Multimedia Tools and Applications (2019) 78:24955–24977
https://doi.org/10.1007/s11042-019-7681-6
Rich-information reversible watermarking scheme
of vector maps
Yinguo Qiu 1 & Hongtao Duan 1 & Jiuyun Sun 2 & Hehe Gu 2
Received: 18 June 2018 / Revised: 11 February 2019 / Accepted: 24 April 2019 /
Published online: 16 May 2019
# Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract
With the increasing rampant infringements of vector maps, rich-information watermarking
technology is being more and more essential for forceful copyright declaration. Most of the
existing watermarking algorithms of vector maps, however, cannot embed abundant copyright
information. In this paper, a rich-information and reversible watermarking scheme is proposed
for vector maps based on the ideas of compression coding of watermarking image and
decimal-hex conversion of vertex coordinates. It recodes the original watermarking image to
shorten the length of the final watermark data and groups map vertices to choose cover data for
watermark embedding. And the reversible embedding is then carried out by modifying the
polar coordinates of map vertices. While the proposed compression coding method of
watermarking image and the decimal-hex conversion of map vertices guarantee the embedding
of rich-information watermark data, the reversible watermarking method provides recovery of
the original map content. Comprehensive experimental results show that the proposed scheme
is suitable for vector map applications where abundant copyright information is required while
the number of map vertices is limited.
Keywords Rich-information watermarking . Reversible watermarking . Vector map . Copyright
protection
1 Introduction
Big spatial data, the main data set of big data, forms the basic framework and spatial datum for
describing various geo-objects and phenomena in the era of big data. As the basic component of big
* Hehe Gu
qiuyinguo@foxmail.com
1
Key Laboratory of Watershed Geographic Sciences, Nanjing Institute of Geography and Limnology,
Chinese Academy of Sciences, Nanjing 210008, China
2
School of Environment Science and Spatial Informatics, China University of Mining and Technology,
Xuzhou 221116, China
24956
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spatial data, vector maps are playing a more and more important role in all walks of life in the
construction of national economy [26]. On the one hand, vector maps need to make breakthroughs
in data opening and sharing to make full use of their own value [24]. On the other hand, the content
of vector maps is of both high positioning precision and high production cost [22], and the rights of
map owners, the sharing of map data and even the national security will be affected in the event of
piracy, tampering, illegal dissemination, etc. Accordingly, it is an urgent problem to realize copyright
protection of vector maps in the environment of data sharing.
In the past decades, steganography [1–5, 9, 10, 12–16] and digital watermarking [6, 7, 11,
17–21, 23, 25] have been widely employed for security protection of various digital products.
Traditional methods, however, may cause distortion to the original data and affect its value in
use to a certain extent. Consequently, reversible watermarking, also known as lossless
watermarking, has been considered as a promising solution for copyright protection of digital
products. Under this background, reversible watermarking technology has been applied to the
area of copyright protection of vector maps, and lots of efficient algorithms have been
proposed. The research emphases of current reversible watermarking schemes of vector maps
are algorithms of watermark embedding and extraction, while few works have been done
focusing on rich-information watermark generation and embedding. Voigt et al. [20] proposed
a reversible watermarking scheme, in which watermarks are embedded by modifying the
coefficients in the 8-point integer DCT domain. To improve the watermark capacity, Voigt
et al. [21] proposed another optimized algorithm, exploiting both a bit-shift method and a
distortion-limitation scheme to guarantee a maximal map difference after watermark embedding. Watermarking algorithms in [20, 21] focus on the selection of the best watermark
embedding position, which have been considered as two representative watermarking algorithms of vector maps. Another reversible watermarking algorithm was proposed for vector
maps by Yang et al. [25] based on coordinate mapping, which realizes the blind detection and
extraction of watermarks by constructing mapping relationship between embedding position
and watermark bits. Nevertheless, the watermark data of the scheme in [25] consists of only
several simple characters, and it cannot express efficaciously rich copyright information. Cao
et al. [6, 7] proposed two improved reversible watermarking algorithms for vector maps based
on nonlinear scrambling [6] and iterative embedding [7], and some progress has been made by
them in enhancing the robustness and capacity of watermarking algorithms. The performance
of their algorithms with regard to rich copyright information expression, however, is not
significantly improved. Qiu et al. [17] proposed a reversible watermarking algorithm of vector
maps, which focuses on the detection and correction of error bits after watermark extraction. In
the algorithm in [17], the final watermark data consists of both the copyright watermark data
and its corresponding ECC, which is conducive to the robustness improvement of the
watermarking algorithm. This scheme, however, has little contribution to rich-information
watermark embedding, and complex copyright information embedding is still not supported.
Another watermark algorithm was put forward by Sun et al. [19] based on BP neural network,
in which watermarks are converted to binary bits and manipulated as the coefficients of neural
network. The scheme in [19] is robust and with preferable invisibility, but its performance in
the respect of rich-information watermark embedding is not promoted obviously. With the
purpose of embedding more watermark bits, Xiao et al. [23] designed a reversible
watermarking algorithm for 2D CAD vector graphics based on an improved difference
expansion method. By improving the watermark embedding capacity, this scheme improves
the length of the original copyright information to a certain extent. Qiu et al. [18] presented a
high-payload reversible watermarking scheme of vector maps based on QR code, which
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realizes the embedding of rich-information watermark embedding to some extent by taking a
QR code as the container of copyright information.
