Digital Watermarking in Contourlet Domain

Digital Watermarking in Contourlet Domain Jayalakshmi M., S. N. Merchant, Uday B. Desai SPANN Lab, Electrical Engineering Department,Indian Institute of Technology, Bombay, India (jlakshmi, merchant, ubdesai)@ee.iitb.ac.in

Abstract Digital watermarking has been proposed as a method of copyright protection of audio, images, video and text. We propose to use the newly introduced transform for two dimensional signals, namely, the contourlet transform for image watermarking application. We have carried out simulations with two kinds of images- maps consisting of lot of curves and texts and those with textures. The watermarked images were subjected to different attacks like mean filtering, quantization and JPEG compression. It is observed that the contourlet based algorithm outperforms wavelet and DCT based methods in this application. It is also apparent from the simulation results that contourlet based techniques give a distinct advantage over conventional techniques in images like maps which consist of lot of curves and texts.

1. Introduction Digital watermarking primarily means inserting a copyright information into a cover work and is proposed as a solution to illegal copying and tampering of the original data. The digital watermark embedded should be transparent and at the same time robust against intentional and non-intentional attacks. The existing transform domain techniques locate regions of high frequency or middle frequency to embed information imperceptibly. The transforms usually selected for digital watermarking are Discrete Cosine Transform(DCT), Discrete Fourier Transform(DFT) and Discrete Wavelet Transform(DWT) [6],[7]. Of the proposed algorithms so far wavelet domain algorithms perform better than DCT based algorithms. It has been proved that wavelets are good at representing discontinuities in one dimension or point singularities [3]. But, since in higher dimensions there are more types of singularities which wavelets fail to represent, we need to go for transforms like curvelets and contourlets for better performance. Curvelet transform [3] was defined in the continuum space R 2 and its discretization is a challenge when critical sampling is

desired [5]. Contourlet transform was proposed as an improvement on curvelet transform using a double filter bank structure. Contourlet transform provides a flexible multiresolution representation for images. One of the unique properties of contourlet transform is that we can specify the number of directional decompositions required at every level of multiresolution pyramid. The first algorithm proposes a decomposition scheme where the number of directional bands doubles at every scale of multiresolution pyramid. Watermark embedding with a different decomposition which obeys the curve scaling relation of curvelets is presented in the second algorithm. The watermarked images using the proposed methods were of very good visual quality irrespective of the nature of the images chosen. Also the watermarked images retained the embedded watermark even after attacks like mean filtering, quantization and JPEG compression. It was observed that contourlet based methods performed much better than wavelet and DCT based methods in images like maps. The paper covers a brief introduction to contourlet transform in Section 2. Section 3 describes the proposed algorithms. Experimental results and conclusion are included in Section 4 and Section 5 respectively.

2. Contourlet transform Contourlet transform gives a multiresolution, local and directional expansion of images using Pyramidal Directional Filter Bank(PDFB) [5]. Consider a contour C p which has finite length inside the unit square [0, 1]2 . Assuming representation by orthonormal wavelet transform with separable Haar wavelet, at level j, the basis functions have support on dyadic squares of size 2−j . Thus there are O(2 j ) nonzero wavelet coefficients at scale 2j . This performance can be improved by grouping the nearby wavelet coefficients since their positions are locally correlated. The curve scaling relation suggests to group 2j/2 nearby wavelet basis functions into one basis function with a linear structure so that the width is proportional to the length squared. The PDFB combines Laplacian Pyramid(LP) [2] with a

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directional filter bank [1]. The former captures point discontinuities and the latter links these into linear structures. The PDFB can be represented as in Figure 1.

Figure 1. Pyramidal Directional Filter Banks (a) Method 1

(b) Method 2

3. Proposed Algorithm Figure 2. Contourlet decomposition This section describes the two proposed algorithms. In the first method, number of directional bands are doubled at every stage and the second method follows the curve scaling relation of curvelets. As mentioned previously it is apparent that smooth contours are very well captured in the contourlet domain. In both proposed methods we select high absolute valued coefficients for watermarking.

where mk is the watermark bit obtained after randomizing the binary watermark selected. The embedding method and the multiplication factor are the same for both the algorithms in this paper.

