by altering the

direction of vertex traversal: clockwise or

counterclockwise, depending on the bit value.

The second idea of the method is to use a raster

image superimposed on a selected fragment of the

vector map as a watermark. Certainly, the vector

map does not provide an opportunity to place raster

data, but its objects (in our case, polygons) can be

mapped to the image in such a way as to

geometrically coincide with some pixels. The set of

pixels, corresponding to polygons, forms an

irregular grid, and thus the entire image can be

approximately restored by using one of the existing

interpolation methods (Vybornova, 2018).

2.2 Proposed Enhancement of Original

Method

In method (Vybornova and Sergeev, 2019), the

raster image itself is used as a robust watermark

providing copyright protection for a digital map.

Accordingly, the map authentication is performed by

visually matching the original watermark with the

image restored (usually with large errors) after

extracting from the vector map. So, this can be

regarded as an obvious limitation on the method

applicability.

Developing the basic method, we propose to use a

noise-like image as a secondary carrier for the

watermark, represented in the form of a bit sequence

(Glumov and Mitekin, 2010). This allows to

automate the map authentication procedure, since

Method for Vector Map Protection based on using of a Watermark Image as a Secondary Carrier

285

the watermark sequence can itself carry all the

necessary identifying information and its analysis

does not require the comparison with the original

watermark.

In order to ensure robustness of the embedded bit

sequence against image interpolation errors, addition

or removal of map objects, geometrical

transformations and cropping of the map, and etc.,

each bit embedded in the carrier image should not

correspond to a separate point (pixel) or a local area

on the image plane. We propose to embed a bit

sequence in the spatial-frequency domain of the

carrier image so that each bit is extended on the

entire image plane "holographically", i.e. in the form

of a two-dimensional sinusoid of the corresponding

spatial frequency.

2.3 Watermark Image Construction

For simplicity, we assume the carrier image is

continuous – f

, t

). We also assume it carries a

watermark in the form of an arbitrary binary

sequence S of length L.

We propose to form a two-dimensional spatial

spectrum - F

(ω

, ω

) - of an image represented as

2(L+2) two-dimensional unit impulses located in the

spectral domain on two rings of different radii: r и

r+Δr, as illustrated in Fig. 1 for one half-plane of the

two-dimensional spectrum (because the image is real

the second half-plane displays the spectrum

symmetrically about the center). In figure 1, unit

impulses are indicated with black circles. All but

two impulses are located with equal step (angle)

starting from the spectrum origin on a ring of

smaller or larger radius, depending on the value of

the corresponding bit of the watermark sequence.

Two impulses located on both rings at the same (e.g.

zero) angle indicate the beginning of the sequence.

Figure 1: Embedding of a binary sequence into image

spectrum.

The resulting spectrum of an image can be

described by the formula:

1 2 1 2

( , )

( cos , sin )

( , ) ( , )

( cos , sin )

( , ) ( , ).

l l l l

r r r



      

     

      

     



   

      

   

     



(1)

where

r s r



  









, and

( , )

  

is a

two-dimensional unit impulse.

To get the two-dimensional image function, we

apply the two-dimensional inverse Fourier transform

to the spectrum (1):

1 1 2 2

()

1 2 1 2

( , )

( , ) d d .

i t t

f t t



   







 





(2)

By substituting (1) into (2), and taking into

account the Euler's formula, we obtain:

1 2 1

2 1 2

( , ) cos[( cos )

( sin ) ] cos( ) cos[( ) ]

c l l

f t t t

t rt r r t























    







(3)

The above relations describe only the idea of

how to embed a binary sequence into a carrier

image. In practice, when working with a digital

image instead of a continuous spectrum, it is

necessary to use a discrete Fourier transform (DFT),

taking into account the well-known features of such

a conversion: integer arguments in the spatial and

spectral domain, periodicity of functions in two

dimensions, possible overlap effects, etc. In this

case, there are two ways to form a noise-like image,

carrying a watermark of size

NN

pixels:

1) By directly using the "discretized" analogue of the

formula (3):

1 2 1 2

cos sin

( , ) cos[2 ( )]

2 2 ( )

cos( ) cos[ ],

l l l l

f n n n n

r r r

   







  







SECRYPT 2019 - 16th International Conference on Security and Cryptography

286

where

,nn

are the integer arguments of the digital

image,

1 1 2 2

0 1, 0 1n N n N     

2) By directly using the "discretized" analogue of

unit impulse delta function, called unit sample

function. Unit samples are arranged on two rings in

two-dimensional discrete spectral domain as

described above, and then the resulting image can be

obtained by using the inverse DFT.