In summary, the existing watermarking schemes of vector maps mostly concentrate on the
methods of watermark embedding and extraction, while little attention has been paid to the
generation and embedding methods of rich-information watermark data. With the increasingly
rampant torts of vector maps, rich-information watermark data is being more and more
significant for powerfully declaring of ownership. In the case of a limited number of vertices,
researchers used to improve watermark capacity to the best of their ability, for the purpose of
embedding more watermark information into vector maps. The effect, however, is not ideal. In
some special applications, where the number of map vertices is limited and rich copyright
information is required, current watermarking algorithms cannot meet the demand.
To fill this gap, a novel rich-information reversible watermarking algorithm is put forward
for vector maps in this paper, based on the compression coding method of watermarking image
and the decimal-hex conversion of vertex coordinates. The original watermarking image,
containing rich copyright information, is firstly losslessly compression coded to shorten the
length of the final watermark data, so that the robustness of this scheme can be guaranteed
under the condition of rich-information watermark embedding. After watermark extraction, the
original watermarking image can be generated by decompressing the extracted watermark
data. The most important innovation of this paper is that the length of final watermark data is
reduced significantly exploiting the designed lossless compression coding method, which will
also be a certain reference for some other technically related applications, e.g., steganography,
data hiding, etc.
The rest of this paper is organized as follows. Section 2 describes the basic principle of
lossless compression coding of watermarking image. Then, the designed rich-information and
reversible watermarking scheme of vector maps is introduced in detail in Section 3. Finally,
performance study and conclusions are given in Section 4 and Section 5, respectively.
2 Compression & decompression coding of watermarking image
2.1 Compression coding of watermarking image
For a given meaning of copyright information, whether its type is text, sound, image or video,
it is generally required to be converted into a sequence of binary values (0 and 1, or 1 and − 1),
so that it can be embedded expediently into the host data. Accordingly, binary images are
usually exploited in common digital watermarking algorithms, as the carrier of copyright
information. Given a a × b (unit: pixel) watermarking image s, the process of compression
coding can be demonstrated as follows:
(1) Divide s into several 2 × 2 blocks. It is obviously that both a and b should be even
numbers, so that the division process can be successfully completed. Here, if a (resp. b) is
an odd number, a new column (resp. row) on the right (resp. bottom) side will be added
into s, and all the newly added pixels are set white.
(2) Replace every 2 × 2 block with a single value. It can be inferred that there are 16 (24)
possible values of 2 × 2 blocks in s, for the two-value characteristic of pixels. Therefore,
each 2 × 2 block can be expressed by a hex value. The correspondence established in this
paper between hex values and all possible 2 × 2 blocks is shown in Table 1.
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Table 1 The correspondence between hex values and 2 × 2 blocks
Hex value
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
2×2 block
Hex value
2×2 block
(3) Generate a 2D array s′ based on s, replacing every 2 × 2 block with its corresponding
hex value. s′, the result of compression coding of s, is taken as the final watermark
data. It can be inferred that the size of s′ is a =2 b 2 . Here, ⟨∙⟩ means the
rounding function.
An example of watermark generation based on compression coding is shown in Fig. 1, where
Fig. 1a is the original binary watermarking image whose size is 22 × 17 (unit: pixel), Fig. 1b
represents the pretreated counterpart of Fig. 1a whose size is 22 × 18 (unit: pixel), and Fig. 1c
is the final generated watermark data whose size is 11 × 9.
2.2 Decompression coding of watermark extraction result
Let w ′ , a a ′ × b ′ 2D array, be the result of watermark extraction. The original
watermarking image can be generated by decompressing w′, the process of which can
be described as follows:
(1) Define a 2a′ × 2b′ blank image, named s′′.
(2) For each w′[i, j], exploit its corresponding 2 × 2 block (assumed M[i, j]) to assign s′′. Let
M[i, j]1 M[i, j]2, M[i, j]3 and M[i, j]4 denote the upper-left, upper-right, lower-left and
lower-right pixel of M[i, j], respectively. Then, order s′′[2i, 2j] = M[i, j]1, s′′[2i, 2j + 1] =
M[i, j]2, s′′[2i + 1, 2j] = M[i, j]3, s′′[2i + 1, 2j + 1] = M[i, j]4.
(3) For the assigned s′′, if the row (resp. column) at the bottom (resp. right) side is composed
of only white pixels, remove it from s′′.
(4) The processed s′′ is considered as the decompression result of w′, i.e., the obtained
watermarking image.
(a) The original binary image
(b) The pretreated counterpart of (a)
Fig. 1 An example of watermark generation
(c) The obtained watermark data
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Figure 2 shows an example of decompression coding of watermark extraction result, where
Fig. 2(a) stands for the result of watermark extraction whose size is 11 × 9, Fig. 2(b) denotes
the generated binary image according to Fig. 2(a) whose size is 22 × 18 (unit: pixel), and Fig.
2(c) stands for the final obtained watermarking image whose size is 22 × 17 (unit: pixel).
3 The proposed scheme
The proposed watermarking scheme will be described in four stages in this section. The method of
map vertex grouping will be explained firstly in Section 3.1. Then, it will be represented in
Section 3.2 that how to generate watermark data. After that the procedure of watermark
embedding and extraction will be described in detail in Section 3.3 and Section 3.4, respectively.
