Digital Image Watermarking in different Color Models Rastislav HOVANČÁK, Dušan LEVICKÝ Dept. of Electronics and Multimedia Telecommunications, Technical University of Košice, Park Komenského 13 Košice, Slovak Republic,
[email protected],
[email protected]
Abstract: In recent years, access to multimedia data has become much easier due to the rapid growth of the Internet. While this is usually considered an improvement of everyday life, it also makes unauthorized copying and distributing of multimedia data much easier, therefore presenting a challenge in the field of copyright protection. Digital watermarking, which is inserting copyright information into the data, has been proposed to solve the problem. In this paper four original watermarking schemes based on DCT and DWT transformation for ownership verification and authentication of color images were proposed.
Keywords: Watermark; digital watermarking; watermark embedding and extraction.
1
Introduction
The rapid growth of the Internet increases access to multimedia data tremendously. Multimedia and computer networking have known rapid development and expansion. These facts, combined with more powerful image processing software present a challenge to copyright protection of multimedia data as unauthorized copying and distributing of digital images, video, etc. also become easier. Watermarking is a potential method for protection of ownership rights on digital data. Digital watermarking is a concept that emerged in the digital signal processing community in early 1990. It is process of embedding information directly into the digital data, also called original data, by making small modifications to them. The embedded information is called watermark. Depending on the application, the watermark itself may be a string of characters, a number, an image, a piece of sound, or just a 1-bit piece of information to indicate if the data has been watermarked [1].
The watermarks can be perceptually visible or invisible. We focus on invisible watermarks in this paper. With the detection/extraction of the watermark from the watermarked data, it has been claimed that digital watermarks can be used to identify the rightful owner, as well as the authenticity of a digital data. In general, there are two most common requirements of invisible watermarks. The watermarks should be perceptually invisible, i.e., they should not interfere with the media being protected. They should also be robust to common signal processing and intentional attacks. Attacks on digital watermarking schemes have two effects: either they reduce the effective channel capacity or fully disable the detection of the embedded watermark. Because it is not possible to enumerate all possible attacks, it is very difficult or even impossible to assess if a given system is robust in the general sense [2]. This paper deals with color image watermarking by using four different methods. Digital watermarks have form of binary images which are embedded into the different color models of original images.
2
Methods of Embedding and Extracting
In digital watermarking can be used many different approaches and techniques for watermarks embedding. Very important techniques are digital watermarking based on two-dimensional discrete cosine transformation (2D DCT) and twodimensional discrete wavelet transformation (2D DWT) [3,4]. In field of digital watermarking two basic methods are used: method using original image for extraction of watermark from image under test and method without using original image for extraction of watermark from image under test.
2.1
Methods 1 and 3 - DCT and DWT Method using Original image for Extraction of Watermark
In method 1 the original image X is divided into blocks of 8x8, and each block is DCT transformed independently. Only ((64xM1xM2)/N1xN2) coefficients are selected out of the 64 DCT coefficients for each 8x8 image block. Those selected coefficients are then mapped into reduced image blocks of size (M1x8/N1)x(M2x8/N2). The coefficients selected from the image of size (N1xN2) are collected to compose a reduced block of coefficients. This block has same size (M1xM2) as the binary watermark. We denote watermark’s coefficient as w(x,y) and c(x,y) as DCT coefficient. Modified coefficient can be expressed in the form:
Watermark (M1 x M2)
Original Image (N1 x N2)
W
X
Image under test
Secret Key
XT
K
X
Methods 2,4 Choice of primary from Color model
Pseudorandom permutation
2D transformation
Original Image
Methods 1,3
Choice of primary from Color model
Choice of primary from Color model
2D transformation
2D transformation
Modification of transformation coefficients
Extraction and comparison of transformation coefficients
Inverse 2D transformation
Inverse permutation
Watermarked Image
Secret
XW
K Key
Extracted Watermark
W´
Fig. 1 Embedding and extracting process
m( x,y ) = c ( x, y ) + α if w( x, y ) = 1
(1)
m(x,y ) = c ( x, y ) − α if w( x, y ) = 0
(2)
where α is a real number. Extracting process is shown in Fig.1. After transformation of image under test and original image we compute differences between coefficients as follows:
if m( x, y ) − d ( x, y ) ≥ 0 ⇒ w′( x, y ) = 1
(3)
if m(x, y ) − d ( x, y ) < 0 ⇒ w′( x, y ) = 0
(4)
where m(x,y) is watermarked coefficient, d(x,y) is original coefficient and w´(x,y) is coefficient of extracted watermark. Embedding process of method 2 is very similar to embedding process of method 1. Firstly, the original image X is transformed using 2D DWT. Then some coefficients are extracted from the block of DWT coefficients to compose a reduced block of coefficients. This block (M1xM2) is modified using equastions
(1) to (4). Finally modified coefficients are transformed using inverse 2D DWT to obtain watermarked image.
