A Robust Digital Image Watermarking Scheme using Singular Value

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					                            ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

        A Robust Digital Image Watermarking Scheme using Singular Value
          Decomposition (SVD), Dither Quantization and Edge Detection
                                 B.Chandra Mohan#, S.Srinivaskumar$, B.N.Chatterji*
                   Research Scholar, JNTU College of Engineering, Kakinada, Andhra Pradesh, India.
                  Professor, ECE Dept, JNTU College of Engineering, Kakinada, Andhra Pradesh, India.
           Former Professor, Dept of E & ECE, Indian Institute of Technology, Kharagpur, West Bengal, India.

Abstract                                                          Significant Substitution (LSB) is a simplest technique in
This paper presents a robust algorithm for digital image          the spatial domain [3,4,5]. In LSB technique, the
watermarking based on Singular Value Decomposition                watermark is embedded by replacing the least significant
(SVD) and Dither Quantization. The eigen matrix in the            bits of the image data with a bit of the watermark data.
singular value decomposition is explored for data                 There are many variants of this technique. The data
embedding. The perceptibility of the watermarked image            hiding capacity of these algorithms is high. However,
is enhanced by embedding the watermark image in some              these algorithms are hardly robust for various attacks and
selected and most complex blocks of the host image. A             prone to tamper by unauthorized users. Correlation based
block is said to be a complex block, if the number of             approach [6,7] is another spatial domain technique in
edges in the block is more than a predefined threshold.           which the watermark is converted to a PN sequence
The proposed method is robust and the watermark image             which is then weighted & added to the host image with a
can survive to many image attacks like rotation, scaling,         gain factor k. For detection, the watermark image is
noise, JPEG compression, JPEG 2000 compression, low               correlated with the watermark image. Watermarking in
pass filtering, biplane removal, row column blanking,             transform domain is more secure and robust to various
row column copying, cropping, image tampering and                 attacks. However, the size of the watermark that can be
gamma correction. Results are compared with an                    embedded is generally 1/16 of the host image. Image
existing and recent method and found to be superior in            watermarking algorithms using Discrete Cosine
terms of the quality of the extracted watermark image             Transform (DCT) [8,9], Discrete Wavelet Transform
and resilience to attacks. The metric used to test the            (DWT) [10,11,12,13], Singular Value Decomposition
robustness of the proposed algorithm is the Normalized            (SVD) [14,15,16,17,18,19,20,21,22] are available in the
Cross correlation (NC).                                           literature. The basic philosophy in majority of the
                                                                  transform domain watermarking schemes is to modify
Keywords : Digital Image Watermarking, Singular Value             transform coefficients based on the bits in watermark
Decomposition, Dither Quantization.                               image. Most of the domain transformation watermarking
                                                                  schemes works with DCT and DWT. However Singular
1. Introduction                                                   Value Decomposition (SVD) is one of the most powerful
Digital Watermarking is a process of embedding                    numerical analysis techniques and used in various
information in the multimedia content (host or cover              applications [23,24]. Gorodetski et al. used SVD domain
image) for image authentication. An ideal watermarking            for watermarking a 600x512 RGB image. They quantized
system would embed an amount of information that could            the Singular Value (SV) of each 4x4 block of R, G and B.
not be removed or altered without making the cover                The watermark is a 240x120 gray scale image. But, this
object entirely unusable. Over the past few years digital         is shown to resist only for JPEG compression. Liu and
watermarking has become popular due to its significance           Tan applied SVD to the entire host image. The
in content authentication and legal ownership for digital         watermark is a pseudo gaussian random number matrix
multimedia data. A digital watermark is a sequence of             weighed with appropriate scaling factor is added to the
information containing the owner’s copyright for the              diagonal matrix of SVs. The modified D (Diagonal
multimedia data [1]. It is inserted invisibly in another          matrix) is inserted back in the host image. This method is
image so that it can be extracted at later times for the          able to resist Gaussian Noise, Gaussian Low pass filter,
evidence of rightful ownership. Available digital                 JPEG with 5% compression, rotation of 300 and cropping.
watermarking techniques can be categorized into one of            Chandra et al. proposed an algorithm based on the SVD
the two domains, viz., spatial and transform, according to        of both the host image and visual watermark. The
the embedding domain of the host image [2]. Least                 singular values (SV) of the watermark are multiplied by a