3.1 Vertex grouping
Map vertices are grouped in this paper to enhance the robustness of the proposed scheme,
based on feature vertex extraction. Given a vector map, the procedure of vertex grouping can
be summarized as follows:
(1) Extract feature vertices exploiting the classic Douglas-Peucker algorithm [8]. Given a
polyline, the procedure of feature vertex extraction can be demonstrated as the
following steps:
Step 1: Make a dotted line which connects the starting and the finishing vertex of the
polyline.
Step 2: Calculate distances from each vertex to the made dotted line, and then select the
maximum distance value (assumed dmax).
Step 3: According to the given simplified threshold T, the extraction of feature vertices can
be summarized as follows:
If dmax < T: Ignore all vertices of the polyline, and there is no feature vertices.
If dmax ≥ T: Select the corresponding vertex of dmax, based on which the polyline can be
divided into two individual parts. Then, repeat the extraction operation for each part,
respectively.
An example of Douglas-Peucker algorithm is shown in Fig. 3.
(2) Determine the reference vertex of the given vector map, based on the extracted feature
vertices. The coordinate of the reference vertex can be calculated by Eq. 1, where (xr, yr)
represents the rectangular coordinate of the determined reference vertex, (x*i ; y*i ) denotes
(a) The extracted watermark data
(b) The assigned
Fig. 2 An example of decompression coding of watermark extraction result
(c) The obtained watermarking image
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v3
v3
v1
v4
v2
v1
v5
v0
v4
v2
v6
v0
v5
v6
(a) Step 1
(b) Step 2
v3
v3
v1
v1
v2
v0
v6
(c) Step 3
v0
v6
(d) Step 4
Fig. 3 An example of feature vertex extraction
the integer portion of rectangular coordinate of the i − th feature vertex, n means the
number of feature vertices and ⟨∙⟩ stands for the rounding function.
8
n−1
>
> xr ¼ 1 ∑ x*i
<
n i¼0 ð1Þ
1 n−1 *
>
>
: yr ¼
∑ yi
n i¼0
Assume that vf = {v1, v2, v3, v4, v5} is the sequence of feature vertices, and (137.365467,
269.654654), (256.565845, 452.944654), (217.346216, 328.415594), (319.761462,
442.573615) and (618.721209, 411.436385) are the rectangular coordinates of v1, v2, v3, v4
and v5, respectively. Then,
1
ð137 þ 256 þ 217 þ 319 þ 618Þ ¼ h309:4i ¼ 309
xr ¼
5
yr ¼
1
ð269 þ 452 þ 328 þ 442 þ 411Þ ¼ h380:4i ¼ 380
5
(3) Group map vertices based on the obtained reference vertex. Make a number of concentric
circles, taking the determined reference vertex as the center. The vertices between every
two adjacent concentric circles form a vertex group. The diagram of vertex grouping is
shown in Fig. 4.
It is obvious that the result of vertex grouping is immune to geometric transformation,
which can improve theoretically the robustness of the proposed scheme to a certain
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ĂĂ
Reference vertex
Map vertex
Fig. 4 The diagram of map vertex grouping
extent. It can be also concluded here that the value of radii of the concentric circles
determine directly the result of vertex grouping. Consequently, radii of the concentric
circles must be systematically chosen so that the result of vertex grouping can be
relatively stable. In this paper, radii of the concentric circles form an arithmetic progression, the common difference of which is calculated according to the vertex density of the
host vector map, i.e., the number of vertices per square kilometer. And the obtained
common difference of radii of the concentric circles is taken as secret key, which will be
exploited again in the watermark extraction phase.
3.2 Watermark generation
Given a D × D (unit: pixel) watermarking image, the procedure of watermark generation can
be summarized as the steps listed below:
(1) Scramble the given watermarking image exploiting Arnold transformation, so that the
security of the original copyright information can be further enhanced.
Eq. 2 shows the formula of Arnold transformation, where (x, y) and (x′, y′) denote the original
and the transformed coordinates of a pixel respectively.
x′
1 1
x
¼
mod D
ð2Þ
y′
1 2
y
An example of Arnold transformation is shown in Fig. 5, from which it can be seen that Arnold
transformation is cyclical. It can be thus inferred that the scrambling operation has a small secret key
space due to the periodicity of Arnold transformation. An optimized scrambling algorithm is
exploited in this paper to solve this problem, which can be demonstrated as the following two steps:
Step 1: Select four square sub-images Q0, Q1, Q2 and Q3 from the original image, satisfying
the condition that Q0 ∪ Q1 ∪ Q2 ∪ Q3 = P and Qi ∩ Qj ≠ ∅ (0 ≤ i ≤ 3, 0 ≤ j ≤ 3).
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(a) Original image
(b) Once
(c) 12 times
(d) 24 times
(e) 48 times
Fig. 5 An example of Arnold transformation
Step 2: One after another, conduct Arnold transformation on Q0, Q1, Q2 and Q3 for t0, t1, t2
and t3 times, respectively.
Take the image shown in Fig. 5(a) as example, whose size is 64 × 64 (unit: pixel), the result of
sub-image selection is shown in Fig. 6. Here, the sizes of Q0, Q1, Q2 and Q3 are 40 × 40, 50 × 50,
55 × 55 and 45 × 45, respectively (unit: pixel). And t0, t1, t2 and t3 are assigned 10, 20, 26 and 40,
respectively. The scrambling result exploiting the optimized algorithm is shown in Fig. 7.