3.2 3.1

Method 2

Method 1

The highest absolute valued coefficient in any band would represent a strong edge or a high frequency component in that respective direction. Hence it would be advantageous, as far as transparency is concerned, if we select those pixels. In our simulations we have selected the highest 256 coefficients which is equal to the size of the watermark. Figure 2a shows the directional decomposition at every level through contourlet transformation that is used in this particular method. From Figure 2a it is apparent that ‘L’ is the low pass version of the image and W, X, Y and Z are the directional detail bands at different levels. Directional bands in four levels of multiresolution are divided into 2, 4, 8 and 16 directional subbands from coarse to fine scales respectively. The pixels from band W, the coarsest bandpass images, are selected for watermark embedding. Let W(x,y) be a high absolute valued pixel selected for watermarking from band W and ‘α be the multiplication factor used for embedding. Then the corresponding watermarked pixel W’(x,y) is given by W (x, y) = W (x, y) + αmk

(1)

In this method the directional decomposition is performed according to curve scaling relation. Here the number of directions in the band pass image is doubled at every other scale of decomposition. The decomposition of image into low frequency band L and the directional bands A, B, C and D are shown in Figure 2b. The selected pixels are those with highest absolute values from band A. Additive watermark embedding of the selected pixels are performed according to equation 1.

3.3. Watermark retrieval and performance measures The multiplication factor selected in our algorithm is the same for all the methods for the purpose of comparison. However, it is possible to differently quantize pixels. To keep the visual distortions to minimum we calculate the Peak Signal to Noise Ratio (PSNR) of the watermarked image. With the chosen α factor the PSNR is found to be approximately 47 and above for all the test images. For retrieving the watermark we need a copy of the original image and hence the proposed algorithm is non-blind.


Subtracting the original image pixels from the watermarked pixel in the transform domain gives the scaled watermark. After retrieving the watermark we calculate the normalized correlation coefficient of the retrieved watermark(m ) with the original watermark(m) to prove authenticity. Suppose there are K pixels in the watermark. Then the normalized correlation coefficient(γ) between m and m’ is defined as follows. K mi m (2) γ = i=1 i K K 2 2 m m i i i=1 i=1

(a)

(b) Image 1

(c) Method1

4. Experimental results In this section we have included the simulation results of the proposed methods and two other transform domain methods for comparison. The former method of comparison is in wavelet domain and the latter is in DCT domain. The number of coefficients selected remains same for all the methods. In wavelet based method, the four level decomposition of the original image is performed and the coefficients with highest absolute magnitude from horizontal, vertical and diagonal detail bands of the fourth level are selected for watermark embedding. In DCT domain the highest 256 absolute valued coefficients, excluding the DC component, are selected for embedding [4]. We experimented with seven images: four of them are maps, depicted in Figure 3 and Figure 4b. The other three are Lena, Barbara and Baboon. Since they are well known images, due to space limitation we have not included them. Nevertheless, all simulations were carried out on these images and the results have been tabulated in the respective tables. The binary watermark chosen is of size 16 × 16 and

(d) Method2

(e) Wavelet

(f) DCT

Figure 4. Original and watermarked images

image and would try to distort the embedded message. Since maps include lot of texts and curves, conventional signal processing operations like Gaussian noise addition and median filtering distort the image considerably. In this paper, we have considered only those attacks which do not distort the watermarked image. In particular, we consider attacks like mean filtering, quantization and JPEG compression. The correlation coefficients after mean filtering the watermarked image, with a 3 × 3 window, by different methods are tabulated in Table 1. The retrieved watermarks after mean filtering from Image 1 with different embedding methods are shown in Figure 5.

Table 1. Normalized correlation coefficient after mean filtering

(a) Image 2

(b) Image 3

(c) Image 4

Image

Method 1

Method 2

Wavelet

DCT

Image 1

0.8516 0.9297 0.8516 0.5938 0.9453 0.8516 0.9922

0.8750 0.8750 0.7969 0.5859 0.8516 0.9141 0.9062

0.5234 0.7812 0.4766 0.6250 0.9531 0.9219 0.9688

0.6797 0.9453 0.7812 0.5234 0.9141 0.9141 0.8047

Image 2

Figure 3. Test images

Image 3 Image 4 Lena

is shown in Figure 4a. The watermarked copies of Image 1 by both the methods in contourlet domain, one in wavelet domain and one in DCT domain are shown in Figure 4c to 4f. Watermarked images should be resistant to those attacks which would retain the visual quality of the watermarked

Barbara Baboon

We have considered two different cases of quantization of the watermarked image. Table 2 shows the results after quantization of watermarked image pixels to gray levels


Table 4. Normalized correlation coefficient after JPEG compression- Image 1 (a) Method1

(b) Method2

(c) Wavelet

(d) DCT

Quality 60 50

Figure 5. Retrieved watermark from Image 1

40 30 20

which are multiples of 10. Table 3 shows the results with quantization values selected as multiples of 20.