                            ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

scaling factor and added to the SV of the host image. The          In section 2 SVD Transformation is discussed. The
attacks used are JPEG (QF =25 and 10), and 3x3 low                 proposed method is introduced in section 3. In section 4
pass filter. But this method is non-blind in nature. In            the experimental results are shown. The conclusions are
2002, Sun et al. Proposed an SVD and quantization                  given in section 5.
based watermarking scheme where in D component with
a diagonal matrix is explored for embedding. The basic             2. Singular Value Decomposition
mechanism used is the quantization of the largest                  SVD is an algorithm of matrix transformation based on
component with a fixed constant integer, called                    eigen vector. SVD is a mathematical tool used to analyze
Quantization coefficient. A trade-off can be achieved              matrices. In SVD, a matrix is decomposed into three
between transparency and robustness by varying the                 matrices of same size. Let A be m x n matrix with m ≥ n.
quantization coefficient. However, the method failed in            One form of singular value decomposition of A is
extracting the watermark with zero error rate. The                  A= UTDV. Here U and V are orthogonal and D is
original watermark image and retrieved watermark image             square diagonal. That is, UUT = Irank(A), VVT= Irank(A), U is
are not exact. Later in 2005, Chang et al. Proposed a              rank(A) x m, V is rank(A) x n and
watermarking scheme based on SVD domain. Later in
2005 Chang et al. proposed a watermarking scheme
                                                                       ⎛σ 1 0 . . .      0            0 ⎞
based on SVD domain. They explored U matrix for                        ⎜                                      ⎟
watermark embedding. They used a 512x512 Lena,                         ⎜ 0 σ2 . . .      0            0 ⎟
Airplane and Baboon as host images and two watermark                   ⎜ .  . . . .      .            . ⎟
images IEEE logo and CCU logo of 32x32 size. Here U                    ⎜                                      ⎟
                                                                   D = ⎜ .  . . . .      .            . ⎟
matrix is explored for data embedding. They modified
the absolute difference between two rows of U matrix.                  ⎜ .  . . . .      .            . ⎟
They identified that the positive relationships between                ⎜                                      ⎟
the rows of U matrix is preserved even after JPEG                      ⎜0   0 0 0 0 σrank ( A) − 1    0 ⎟
                                                                       ⎜                                      ⎟
compression. The attacks shown in their paper are only
                                                                       ⎝0   0 0 0 0      0         σrank ( A) ⎠
JPEG (QF=70), Gaussian Noise, Cropping, sharpening,
blurring and tampering. The watermarked image is of
                                                                    is a rank(A) x rank(A) diagonal matrix. These diagonal
good quality. They embedded a 32x32 binary logo in a
                                                                   entries σi' s are called singular values of A and their
512x512 image. There are two major issues with Chang
et al.’s method. The first one is, the watermark extraction        number is equal to the rank of A. These singular values
is not complete. The error rate between the original               satisfy the relation
watermark and extracted watermark is not zero. It is very                     σ 1 ≥ σ 2 ≥ σ 3......σrank ( A) > 0.        (2)
close to zero. That means, the Normalized correlation              Each singular value specifies the luminance of an image
coefficient is not ‘1’. If perfect extraction is required,         layer while the corresponding pair of singular vectors
robustness has to be sacrificed. Both robustness and               specifies the geometry of the image. For majority of the
perfect extraction (zero error rate) cannot be achieved            attacks, the change in the largest singular value is very
simultaneously. The reason for this can be attributed to           small.
the nature of U matrix elements, which are real numbers                        The concept of dither quantization was
of magnitude less than ‘1’. Any modification of U matrix           introduced to digital watermarking community by Chen
values beyond the threshold value will affect the                  and Wornell.        Dither quantizers are set of basic
extracted watermark. The second issue is in the process            quantizers.      Each quantization cell in the set is
of complex block selection. A block is said to be a                constructed from a basic quantizer. The basic quantizer is
complex block if the block’s diagonal matrix contains              shifted to get the reconstruction point. The shift depends
more number of non zero coefficients. It has been                  on the watermark bit. The basic quantizer is a uniform
observed that for majority of the blocks, the number of            scalar quantizer with a fixed step size t. A quantizer in
non zero coefficients is same. So, it is difficult to              the ensemble consists of two quantizers shifted by t/2
identify a block as complex block based on the number of           with respect to each other. In the proposed algorithm the
non zero coefficients in the diagonal matrix of the block          largest singular values of each 8 x 8 block are quantized
in the host image. In this          paper, we propose an           using either quantizer 1 or quantizer 2 which depends on
algorithm which addresses both the issues. The first issue         watermark bit to be embedded. The quantized value is the
is resolved by exploring the diagonal matrix using dither          center of the quantizer.
quantization [25] and the second one is resolved by
identifying a complex block based on the number of
edges in a block. We define a block as a complex block if          3. The Proposed Scheme
the block contains more number of edges. So an edge                In the proposed scheme diagonal matrix (D) is used for
detection algorithm [26] is applied for this purpose prior         watermark embedding. Any modification of D
to watermark embedding. The proposed method is highly              component degrades the perceptibility of the
robust and the perceptibility of the image is better than          watermarked image. To improve perceptibility, the
Chang et al.’s method. In terms of robustness also our             watermark is embedded in some selected complex blocks
method is superior to Chang et al.’s method as our                 only. The strategy for selecting a block is based on the
method can survive to many attacks.                                number of edges in a block. A block is qualified as a
                                                                   complex block if the number edges in a block is greater