From the example shown in Fig. 6 and Fig. 7 it can be obviously seen that the security of
copyright information is doubly guaranteed. Firstly, the selection result of four sub-images is
secretive, it is accordingly difficult to break through the scrambling method. Moreover, the
confidentiality of both the times and the order of transformation of the four sub-images can
further enhance the security of original copyright information. Consequently, it is hardly
possible in theory for unauthorized users to break the optimized algorithm.
(2) Generate the final watermark data based on the scrambled watermarking image, as
described in Section 2.1. It can be inferred that the obtained watermark data is a 2D
array, the number of rows and columns of which is both D =2 . Here, ⟨∙⟩ means the
rounding function.
3.3 Watermark embedding
It is obvious that the final watermark data in this scheme is a sequence of hex values. To embed
watermarks, vertex coordinates are decimal-to-hex converted accordingly, and the
watermarked hex coordinates are converted into decimal ones after watermark embedding.
Given
the
original
vector
map
V
and
watermark
data
D D w ¼ w½i; j; 0≤i ≤ =2 −1; 0≤ j ≤ =2 −1 , the procedure of watermark embedding is
shown in Fig. 8, which can be demonstrated as the following steps:
Step 1: Group map vertices as described in Section 3.1.
Step 2: Group by group, convert rectangular coordinates of map vertices into polar ones,
taking the reference vertex as coordinate origin and any random direction as basic
axis. The formula of polar coordinate conversion is shown in Eq. 3, where (xi, yi) and
Q0
Q1
Fig. 6 The selection result of four sub-images
Q2
Q3
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(a) Result after scrambling
(b) Result after scrambling
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(c) Result after scrambling
(d) Result after scrambling
Fig. 7 An example of the optimized Arnold transformation
(ρi, θi) are the rectangular and the polar coordinate of the i − th vertex respectively,
(xr, yr) denotes the rectangular coordinate of the reference vertex.
8
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
>
< ρi ¼ ðxi −xr Þ2 þ ðyi −yr Þ2
y −y
>
:
θi ¼ tan−1 i r
xi −xr
ð3Þ
Step 3: Establish correspondence between watermark bits and map vertices. Take a vertex Vt
as example, the homologous watermark bit wt can be calculated by Eq. 4, where
Hash1(∙) and Hash2(∙) are two existing functions which transform an input with
arbitrary length into an output with a fixed length, x*t ; y*t denotes the integer
portion of the rectangular coordinate of Vt, and (xr, yr) means the rectangular coordinate of the reference vertex.
8
¼ w½ f ðxÞ; gðxÞ ffi
wtffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
>
q
>
>
>
2
2
<
f ðxÞ ¼ Hash1
mod D 2
x*t −xr þ y*t −yr
ð4Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
>
>
D 2
2
>
>
mod
x*t −xr þ y*t −yr
: gðxÞ ¼ Hash2
2
Feature
vertices
Original vector
map V
Feature vertex
extraction
Non-feature
vertices
Vertex
grouping
Vertex
groups
Polar coordinate conversion
Decimal-to-hex conversion
Watermark
data w
Watermark
embedding
Watermarked
coordinates
Converted
coordinates
Hex-to-decimal
conversion
Fig. 8 The flow chart of watermark embedding procedure
Rectangular
coordinate
conversion
Watermarked
vector map V
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Step 4: Embed watermark bits into polar coordinates of all map vertices. Take a vertex Vn as
example, let (ρn, θn) and wn be its polar coordinate and corresponding watermark bit,
respectively. The portion after the fifth digit after decimal point of ρn is firstly converted
into hex values and a new number (assumed ρn(h)) can be obtained, and wn is then
inserted into ρn(h), between the fifth and the sixth digit after decimal point. Finally,
0
0
convert the watermarked ρn(h) (assumed ρn ðhÞ) into a decimal value (assumed ρn ).
For example, assume that ρn = 693.52761263 and wn = 6, then,
ρn ðhÞ ¼ 693:52761107
↓
0
ρn ðhÞ ¼ 693:527616107
↓
0
ρn ¼ 693:5276124839
0
It can be obviously seen from this step that Δρ ¼ ρn −ρn < 1 10−5 . Moreover, it can be
0
0
inferred that Δx ¼ xn −xn < 1 10−5 and Δy ¼ yn −yn < 1 10−5 , in the light of the
relation between Cartesian and polar coordinates. Therefore, the integer portion of rectangular
coordinates of map vertices will not be changed during the watermark embedding process. It
can be accordingly concluded that the established mapping relation between map vertices and
watermark bits is constant during the watermark embedding procedure. Furthermore, the result
of vertex grouping will not be distorted during the watermark embedding procedure in theory.
Step 5: Convert the watermarked polar coordinates of map vertices into rectangular ones.
Taking a vertex Vn as example, the method of rectangular coordinate conversion is
0
0
0
shown in Eq. 5, where ρn ; θn and xn ; yn denote the watermarked polar and
rectangular coordinate of Vn respectively, (xr, yr) means the rectangular coordinate of
the reference vertex.
0
0
xn ¼ xr þ ρn •cosθn
0
0
yn ¼ yr þ ρn •sinθn
ð5Þ
From the aforementioned watermark embedding process it can be inferred that a watermark bit
can be embedded into several vertices simultaneously, which can improve the robustness of this
scheme under certain map attacks, e.g., vertex deleting, data compression, map clipping, etc.