2.2
Method 2 and 4 - DCT and DWT Method without using Original image for Extraction of Watermark
Methods 2 and 4 have main advantage opposite to Methods 1and 3, that don’t need original image in extracting process [4]. One bit of watermark for 3 DCT (DWT) coefficients is used, therefore number of necessary coefficients from each block of 8x8 DCT coefficients for whole watermark is 3x((64xM1xM2)/N1xN2). Similarly, 3 DWT blocks of size (M1xM2) are needed for embedding in method 4. Extracted coefficients are compared each other (L-low, M-medium, H-high). It stands to reason, there exist 33=27 combinations, but some combinations are not used. All combinations, which represent embedding of watermark bit 0 or 1 are in Tab.1. Embedding of watermark means changing arbitrary combination to required combination in this method. If extracted combination doesn’t corresponds with combination from Tab.1 we have to change this combination. Embedding process for bit “0” of watermark is described in Tab.2. Firstly extracted combination with combinations represent bit “0” of watermark is compared, and from this comparison type (sequence) of choice of coefficients is obtained. Finally extracted coefficients are changed using constant “α”. Bit of watermark
0
1
Combinations C1
C2
C3
L
M
H
M
L
H
L
L
H
M
H
L
H
M
L
H
H
L
Tab.1 Combinations represents embedded bit 0 and 1.
For extraction of watermark, at first DCT or DWT coefficients using information about type of choice are extracted. Result of this operation are combinations (LMH, etc.), which are compared with combinations from Tab.1. If extracted combination is identical with one of first three combinations (for example MLH), then extracted bit of watermark is “0”. Extracting process for bit “1” is same. If extracted combination is not in Tab.1, then extraction of bit is failed [4].
“0”
Change of combination
Type of choice
CW1
1.
LMH
1
2.
MLM
1
3.
LLH
4.
CW2
CW3
C1-α
C2
C3+α
C1
C2-α
C3+α
1
C1-α
C2-α
C3+α
MHL⇒MLH
2
C1
C2+α
C3-α
5.
HML⇒LMH
3
C1+α
C2
C3-α
6.
HHL⇒HML⇒LMH
3
C1+α
C2
C3-α
7.
MMM⇒LMH
1
C1-α
C2
C3+α
8.
LHL⇒LLH
2
C1-α
C2+α
C3-α
9.
LHH⇒LMH
1
C1-α
C2
C3+α
10.
LHM⇒LMH
2
C1-α
C2+α
C3
11.
HLL⇒LLH
3
C1+α
C2-α
C3-α
12.
HLH⇒MLH
1
C1
C2-α
C3+α
13.
HLM⇒MLH
3
C1+α
C2-α
C3
Tab.2 Modification of transformation coefficient, when bit of watermark is 0.
3
Color Models
Set of basic color, method of color mixture and rules of alternating color characteristics characterize the color models. In all watermarking methods are used the following color models:
4
•
RGB model (Red, Green, Blue)
•
CMY model (Cyan, Magenta, Yellow)
•
YUV model (Y-luminance primary, U,V-chrominance primary)
Experimental Results
For our experimental results we used pictures lenna, montage and camera (256x256x24b) and two digital watermarks (32x32x1b). Four different groups of attacks can be identified: removal attacks, geometrical attacks, cryptographic attacks, and protocol attacks. Watermarked images were tested under some types of attacks, e.g.: increasing and decreasing of brightness, adding noise (“Gaussian”, “salt & pepper”), loss of part of watermarked image, JPEG quantization, scaling, rotation, gamma correction, etc.