                              ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

than some predefined threshold.            The    watermark                5.    A look-up table is formed with the entries
embedding algorithm is as follows:
                                                                                [[dmin-t dmin],[dmin dmin+t],…. …..[dmax dmax+t]]
1. Cany’s edge detection algorithm is applied to the
   entire host image of size 512x512.                                                                                                          [6]

2. In each 8x8 non-overlapping block, number of edges is                   6.    The dlarge value of each selected block is
   computed.                                                                     checked for its position in the look-up table.

3. Blocks are arranged based on descending order of                        7.    The watermark bit is ‘1’ if dlarge lies in the
   the number of edges in each block. The first 1024                                                        dl + dh
                                                                                 interval        dl to                        .
   (32x32) blocks having more number of edges are                                                              2
   selected and indexed for watermark embedding.                                                                                               [7]
                                                                           8.    The watermark bit is ‘0’ if dlarge lies in the
4. SVD transformation is applied on each          individual
                                                                                             dl + dh
   selected block.                                                               interval            to dh
5. A matrix Dlarge, is formed with largest singular values                                                            [8]
   of each block. The size of the Dlarge is 32 x32.                              The embedding methodology and extraction
                                                                                 technique are summarized in the flow chart
6. The maximum and minimum values of Dlarge are                                  (Figure 1(a) & Figure 1(b)).
   represented as dmax and dmin respectively. The range
   [dmax dmin] is divided into uniform intervals [dl dh] of                                           Host Image
   width t.
[[dmin-t dmin], [dmin dmin+t],…. ……..[dmax dmax+t]]                                                    Apply Edge
7.    For each selected block, identify the interval j to
     which the block belongs, based on its dlarge value,
                                                                                                  block Decomposition
     and modify it as:

                  dl + dh                                                                        Sorting of selected Blocks
           dl +
dlarge =             2      , if the watermark bit is ‘1’                                         SVD (Block wise)
                   2                                                                             U, D, V Decomposition
              dl + dh                                                                   1                                         0
         dh +
dlarge =         2    , if the watermark bit is ‘0’
                                                            [5]           Modify                                                  Modify
                                                                          Dlarge as in Eq [ 4]                                    Dlarge as in Eq [5]
8. After the modification of dlarge values, inverse SVD
   is applied on each selected block to get the
   watermarked image.
                                                                                                     Inverse SVD

The watermark extraction algorithm is as follows:
                                                                                                 Watermarked Image
      1.   The watermarked image is partitioned into 8 x 8
           non overlapping blocks.
                                                                                Figure 1.(a) Embedding Methodology
      2.   Blocks having number of edges greater than the
           predefined threshold are identified.

      3.   SVD transformation is applied on each selected
                                                                       4. Experimental Results
                                                                       To test the robustness of the proposed scheme,
                                                                       experiments are conducted using host image ‘Lena’ as
                                                                       shown in Figure 2. The size of the host image is 512 x
      4.   A matrix Dlarge is formed with the dlarge values
           of the individual D matrices.                               512. The watermark image is of 32 x 32 size which is a
                                                                       logo having the letters ‘JNTU’ as shown in Figure 3. In
                                                                       Figure 4(a) watermarked LENA is shown and in Figure
                                                                       4(b) tampered Lena is shown.