3.4 Watermark extraction
As shown in Fig. 9, the watermark extraction procedure is the reverse procedure of watermark
embedding. Given a watermarked vector map V′, the procedure of watermark extraction can be
demonstrated as follows:
Step 1: Group map vertices and convert rectangular coordinates of map vertices into polar
ones, as described in Step 1 and Step 2 of Section 3.3.
0 0
0
Step 2: Extract watermark bits from map vertices. For each map vertex V n ρn ; θn , convert the
0
portion after the fifth digit after decimal point of ρn to hex values and a new number
0
(assumed ρn ðhÞ) can be obtained. Afterwards, extract the sixth digit after decimal point
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Feature
vertices
Watermarked
vector map Vÿ
Feature vertex
extraction
Vertex
grouping
Vertex
groups
Non-feature
vertices
Polar coordinate conversion
Decimal-to-hex conversion
Converted
coordinates
Original
watermarking
image
Recovered
vector map Vā
Watermark
data wÿ
Decompression
Arnold inverse
transformation
Rectangular
coordinate
conversion
Watermark
extraction
Hex-to-decimal
conversion
Non-watermarked
coordinates
Fig. 9 The flow chart of watermark extraction procedure
0
0
0
0
of ρn ðhÞ as watermark bit wn . Then, remove wn from ρn ðhÞ, and another new value
0
(assumed ρn0 ðhÞ) can be generated. Finally, convert the portion after the fifth digit after
0
0
decimal point of ρn0 ðhÞ into decimal values, and a new number (assumed ρn0 ) can be
0 0
0
obtained. ρn0 ; θn is considered as the recovered polar coordinate of V n .
0
Take the data in Step 4 of Section 3.3 as example, i.e., ρn ¼ 693:5276124839, then,
0
ρn ðhÞ ¼ 693:527616107
↓
00
0
ρn ðhÞ ¼ 693:52761107; wn ¼ 6
↓
00
ρn ¼ 693:52761263
0
0
Step 3: Define a 2D array w ¼ w ½i; j; 0 ≤i≤ D =2 −1; 0≤ j ≤ D =2 −1 , and assign it
based on the extracted watermark bits. Correspondence between elements of w′
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and the obtained watermark bits can be established by the same method with that in
Eq. 4. And a simple statistical strategy is used here for optimal value selection.
Step 4: Decompress w′ exploiting the method mentioned in Section 2.2. And a binary image
can be obtained, assumed c.
Step 5: Conduct Arnold inverse transformation on c. Firstly, select four square sub-images
0
0
0
0
Q0 , Q1 , Q2 and Q3 from c, as described in Section 3.2. Then, one after another,
0
0
0
0
conduct Arnold transformation on Q3 , Q2 , Q1 and Q0 for (T3 − t3), (T2 − t2), (T1 − t1)
and (T0 − t0) times, respectively. Here, T0, T1, T2 and T3 respectively stand for the
0
0
0
0
Arnold transformation cycle of Q0 , Q1 , Q2 and Q3 , and t0, t1, t2 and t3 are explained
in Section 3.2. The transformed c, assumed c’, is considered as the obtained
watermarking image.
4 Experiments and discussion
Fifty different vector maps (in .shp format) are adopted in this section as original data to test
the performance of the proposed watermarking scheme. Table 2 lists some basic properties of
the fifty maps, i.e., scale, number of features, number of vertices and coordinate range. The
experiments mentioned in this section are implemented on a PC with Intel Core i5 CPU
(2.9GHz), 4G RAM and Win7 Professional, exploiting ArcGIS 10.2, Visual Studio 2010 and
C# programming language.
The exploited watermarking image, a 60 × 54 (unit: pixel) binary image, is shown in Fig.
10. The watermark data is generated according to the method mentioned in Section 3.2, which
is then embedded into the fifty experimental vector maps respectively, exploiting the method
introduced in Section 3.3.
In addition, to evaluate further the ability of the proposed watermarking scheme in aspects
of robustness and rich copyright information expression, four representative watermarking
schemes are selected for contrast experiments. The basis for selecting schemes in this paper
contains two aspects, i.e., published in recent five years and has a preferable performance in
aspects of both robustness and rich copyright information expression.
4.1 Discussion about rich-information characteristic
It is a common goal for all watermarking algorithms to embed watermark bits into cover data
as more as possible, and a great deal of achievements have been obtained. The main purpose of
conventional schemes, however, is to increase the repeated embedding times of watermark bits
and thus enhance the robustness of watermarking algorithms, and watermark capacity is
generally exploited as the evaluating factor. Nevertheless, traditional evaluating methods
cannot be directly applied to estimate the rich-information characteristic of watermarking
schemes, for the essential difference between the total embedded watermark bits and the
length of copyright information contained in the watermark data. To evaluate effectively the
performance of watermarking algorithms in terms of rich-information watermark embedding,
watermark payload is exploited in this paper as the evaluating indicator, which means the ratio
of the length of copyright information and the total number of watermark bits.