Primary G from model RGB gives the best results of robustness of extracted watermarks for methods 1,2,3. Similarly the best results are obtained if watermarks are embedded to primary M from color model CMY. The most suitable primary for embedding to model YUV is primary Y for methods 2 and 4, primary U for method 3 and primary V for method 1 as is shown in table 3. Conclusions In this paper four original methods using DCT or DWT transformation for invisible embedding digital watermark into the still color images is presented. Experimental results show, that both methods have advantage in few points of view in opposite to another methods. Better robustness and effectivity are obtained by using combination of proposed methods i.e. using multiembedding of watermarks or consecutive multiembedding also called hybrid watermarking. Acknowledgements The work presented in this paper was supported by Grant of Ministry of Education and Academy of Science of Slovak republic VEGA under No. 1/1057/04. References [1] Katzenbeisser, S., Petitcolas, F.A.P,: Information hiding techniques for Steganography and Digital Watermarking, Artec House,INC., 2000, ISBN 158053-035-4 [2] Petitcolas, F.A.P., Anderson, R.J., Kuhn, M.G.: Attacks on copyright marking systems. Proceedings of the Second International Workshop on Information Hiding, Portland, April 14-17, 1998, pp.218-238 [3] Levický, D., Hovančák, R., Klenovičová, Z.: Digital watermarking. Principles, systems and applications. (in Slovak) Slaboproudý obzor, Czech Republic, pp.1-5, ISSN 0037668X [4] Hovančák, R., Levický, D.: Comparison of watermarking methods using DCT transformation. RADIOELEKTRONIKA 2003, 13th International Czech Slovak Scientific Conference, Brno, Czech Republic, May 6-7, 2003, pp.403-406
Method
Primary
Color Model
Attacks / MSE of extracted watermarks
RGB CMY YUV
1 2 R 3 4 1 2 G 3 4 1 2 B 3 4 1 2 C 3 4 1 2 M 3 4 1 2 Y 3 4 1 2 Y 3 4 1 2 U 3 4 1 2 V 3 4
JPEG loss ¼ of image
kvant.
Gamma correct.
Gauss. noise
'salt & pepper' density=
Scaling (resize to1/2)
Rotation 0,5°
Q=50
(+0,5)
mean=0; var.=0,01
0,1230 0,2578
0,0098 0,1914
0,0068 0,0400
0,0889 0,3330
0,1514 0,3516
0,0410 0,1426
0,1279 0,2139
0,1377 0,25 0,1299 0,2539
0 0 0 0,1240
0,4668 0 0 0,0244
0,1885 0,0498 0,0811 0,2793
0,1777 0,0420 0,1133 0,3340
0,0645 0,0205 0,0391 0,0967
0,1289 0,0215 0,1387 0,1738
0,1201 0,25 0,1279 0,2568
0 0 0,3428 0,2275
0,4668 0 0 0,0303
0,1484 0,0391 0,0869 0,3242
0,1006 0,0195 0,1230 0,3311
0,0498 0,0068 0,0449 0,1465
0,1514 0,0195 0,1387 0,1982
0,1396 0,25 0,1260 0,2598
0 0 0,0039 0,1934
0,4668 0 0,0088 0,0430
0,1338 0,0244 0,0957 0,3262
0,1113 0,0244 0,1387 0,3330
0,0547 0,0088 0,0469 0,1348
0,1025 0,0137 0,1416 0,2002
0,1211 0,1484 0,1240 0,2539
0 0 0,0010 0,1104
0,5332 0 0 0,0381
0,1572 0,0693 0,0820 0,2852
0,1250 0,0459 0,1357 0,3066
0,0527 0,0225 0,0488 0,1152
0,1025 0,0273 0,1465 0,1377
0,1123 0,1182 0,1230 0,2520
0 0 0,3379 0,2314
0,5332 0 0 0,0225
0,1514 0,0391 0,0918 0,3428
0,0938 0,0332 0,1299 0,3564
0,0420 0,0088 0,0430 0,1309
0,1387 0,0205 0,1533 0,1611
0,1104 0,1279 0,1240 0,2559
0 0 0 0,1104
0,5332 0 0,0127 0,0391
0,1523 0,0625 0,1455 0,2510
0,0918 0,0488 0,1953 0,2891
0,0586 0,0107 0,1074 0,1143
0,1133 0,0166 0,1904 0,1768
0,1309 0,25 0,1260 0,3242
0 0,0010 0,5078 0,3789
0,4668 0,0010 0 0,2646
0,1533 0,0469 0,1191 0,4619
0,1299 0,0342 0,1494 0,4795
0,0635 0,0293 0,0068 0,2197
0,1846 0,0322 0,1035 0,2617
0,1230 0,25 0,1074 0,3105
0 0 0,4873 0,3770
0,4277 0,0254 0 0,3477
0,1035 0,1016 0,0986 0,4326
0,0771 0,0576 0,1465 0,4863
0 0 0,0029 0,2607
0,0283 0,0059 0,0791 0,2744
0,1348
0
0,4453
0,1309
0,0986
0,0020
0,0254
0,25
0
0,0293
0,0820
0,0557
0,0088
0,0127
0,05
Tab.3 Experimental results
