On Watermarking In Frequency Domain 1
Narendrakumar Ramchandra Dasre ,
2
Hemraj Ramdas Patil
E-mail: 1)
[email protected] (Corresponding author), 2)
[email protected]
Ramrao Adik Institute Of Technology, Sector-07, Nerul, Navi Mumbai-400 706 INDIA ABSTRACT: A wavelet-based image watermarking scheme is proposed, based on insertion of ‘logo’ image as watermark in mid-frequency domain. This new approach provides flexibility in determining the pixel to be watermarked and increases the data hiding capacity. It is easy to implement watermark embedding algorithm as well as the corresponding detection algorithm. The watermarking algorithm is tested under different attacks such as median filtering, image cropping and image compression. It is also robust. The experimental results prove that the method is more tamper proof and less perceptible for any type of images other than well known private methods in frequency domain. In the proposed approach, an original image is decomposed into wavelet coefficients then watermark is embedded through algorithm. The wavelet transform filters can be used as security key for the extraction of inserted watermark. The proposed watermark extraction technique is independent of the original image. The watermark embedded image is produced by taking the inverse 2-D discrete wavelet transform of the altered wavelet decomposition. Here we have given the relation between the area of the channel in which we insert the watermark and the area affected in original image. Key words: Wavelet decomposition, watermarking, image processing and jpeg compression.
1. INTRODUCTION: In the past decade, digital watermarking has become an attractive method for data hiding and copyright protection [1-14]. The two traditional approaches for watermarking are spatial and spectral domain technique [13]. In spatial domain the watermark is embedded in selected regions chosen based on texture of the given image [13]. This approach is usually not robust to most signal processing attack. While in spectral domain, the watermark is embedded in the transform domain using methods such as DCT and DWT, in the mid-frequency range to ensure transferency and robustness of watermark simultaneously[14]. Some desirable properties of watermarking technique[10] include the following: The inserted watermark should not introduce visible artifacts. The watermark should not be easily removable. The watermark should be resilient to lossy data compression such as jpeg. The watermark should be resilient to image processing technique such as median filtering and image cropping. The original image is not required in watermark extraction. The watermark can only be extracted by privileged individuals for given the security key. Since Spatial domain technique generally requires a lower computational cost compared to transform domain techniques. They are also generally easier to implement. A major concern of digital image watermarking is the trade-off between image degradation verses ease in removal of the inserted watermark via compression, filtering or cropping. Spatial domain techniques generally do not balance this trade-off well, hence transform techniques are preferred. This paper describes algorithm that inserts a watermark into a mid-frequency channel of a image’s 2-D wavelet transform. Here we use non-zero sealing factor and other parameters as security keys. These security keys are only clues to extract watermark.
2. HISTORY AND WATERMARKS INSERTION: 2.1 Wavelet history and selection of channel: Let ‘I’ be the original digital image of size N1 x N1 and ‘W’ be the 3-level 2-D wavelet transform of I. The details of 3-level 2-D wavelet transform can be found in [8, 10]. Since it will be necessary to use the same wavelet transform for the watermark extraction. The filters used in these transformations can be determined by the owner of the image and used as a part of security key. The necessary condition for a transform is the wavelet analysis and subsequent synthesis transform gives an exact reconstruction system. A 3-level 2-D wavelet image decomposition W consist of 10 wavelet channels: LL3, LH3, HL3, HH3, LH2, HL2, HH2, NH1, HL1 and HH1. These channels correspond to sub-band frequencies of the image I given in the figure .We know that the energy of most natural images is