The watermark payload of this scheme is higher in theory than traditional schemes, owing
to the significant reduction of the length of watermark data. To evaluate the performance of the
Scale
1:500,000
1:500,000
1:500,000
1:500,000
1:500,000
1:500,000
Vector map
map-0
map-1
map-2
map-3
map-4
Average of 50 maps
151
219
599
221
48
328.6
Number of features
Table 2 Properties of experimental vector maps
8757
9420
15,936
8106
7609
10,165.2
Number of vertices
Coordinate range (y)
2,375,444.14238~6,309,648.62964
4,641,428.40461~5,907,139.84753
3,594,108.59874~3,846,608.94995
516,977.54559~6,385,320.29008
1,574,799.81646~6,106,427.17171
2,434,361.75436~3,853,206.23831
Coordinate range (x)
−1,506,755.72638~2,041,078.07683
−2,543,657.93085~ − 693,356.65491
670,494.17024~976,724.06626
−1,878,821.94721~2,092,054.12033
−2,499,621.79553~1,962,910.54399
−3,240,483. 68,131~202,054.09658
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Fig. 10 The watermarking image
proposed watermarking scheme in terms of rich-information characteristic, comparisons have
been made among this scheme and four state-of-the-art works. The comparison result is shown in
Table 3, from which it can be obviously seen that the length of watermark data in the proposed
scheme is shortened by a big margin without affecting evidently the expression of copyright. The
result in Table 3 indicates that the proposed watermarking scheme has a satisfying performance in
terms of rich-information characteristic, compared with conventional schemes.
4.2 Discussion about reversibility
The watermark extraction procedure explained in Section 3.4 shows that the embedded
watermark bits can be precisely removed from the watermarked vector maps. The proposed
algorithm is thus accurate reversible in theory. A set of experiments were carried out to verify
the reversibility of this scheme, exploiting the fifty watermarked vector maps. Firstly, extract
watermark bits and recover the original map content, as described in Section 3.4. Afterwards,
calculate coordinate difference between original map vertices and their recovered counterparts.
0
0
0
Taking an original vertex vi(xi, yi) and its recovered counterpart vi xi ; yi as example, the
corresponding coordinate difference can be calculated according to Eq. 6.
Erðvi Þ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 2
0 2
ðxi −xi Þ þ ðyi −yi Þ
ð6Þ
The experimental result shows that for each vi(0 ≤ i < n), Er(vi) = 0 (n denotes the amount of
map vertices). The reversibility of the proposed scheme is thus well validated.
Table 3 Comparison result of watermark payload
Watermarking scheme
The length of copyright
information (bit)
The length of watermark
data (bit)
Watermark payload
Scheme in [24]
Scheme in [6]
Scheme in [19]
Scheme in [18]
This scheme
16
232
328
688
320
2048
6400
2112
2401
810
0.0078
0.0363
0.1553
0.2865
0.3951
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4.3 Discussion about invisibility
As discussed in Step 4 of Section 3.3, only the digits after the fifth digit after decimal point of
vertex coordinates are disturbed during the watermark embedding procedure. Accordingly, the
original vector maps will not change tremendously in sight after watermark embedding in
theory. Figure 11 shows one of the fifty experimental vector maps, as well as its watermarked
counterpart. Figure 11 verifies that it is difficult to distinguish the two vector maps from the
visual point of view.
Error analysis was then carried out between the original vector maps and their watermarked
counterparts to thoroughly test and verify the invisibility of this scheme. Max. Error and rootmean-square error (RMSE) were adopted here to express the distortion of the experimental
vector maps, which can be calculated by Eq. 7. Here, n means the total number of map
0
0
vertices, (xi, yi) and xi ; yi stand for the rectangular coordinate of the i − th vertex and its
watermarked counterpart, respectively.
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
8
0 2
0 2
>
>
ðxi −xi Þ þ ðyi −yi Þ ; 0≤i ≤n−1
>
< Max:Error ¼ Max
ffi
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
>
1 n−1
0 2
0 2
>
>
∑ xi −xi þ yi −yi
; 0≤i ≤n−1
: RMSE ¼
n i¼0
ð7Þ
The result of error analysis is illustrated in Table 4, from which it can be seen that both Max.
Error and RMSE of the fifty experimental vector maps are acceptable (less than 1 × 10−5). A
conclusion can be thus drawn that the visualization of the fifty vector maps is not affected
during the watermark embedding procedure.
(a) The original vector map and its local magnification effect
(b) The watermarked vector map and its local magnification effect
Fig. 11 An example of watermark embedding
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Table 4 Result of error analysis
Vector map
Max.Error
RMSE
map-0
map-1
map-2
map-3
map-4
Average of 50 maps
0.00000876
0.00000835
0.00000908
0.00000785
0.00000896
0.00000835
0.00000488
0.00000364
0.00000420
0.00000408
0.00000293
0.00000364
4.4 Discussion about robustness
As a kind of digital products, vector maps may be attacked during the process of both
transmission and application. According to the different types, the possible attacks that vector
maps frequently suffer can be classified into geometric attacks and non-geometric attacks.
While geometric attacks (e.g., translation, rotation, etc.) may change vertex coordinates
directly and thus affect the result of watermark extraction, non-geometric attacks (e.g.,
simplification, vertex reordering, etc.) disturb watermark extraction by changing the storage
order of vertices, increasing (decrease) the number of vertices, etc.
A series of simulating experiments were carried out in this section to evaluate the ability of
the designed algorithm in resisting common attacks, using BER (Bit error rate, the ratio of
error pixels to the total pixels of the obtained watermarking image) and NC (Normalized
Correction, the similarity between the original watermarking image and the extracted one) are
used to evaluate the effect of watermark extraction. Eq. 8 shows the calculation method of NC,
where w and w′ stand for the original and the extracted watermarking image respectively.