                              ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

                                                                   experiment, first the watermarked image is reduced from
                                                                   512x512 size to 256x256. By using bicubic interpolation
                  Watermarked Image                                its dimensions are increased to 512x512. The extracted
                                                                   watermark as shown in Figure 8(b) is clearly visible. In
                                                                   row column blanking attack, a set of rows and columns
                    Identification of
                   Watermarked Blocks                              are deleted. In this experiment 10,30,40,70,100,120 &140
                                                                   rows and columns are removed. In row-column copy
                                                                   attack a set of rows and columns are copied to the
                  SVD decomposition
                  (On Selected blocks)
                                                                   adjacent or random locations. In this experiment 10th row
                                                                   is copied to 30th row, 40 to 70, 100 to 120 and 140th row
                                                                   is copied to 160th row. Extracted watermarks from row
                 Dlarge Matrix Formation                           column blanking and copying attack are shown in Figure
                                                                   8(c) and Figure 8(d). The watermarked image is attacked
                     Look-up Table                                 by salt & pepper noise with a noise density of
                      Formulation                                  0.001,.002,0.003 and 0.004. The extracted watermarks
                                                                   are shown in Figure 9. All the extracted watermarks are
                                                                   clearly visible indicating the proposed method’s
                  Comparison of dlarge                             resilience to noise attack. But, Chang et al.’s method is
                 with Look Table.Eq [7,8]
                                                                   superior to our method for noise and row column
                                                                   blanking attack. Finally, the proposed algorithm also is
                 Watermark Extraction                              resistant to biplane removal, image tampering, and
                                                                   gamma correction, as shown in Figure 10 and Figure 11.
                                                                   The Normalized Cross correlation value ‘NC’ is used as a
     Figure 1.(b) Extraction Methodology                           metric to compare the robustness and summarized in
                                                                   Table 1.
All the attacks except image tampering and JPEG2000
attack were tested using MATLAB 5.3. JPEG2000
attack is tested using MORGAN JPEG2000 tool box and
image tampering is done with PAINTBRUSH. Various
attacks used to test the robustness of the watermark are
JPEG2000, JPEG compression, rotation, resizing, low
pass filtering, median filtering, cropping, row column
blanking, row column copying, salt & pepper noise, bit
plane removal, image tampering and gamma correction.
The perceptibility of the watermarked image is excellent
with a PSNR of 47.02 dB.
                                                                              Figure 2. 512x512 Lena (Host Image)
The extracted watermarks after applying various attacks
are shown in Figure 5 to Figure 11. The watermarked
image is rotated by 100, 200, 400 and 600 to the right and
then rotated back to their original position using bilinear
interpolation. The recovered watermark shows good                                Figure 3. Watermark Image
similarity with the original watermark image as shown in
Figure 5. The watermarked image is compressed using
lossy JPEG compression. The index of the JPEG
compression ranges from 0 to 100, where 0 is best
compression and 100 is best quality. The reconstructed
watermarks for various indices are shown in Figure 6.
The proposed scheme works well even for extreme
compression. Similarly, JPEG2000 compression is used
to test the robustness with varying quality factor. The
results are extremely good indicating that the proposed                           (a)                   (b)
method is able to survive after JPEG2000 compression.               Figure 4(a). 512x512 Watermarked Lena (b) Tampered
This fact is evident from Figure 7. For low pass filtering                                 Lena
attack a 3x3 mask consisting of 0.9 intensity values is
used. The recovered watermark image as shown in Figure
8(a) is distinguishable, showing its resilience to low
pass filtering attack. Resizing operation first reduces or
                                                                          100          200       400       600
increases the size of the image and then generates the
                                                                         (a)            (b)      (c)      (d)
original image by using an interpolation technique. This
                                                                       Figure 5. Extracted watermarks: Rotation attack
operation is a lossy operation and hence the watermarked
image also looses some watermark information. In this