Table 2. Normalized correlation coefficient after quantization (multiples of 10) Image Image 1 Image 2 Image 3 Image 4 Lena Barbara Baboon

Method 1

Method 2

Wavelet

DCT

0.9375 1 0.9922 0.9688 1 0.9922 1

0.8828 0.9844 0.9922 0.9531 1 1 1

0.8750 1 1 0.9766 1 1 1

0.5938 0.9531 0.9766 0.7031 1 1 1

Table 3. Normalized correlation coefficient after quantization (multiples of 20) Image

Method 1

Method 2

Wavelet

DCT

Image 1

0.8203 0.6875 0.4375 0.5078 0.9375 0.9766 1

0.7500 0.5547 0.2734 0.3594 0.9375 0.9688 0.9922

0.8750 0.7734 -0.0312 0.4609 1 1 1

0.7109 0.4922 0.1797 0.3906 0.7422 0.7734 1

Image 2 Image 3 Image 4 Lena Barbara Baboon

JPEG compression is one of the important attacks which any image watermarking algorithm should be resistant to. It is observed that the proposed contourlet based methods show good resistance to JPEG compression for all the test images. The results after JPEG compression of Image 1 under quality factors varying from 60 to 10 are tabulated. The proposed methods in contourlet domain gave good perceptual quality for the watermarked images. The results of mean filtering attack (Table 1) prove that contourlet domain watermarking is distinctly better than wavelet based methods for applications like maps which include lot of curves and texts rather than texture images. The quantization attack (Table 2 & Table 3) results show that the first

10

Method 1

Method 2

Wavelet

DCT

1 0.9922 0.9922 0.9766 0.8750 0.7656

1 1 1 0.9922 0.9531 0.6328

1 0.9922 0.9922 0.9922 0.9531 0.6719

1 1 0.9766 0.9922 0.8281 0.5703

proposed method is better than the second. The changes in correlation coefficient in JPEG compression (Table 4) are negligible since they hardly distorted the visual quality of the watermark.

5. Conclusion The algorithms proposed for watermarking usually embed more than one copy of watermark into the original data for robustness. We have proposed a method of embedding the copyright information only once in the image, preserving both robustness and transparency. The simulation results prove that contourlet domain watermarking is well suited for two dimensional data like maps where lot of curves and texts are inherently present. Contourlet transform is proposed for watermarking application for the first time.

References [1] R. H. Bamberger and M. J. T. Smith. A filter bank for the directional decomposition of images: theory and design. IEEE Trans. on Signal Processing, 40:882–893, Apr. 1992. [2] P. J. Burt and E. H. Adelson. The laplacian pyramid as a compact image codes. IEEE Trans. on Communications, 31:532– 540, Apr. 1983. [3] E. J. Candes and D. L. Donoho. Curvelets- a surprisingly effective nonadaptive representation for objects with edges. Saint-Malo Proceedings, 1999. [4] I. Cox, J. Kilian, F. T. Leigton, and T. Shamoon. Secure spread spectrum watermarking for multimedia. IEEE Trans. on Image Processing, 6:1673–1687, Dec. 1997. [5] M. N. Do and M. Vetterli. The contourlet transform: An efficient directional multiresolution image representation. IEEE Trans. on Image Processing, 14(12):2091–2106, Dec. 2005. [6] C. T. Hsu and J. L. Wu. Multiresolution watermarking for digital images. IEEE Trans. on Circuit and Systems, 45:1097– 1101, Aug. 1998. [7] D. Kundur and D. Hatzinakos. Towards robust logo watermarking using multiresolution image fusion principles. IEEE Trans. on Image Processing, 6(1):185–198, Feb. 2004.