0
∑ wi; j wi; j
i; j
NC ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
0 2
2
∑ wi; j
∑ wi; j
i; j
ð8Þ
i; j
4.4.1 Vertex reordering
Vertex reordering, one of the common attacks of vector maps, may change the organization
structure of the watermarked vector maps, and thereby influence the result of watermark
extraction. In this scheme, both the vertex grouping result and the watermark embedding
procedure are independent of the result of vertex ordering, and it can be thus inferred that the
designed algorithm is immune to vertex reordering operation.
4.4.2 Map translation and rotation
It can be inferred from the angle of theoretical analysis that the proposed watermarking
algorithm is immune to map translation and rotation, due to the stability of both vertex
grouping result (described in Section 3.1) and polar coordinates of map vertices under
geometric transformation.
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Afterwards, a set of simulating experiments were conducted to test the robustness of this scheme
under map translation and rotation. Table 5 shows the experimental results, where s (θ) means the
distance (angle) of translation (rotation). A conclusion can be drawn from Table 5 that the designed
watermarking algorithm is quite robust under map translation and rotation operations.
4.4.3 Vertex addition and deletion
Vertex addition and deletion are two common attacks that vector maps frequently suffer, which
may impact on the robustness of algorithms for vector maps. Vertex addition attack may draw
into some interference vertices which will affect the result of watermark extraction, while
vertex deletion operation will lead to the loss of a section of map vertices, as well as the
embedded watermarks. As described in Section 3.3, the mapping between watermark bits and
map vertices is a one-to-many relationship, which is theoretically helpful to enhance the
robustness of this scheme under vertex addition and deletion attacks. In addition, the statistical
method for optimal value selection exploited in the watermark extraction phase can further
help to prevent the result of watermark extraction from being affected by the introduced
interference vertices. Accordingly, the watermarking algorithm put forward in this paper is
robust under vertex addition and deletion attacks in theory.
To verify the robustness of this scheme from the angle of simulation experiment, a set of
experiments were designed and carried out in this section. Watermarks were firstly embedded
into the fifty experimental vector maps using the method mentioned in Section 3.3, and then
add (resp. delete) randomly some vertices into (resp. from) the watermarked vector maps.
Finally, extract watermarks from the fifty attacked vector maps based on the method introduced in Section 3.4. Table 6 shows the experimental results, where p and q denote the portion
of the added and deleted vertices, respectively. It can be obviously seen from Table 6 that the
algorithm presented in this paper has a satisfactory performance in resisting vertex addition/
deletion attacks.
4.4.4 Data compression
Data compression is another kind of operations which vector maps frequently suffer during the
process of data transmission and application. It is obviously that data compression will lead to
the loss of some watermarked vertices and thus influence on the result of watermark extraction.
Table 5 Results of watermark extraction after map translation/rotation
Vector map
map-0
map-1
map-2
Average of 50
maps
Translation (s)
Rotation (θ)
s=6.42365
s=58.374512
s=252.385407 θ=3.65°
θ=33.52°
θ=90°
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
BER = 0.00%
NC = 1.0000
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Table 6 Results of watermark extraction after vertex addition/deletion attacks
Vector
map
Vertex addition
Vertex deletion
p=40%
p=50%
p=60%
q=40%
q=50%
q=60%
BER=1.85%
NC=0.9570
BER=3.15%
NC=0.9277
BER=6.27%
NC=0.8586
BER=2.01%
NC=0.9534
BER=3.24%
NC=0.9258
BER=6.48%
NC=0.8527
BER=1.79%
NC=0.9584
BER=2.99%
NC=0.9307
BER=6.02%
NC=0.8634
BER=1.88%
NC=0.9562
BER=3.09%
NC=0.9288
BER=6.14%
NC=0.8590
BER=1.70%
NC=0.9606
BER=2.84%
NC=0.9344
BER=5.59%
NC=0.8727
BER=1.67%
NC=0.9612
BER=2.90%
NC=0.9330
BER=5.77%
NC=0.8679
BER=1.77%
NC=0.9591
BER=2.95%
NC=0.9312
BER=5.98%
NC=0.8655
BER=1.84%
NC=0.9575
BER=3.03%
NC=0.9301
BER=6.03%
NC=0.8610
map-0
map-1
map-2
Average of
50 maps
Simulation experiments have been carried out in this section to evaluate the ability
of the proposed algorithm in resisting data compression operations. Watermarks were
firstly embedded into the fifty experimental vector maps exploiting the method
introduced in Section 3.3, and the classical Douglas- Peucker algorithm was then
conducted on the watermarked vector maps with different intensities. Finally, watermarks were extracted by the method mentioned in Section 3.4. To further validate the
performance of this scheme under data compression, comparisons have been made
among this scheme and four reprehensive schemes [6, 18, 19, 24] under the same
conditions.
The comparison result is illustrated in Table 7, indicating that the watermarking scheme
presented in this paper has a stronger ability than state-of-the-art works in resisting data
compression operations.
4.4.5 Map clipping
Map clipping refers to delete all vertices within the specified area in the original
vector maps. Similar to vertex deletion and data compression, map clipping will also
lead to the loss of some watermarked map vertices and thus have an effect on the
result of watermark extraction.