For small lengths of sequences, the first method

may be computationally more efficient.

Contrariwise, when lengths are large enough, the

second method may perform in a better way.

It should be noted that due to the spectrum

discreteness, the coordinates of unit samples, i.e.

magnitudes

cos



sin



()rr

should be

rounded to integer values and, therefore, may

overlap when arranging on the rings. Thus, the DFT

dimensions and the radii

()rr

must be

sufficiently large, so that rounding errors could not

affect the watermark extraction.

As the last step of constructing the carrier image,

the values of its pixels can be normalized to a

standard range, for example, [0, 255]:

1 2 1 2

255 1 2

1 2 1 2

( , ) min ( , )

( , ) 255

max ( , ) min ( , )

f n n f n n

f n n

f n n f n n







An example of the resulting noise-like image

with embedded watermark sequence corresponding

to spectrum in Figure 1 is shown in Figure 2.

Figure 2: Example of noise-like image carrying the

watermark sequence (N

= N

= 512, r = 8, ∆r = 4, L = 15,

S = {101101001011101).

2.4 Watermark Extraction

The extraction of a sequence from an image

approximately (with interpolation) reconstructed

from a vector map consists of the following obvious

steps:

 calculation of a two-dimensional discrete

spectrum of the image (using DFT);

 detection of spectral components with a large

amplitude (impulses) and determination of

their coordinates;

 detection of the fact of watermark presence, i.e.

the fact that the impulses are located on two

concentric rings in the spectral plane;

estimation of the radii of these rings;

 search of the sequence beginning key, i.e. a

pair of impulses located at the same angle to

the spectrum origin;

 reading of the watermark sequence bits

clockwise or counterclockwise starting from

the sequence beginning key.

The proposed method of watermark construction

(in the form of impulses on circles in the spectral

plane), together with the extraction procedure

described above, ensures the watermark robustness

against the main geometric deformations of the

image and, accordingly, of the vector map into

which this image is embedded: scaling, rotation,

translation and cropping .

3 EXPERIMENTAL RESULTS

AND DISCUSSION

To investigate the potential use of a noise-like image

embedded into the vector map as a secondary

container for the watermark presented in the form of

a bit sequence, we have conducted two

computational experiments.

In all experiments, digital images of size

512 512NN 

pixels are generated. Bit

sequences are embedded into rings of radii

and

()rr

in the discrete spectrum domain of the

image (for certainty, it is assumed that

4,r

since

due to the discreteness of the bitmap it is the

minimum acceptable value). The "low-frequency"

( 10,50)r 

and "mid-frequency"

( 60,100)r 

noise-like images are considered.

The lengths of the bit sequences are ranged from

10 100.L

For each combination of parameters,

100 watermark sequence implementations are

generated. The values of sequence bits are obtained

using a random number generator as equiprobable

and independent in total.

Interpolation of an image extracted from a vector

map is performed using the nearest neighbor method

Method for Vector Map Protection based on using of a Watermark Image as a Secondary Carrier

287

based on a triangulated irregular network

(Vybornova, 2018).

Spectral impulses are determined using a simple

rule:

1 2 1 2

( , ) (0,0)

( , ) max ( , )

F k k F k k





where

( , )F k k

is the image DFT,

,kk

are the

integer arguments of the discrete spectrum

1 1 2 2

(0 1,0 1).k N k N     

3.1 Experiment 1

Obviously, the main sources of errors during the

reconstruction of a carrier image from a vector map

and, consequently, errors during the bit sequence

extraction, are:

- the image is extracted from the map as a set of

spaced pixels corresponding to the polygonal map

objects;

- extracted pixels are quantized due to the fact that

only few binary digits can be embedded into each

polygon.