                            ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

                                                                           Salt&Pepper        0.9516          0.8257
                                                                               Noise          0.9368          0.7374
       30%          40%       60%     100%                                (Noise Density)     0.9148          0.6472
Figure 6. Extracted watermarks: JPEG Compression                         .1%,.2%,.3%,.4%      0.8165          0.5441
                                                                                              0.9502          0.5889
        5%       10%        30%      50%
Figure 7. JPEG 2000 Compression with various Quality
factors                                                                   Row-Column
                                                                                              0.7678          0.7781
                                                                        120,40-160 rows
        (a)         (b)           (c)       (d)                          and columns are
Figure 8. (a) Low pass filtering attack (b) Resizing                          copied
(c) Row column blanking (d) Row column copying                              Cropping
                                                                          1/16th top left     0.5058          0.8941
                                                                                              0.9802          1.0000
                                                                        Bit Plane Removal
       0.001       0.002      0.003        0.004                         1st , IInd & IIIrd   0.9544          0.9009
Figure 9. Salt & pepper noise with various noise densities                                    0.4354          0.8076
                                                                        Image Tampering       0.9353          0.9907
                                                                           Correction         0.1927           0.56
          1st plane       2nd plane 3rd plane                             Gamma=0.9
              Figure 10. Bit plane Removal

                                                                  5. Conclusions
                                                                  In this paper, a watermarking scheme based on Singular
                                                                  Value Decomposition, dither quantization and edge
              (a)             (b)          (c)
                                                                  detection is proposed. The proposed method is highly
     Figure 11 (a). Gamma correction (gamma=0.9)
                                                                  robust and can survive many image processing attacks.
(b) Cropping (1/16th top left corner) (c) Image Tampering
                                                                  The quality of the watermarked image is good in terms of
                                                                  perceptibility and PSNR (47.02dB). The proposed
                                                                  algorithm is shown to be robust to rotation, low pass
Table 1. Performance Comparison with Chang et al.’s
                                                                  filtering, resizing, JPEG compression, JPEG2000
                                                                  compression, salt&pepper noise attack, row column
                                                                  blanking, row column copying attack, cropping, bit plane
                           NC Value          NC Value             removal, image tampering and gamma correction. For
      Type of Attack        Chang et         Proposed             salt & pepper noise attack and row column blanking
                          al.’s Method        Method              attack, Chang et al.’s method is superior to our method.
                              0.5333          0.7422              The proposed method is superior to Chang et al.’s
          Rotation                            0.6874
                              0.4988                              method in terms of NC value of the extracted watermarks.
        (in degrees)
                              0.4712          0.5889              PSNR of the watermarked image is comparable to Chang
                              0.4856          0.6031              et al.’s method. In our future work, we will investigate
         Low pass                                                 in embedding multiple watermarks in D and U matrices
         Filtering           0.0265           0.4890              so that the watermark image can survive to more number
        3x3 Kernel                                                of image attacks.
         Resizing                             0.8155
                             0.2492                               6. References
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                           ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

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                            ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008

                       B.Chandra Mohan is currently                                          B.N.Chatterji is a former
                       working as Professor in ECE                                           Professor        in      E&ECE
                       Department, Bapatla Engineering                                       Department IIT, Kharagpur. He
                       College, Bapatla, India. He is                                        received B.Tech. and Ph.D.
                       working towards his                                           (Hons.)       from       E&ECE
                       JNTU College of Engineering,                                          Department IIT, Kharagpur in
                       Kakinada, India. He received his                                      1965 and 1970, respectively.
                       M.Tech from Cochin University                                         He has served the Institute
                       of Science & Technolgoy,                                              under various administrative
                       Cochin, India. He has fifteen                                         capabilities as Head of
years experience of teaching undergraduate students and           Department, Dean (Academic), etc. He has chaired many
post graduate students.His research interests are in the          international and national symposium and conferences
areas of image watermarking, and image compression.               organized in India and abroad, apart from organizing 15
                                                                  short term courses for Industries and Engineering college
                                                                  teachers. He has guided 35 Ph.D. scholars. Presently, he
                         S. Srinivas Kumar is currently           is active in research by guiding three research scholars.
                         Professor and HOD in ECE                 He has published more than 150 papers in reputed
                         Department, JNTU College of              international and national journals apart from authoring
                         Engineering, Kakinada, India.            three scientific books. His research interests are low-level
                         He received his M.Tech. from             vision, computer vision, image analysis, pattern
                         Jawaharlal Nehru Technological           recognition and motion analysis.
                         University, Hyderabad, India.
                         He received his Ph.D. from
                         E&ECE       Department       IIT,
                         Kharagpur. He has nineteen
years experience of teaching undergraduate and post-
graduate students and guided number of post-graduate
theses. He has published 15 research papers in National
and International journals. Presently he is guiding five
Ph.D students in the area of Image processing. His
research interests are in the areas of digital image
processing, computer vision, and application of artificial
neural networks and fuzzy logic to engineering problems.


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