Another set of simulation experiments were designed and done in this section to test
the robustness of the proposed scheme under map clipping attacks. And to further
evaluate the performance of the proposed watermarking scheme in resisting map clipping
attacks, comparisons were made among this scheme and four reprehensive schemes [6,
18, 19, 24] under the same conditions. The comparison result shows that the
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Table 7 Robustness comparison among this scheme and state-of-the-art works under data compression operations
Vector map
Scheme
40%
50%
60%
BER=2.10%
NC=0.9511
BER=3.12%
NC=0.9283
BER=6.57%
NC=0.8516
BER=2.90%
NC=0.9328
BER=4.20%
NC=0.9026
BER=8.58%
NC=0.8061
BER=2.96%
NC=0.9315
BER=4.29%
NC=0.9023
BER=8.80%
NC=0.8026
BER=3.06%
NC=0.9294
BER=4.44%
NC=0.8981
BER=9.20%
NC=0.7954
BER=2.78%
NC=0.9358
BER=4.01%
NC=0.9074
BER=8.21%
NC=0.8147
This scheme
BER=1.92%
NC=0.9553
BER=3.05%
NC=0.9293
BER=6.07%
NC=0.8613
Scheme in [2]
BER=2.78%
NC=0.9355
BER=4.09%
NC=0.9057
BER=8.44%
NC=0.8099
Scheme in [20]
BER=2.85%
NC=0.9342
BER=4.16%
NC=0.9043
BER=8.64%
NC=0.8068
Scheme in [23]
BER=2.94%
NC=0.9325
BER=4.30%
NC=0.9016
BER=9.02%
NC=0.7993
Scheme in [25]
BER=2.63%
NC=0.9389
BER=3.86%
NC=0.9114
BER=8.03%
NC=0.8191
This scheme
Scheme in [2]
map-0
Scheme in [20]
Scheme in [23]
Scheme in [25]
Average of 50
maps
watermarking scheme put forward in this paper has a stronger ability than state-of-the-art
works in resisting map clipping attacks. Table 8 illustrates the experimental result, taking
one of the fifty experimental vector maps as example.
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Table 8 Robustness comparison among this scheme and state-of-the-art works against map clipping
Clip
ratio
Extraction result
Clip position
This scheme
Scheme in [2]
Scheme in [20]
Scheme in [23]
Scheme in [25]
BER =2.01%
NC=0.9537
BER =2.81%
NC=0.9352
BER =2.87%
NC=0.9337
BER=2.90%
NC=0.9327
BER=2.56%
NC=0.9404
BER =2.96%
NC=0.9320
BER =4.04%
NC=0.9068
BER =4.17%
NC=0.9043
BER=4.32%
NC=0.9005
BER=3.77%
NC=0.9136
BER =6.30%
NC=0.8560
BER =8.30%
NC=0.8118
BER =8.58%
NC=0.8066
BER=8.89%
NC=0.8043
BER=7.75%
NC=0.8259
40%
50%
60%
5 Conclusions
Aiming to realize powerful copyright declaration, this paper proposes a richinformation and reversible watermarking scheme of vector maps based on compression coding of watermarking image and decimal-hex conversion of vertex coordinates.
The proposed watermarking scheme is robust under both geometric attacks (i.e.
translation, rotation and vertex reordering) and common non-geometric attacks (i.e.
vertex addition, vertex deletion, data compression and map clipping). Both theoretical
analysis and simulation experiments have demonstrated the rich-information characteristic, reversibility, invisibility and robustness of the proposed scheme.
The main idea of this paper is to realize rich-information watermark embedding by
shortening the length of watermark data, and there are two kinds of work which are
valuable to be further studied in the future work. Firstly, one of the disadvantages of
this scheme is that it cannot resist map scaling attacks, for the instability of polar
coordinates of map vertices under scaling operations, which is the cover data for
watermark embedding. More efforts should be put in the near future to find geometric
invariants of vector maps and consider them as the carrier for watermark embedding,
so that the robustness of watermarking algorithms against geometric transformation
can be effectively enhanced. In addition, the method of shortening the length of the
final watermark data should be further investigated, and lossless compression methods
of images, e.g., Huffman coding, Run-length coding, etc., may provide novel
solutions.
Acknowledgements This research is supported by the National Natural Science Foundation of China (Grant
No. 41171343) and the Start-up Project for Talents of Nanjing Institute of Geography & Limnology, CAS (Grant
No. NIGLAS2018QD07).
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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional affiliations.
Yinguo Qiu is currently a Research Assistant in Nanjing Institute of Geography and Limnology, Chinese
Academy of Sciences. He received his Ph.D. degree in University of Chinese Academy of Sciences in 2018.
His research interests include vector data watermarking and security of GIS data.
Hongtao Duan is currently a professor and a Doctoral Tutor in Nanjing Institute of Geography and Limnology,
Chinese Academy of Sciences. He received his Ph.D. degree in University of Chinese Academy of Sciences in
2007. His main research directions are digital watermarking and remote sensing of lake water color. He is now a
reviewer of a number of International Journals. In recent years, he has published more than 50 papers that are
indexed by SCI/EI retrieval.
Multimedia Tools and Applications (2019) 78:24955–24977
24977
Jiuyun Sun is currently an associate professor and a Master Tutor in School of Environment Science & Spatial
Informatics of China University of Mining & Technology. His main research directions are security of GIS data
and photographic survey.
Hehe Gu is currently a professor and a Doctoral Tutor in School of Environment Science & Spatial Informatics
of China University of Mining & Technology. His main research directions are cadastral surveying, land use
monitoring and security protection of vector data. In recent years, he has published more than 50 papers that are
indexed by SCI/EI/ISTP retrieval.