To evaluate the effect of these distortions on the

watermark sequence, we conducted the following

computational experiment. K pixels of the generated

noise-like image are selected randomly

(independently and equally likely for each

coordinate). Each pixel is quantized to a b-bit

binary number (i.e. into 2

levels). Next, the image is

interpolated and attempt to extract the watermark

sequence is performed.

As an indicator of the watermark sequence

integrity, the experimentally estimated probability of

its correct extraction, P, depending on the number

of reference pixels K, is considered. Estimation of

the extraction probability is calculated for the

sample of 100 images.

The variable values are: radius r, bit depth (i.e.

number of bits per pixel b), and sequence length L.

The minimum values of r are established

experimentally and can approximately be described

by the formula:

0,36rL

Figure 3 shows the dependence of the extraction

probability on the number of polygons with varying

values of bit depth for the following cases: a) L = 10,

b) L = 50, c) L = 100 (in each case, the radii are

selected in such a way as to provide the most

accurate extraction, i.e. they are assigned the lowest

accebtable values).

(a)

(b)

(c)

Figure 3: Dependence of the extraction probability on the

number of polygons with variable values of bit depth b for

а) L = 10, r = 10; b) L = 50, r = 20; c) L = 100, r = 40.

Figure 4 shows the dependence of the extraction

probability on the number of polygons with varying

values of the radii for the following cases: а) L = 10,

SECRYPT 2019 - 16th International Conference on Security and Cryptography

288

b) L = 50, c) L = 100 (the bit value in this case is

fixed as b = 3)

(a)

(b)

(c)

Figure 4: The dependence of the extraction probability on

the number of polygons with varying values of the radii

for a) L = 10, b = 3; b) L = 50, b = 3; c) L = 100, b = 3.

Some obvious conclusions follow from the

presented results.

The more objects on the map (pixels

corresponding to polygons), the higher the

probability of correct extraction. At the same time,

the longer the watermark sequence, the higher the

requirements for the number of objects needed for

extraction.

The quality of the extraction increases with an

increase in the bit depth of the pixels corresponding

to the map objects. It also looks natural, since an

increase in the bit depth reduces the pixel

quantization noise and, consequently, the error of the

carrier image reconstruction decreases. However,

when setting the bit depth value higher than b = 3,

we see almost no effect of improving the quality.

Moreover, in practical applications it is difficult to

implement persistent high bit depth due to the fact

that on the real map simple polygons (mostly,

quadrangles) dominate: therefore, no more than

three-digit binary numbers can be embedded: two

digits by setting the first vertex in the polygon vertex

list, and one of digit - by altering the direction of

vertex traversal.

For a fixed length of the bit sequence, the

extraction quality is higher, the smaller the r, i.e. the

lower the frequency of the carrier image. On the

other hand, the minimum possible value of this

parameter is limited by the discreteness of the two-

dimensional image spectrum, namely, its ring into

which a sequence of length L is embedded.

Figure 5 shows the dependence of the watermark

image capacity

bL

on the number of polygons for

a fixed values of the achievable probability.

Figure 5: Dependence of carrier image capacity on the

number of polygons for various probabilities.

3.2 Experiment 2

In the previous experiment, the map watermarking

procedure is simulated, but the embedding into real

data is not performed. To confirm the performance

Method for Vector Map Protection based on using of a Watermark Image as a Secondary Carrier

289

of the proposed method for real vector cartographic

data, we have conducted a second experiment using

a fragment of the urban development map containing

9327 polygons (Figure 6). The quantized values of

the corresponding pixels were embedded into each

polygon of the map and then extracted.

Figure 6: Carrier map.

As already mentioned, the proposed map

watermarking method has features that in one way

or another influence the extraction of the binary

vector watermark hidden in the noise-like image:

1) the noise-like image extracted from the map

forms an irregular grid over which interpolation is

performed.

2) despite the fact that when embedding we set pixel

values quantized by a given level, when extraction

these values can be rounded, because to embed a b-

bit number into a polygon without errors, this

polygon should have

b

vertices (obviously, this

condition may not be met).

Consequently, in addition to confirmation of the

method applicability on real data, this experiment is

aimed at the qualitative assessment of the effect

arising from errors introduced by such data

regarding the model case presented in the previous

experiment.

When modeling data from experiment 1,

interpolation is performed on uniformly scattered

points, and quantization is carried out strictly at a

given level. Thus, in experiment 2 we investigate the

probabilities of the correct extraction from noise-like

images of three types at once:

1) The ideal case (model data from experiment 1).

Interpolation is performed using a mask with evenly

scattered 9327 points superimposed on noise-like

images quantized at a given level.

2) Interpolation is performed on an irregular grid of

9327 pixels extracted from a map (Figure 7)

superimposed on noise-like images quantized at a

given level. This data allow us to trace how the

unevenness of the grid affects the result of

interpolation and the result of extraction in general.

3) Data extracted from the map. This data allow us

to trace how the unevenness of the number of

polygon vertices affects the result of extraction.

To calculate the probabilities of correct

extraction, the experiment is conducted on samples

of size 100 for

10,100L 

(in each case, radii are

assigned minimum acceptable values).

Figure 7: Non-uniform interpolation grid.

The dependence of the extraction probability on

the length of the bit sequence with varying values of

b are shown in Figure 8.

For b = 1, 2, the result of the real data extraction

error coincides with errors introduced by

interpolation on irregular grid. For b ≥ 3, when

extraction from real data, rounding errors occur, as

discussed above.

The dependence of the extraction probability on

the number of image quantization levels with

varying values of the sequence length are shown in

Figure 9.

The findings of experiment 1 tell us that the

quality of extraction is higher, the greater the b. On

real data, the statement remains true only for

b = 1,2,3,4. The larger L, the greater the drop in

quality when b > 4. When b = 8, extraction is not

possible for any L.

The results obtained for real map data are mostly

influenced from uneven distribution of the number

of vertices in each polygon. Figure 10 shows the

statistics on the number of vertices for the map from

Figure 6.

SECRYPT 2019 - 16th International Conference on Security and Cryptography

290

(a)

(b)

(c)

(d)

Figure 8: The dependence of the extraction probability on

the sequence length for a) b = 1; b) b = 3; c) b = 5; d) b =

(a)

(b)

(c)

(d)

Figure 9: The dependence of extraction probability on the

number of image quantization levels for a) L = 10; b) L

= 30; c) L = 50; d) L = 60; e) L = 70; f) L = 80.

Method for Vector Map Protection based on using of a Watermark Image as a Secondary Carrier

291

(e)

(f)

Figure 9: The dependence of extraction probability on the

number of image quantization levels for a) L = 10; b) L

= 30; c) L = 50; d) L = 60; e) L = 70; f) L = 80 (cont.).

Figure 10: The distribution of the number of vertices for a

fragment of urban development map.

Embedding of a b-bit number into a polygon can

be performed with no errors, if the polygon consists

of at least 2

b-1

vertices. For example, to embed a 3-

bit number, we should take a polygon of 4 vertices.

Such polygons are most likely for maps representing

buildings. Embedding of 5 bits requires 16 vertices,

which is unlikely for the type of vector maps

considered in this paper.

4 CONCLUSIONS

In this paper, we present a study of the

watermarking method for vector cartographic data

based on a cyclic shift of a polygon vertex list. We

propose a method modification to provide an

accurate authentication procedure, as well as to

increase the method robustness against map contents

modification. The main idea of the improved method

is to use a noise-like image as a secondary carrier for

a watermark, represented in the form of a bit vector.

An algorithm for construction of a noise-like image

carrying a watermark sequence, as well as an

algorithm for extraction of such a sequence, are

given. An experimental study explores the

information capacity of the carrier image and its

robustness against quantization and noise adding, i.e.

distortions simulating the embedding into map

objects. The efficiency of the method is also

demonstrated on real cartographic data. Conclusions

comprise optimal parameters for reliable extraction

depending on the number of polygons on the vector

map.

Future work is supposed to be directed towards the

following issues:

1) a development of computationally efficient and

accurate interpolation methods for restoring the

undefined pixels on irregular grid;

2) a study on the watermark robustness against

geometrical transformations and operations

changing the map contents, such as

simplification (vertex removal), interpolation

(vertex addition), object addition / removal,

and layer removal;

3) a development of methods for increasing the

watermark robustness against various types of

attacks on vector map data.

ACKNOWLEDGEMENTS

This work is supported by Russian Foundation for

Basic Research (grant № 19-07-00474 A).

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