concentrated on the lower frequencies [9]. DWT is considered to be a powerful signal process and analysis tool, especially for the character in time or frequency domain [12]. DWT decomposes an image into four coefficient sets i.e. LL, LH, HL and HH. In most of DWT watermarking schemes, watermark is embedded in low frequency domain i.e. in LL which is good against many signal attacks, including JPEG compression, median filtering and image cropping [12].Since low frequency LL3 channel has more energy than other channels hence the modification of the coefficients of this channel can cause intolerable image degradation. Hence we never insert watermark in this channel. In [12], HH is chosen to embed watermark. While most cases, in order to improve the robustness, watermark is often embedded in low/middle frequency sub-bands. 2.2Algorithm of insertion: Let I be N1 x N1 digital image and W be 3-level, 2-D wavelet decomposition of I[10]. Let M be watermark image/logo, we wish to embed into image I and M = gM , g ε R\{0}, where g is scaling factor which provides a trade-off between image degradation and resiliency to attacks which may remove the watermark [1]. With small value of g, yields less perceptible artifact where as choosing large value of g render more perceptible artifact and resiliency to attacks. Consider the rise of wavelet channel ‘C’ is N1/8 x N1/8 for 3-level 2-D decomposition. Let the size of watermark image M be N2 x N2. It is required that N2 ≤ N1/8. The watermark can be inserted into channel C by any one of the five ways. Figure (1)
I
III
II
V
IV
(a) Partitions of the target Channel Where Watermark can be inserted
Area where the watermark is inserted I II III IV V
Affected area of Vegetable Image ABED BCFE DEHG EFIH JKML
(b)Table of correspondence
A
B J
D
C K
E L
G
F M
H
I
(c) Partition of original Image
For simplicity consider the size of M is 16 x 16 and I = 256 x 256. If we use 3-level 2-D decomposition then channel ‘C’ (LH3, HL3, HH3) size will be 32 x 32. Then the partition of channel can be done in any ways the reader like. For simplicity we are considering the above 5 partitions. Consider the following cases: I) We consider Ist part of the channel. The logo is inserted by following equation. M = g.M, where g is scaling factor. Therefore we have C (n, m) = M (n, m) 1 n 16 , 1 m 16 C (n, m)
otherwise
II) Now we consider Vth part (i.e. the most middle part). The logo is inserted by the following equations M = g.M, where g is non-zero scaling factor. M (n 8, m 8) C (n, m) C (n, m)
9 n 24, 9 m 24 otherwise
The original image size, the wavelet transform filter, the watermark scaling parameter ‘g’ and the channel ‘C’ in which the watermark is inserted are components of the security key.
3. WATERMARK EXTRACTION: Watermark extraction requires that the original image size, the wavelet transform filter the scaling parameter g, and the wavelet channel in which the watermark is inserted are known. The same 3-level 2-D wavelet transform used in embedding algorithm is performed on the watermark embedded image J. The extracted watermark N is recovered from wavelet channel as below. Since we have considered two cases of insertion of watermark, these same cases we will consider for extraction of watermark. Case I: N (m, n) C (m, n) for 1 m 16 Case II: N (m 8, n 8) C (m, n) for 9 m 24 g
1 n 16
g
9 n 24
4. EXPERIMENTAL RESULT: We have performed the experiments on vegetable image which is 256 x 256 pixels with 8 bit (256) gray scale level.
(a) Original Vegetable Image
Figure (2)
(b) 3-level 2-D Wavelet Decomposition
(c) Cropped Image
(d) Watermarked image with g = 1
(f) Watermarked image with g = π/100
(e) Median Filtered Image
We use 16 x16 pixels 8 bit (256) gray level binary image as a watermark which is shown below. Figure (3)
(a)
(b)
(c)
(d)
(a) Original Watermark (b) Watermark extracted after compression (c) Watermark extracted after Cropping (d) Extracted Watermark without any attack.
In this paper we use a length Daubechies one (i.e. ‘db1’) or Haar (i.e. ‘haar’) wavelet which has been shown to be orthogonal system in [8].
4.1 Image Quality: In figure (2d) , the watermark is embedded in the Vegetable image with scaling parameter g =1, the checker board image comes in the corresponding area. If we insert the watermark in HH3 channel. When we take smaller scaling factor g = π /100, the checker board becomes less evident. These checker board is present in the form of ripples. The watermark embedded image of Vegetables with scaling parameter g = π /100 is shown in figure (2f). 4.2 Security Key: The wavelet used, scaling parameter and level of 2-D decomposition are 3 security keys. Only the owner can extract the watermark using these security keys. For experiment, we have used ‘db1’ wavelet in the embedding process .For extraction process, we use the same wavelet. If other than this wavelet is used Ex. ‘db2’ then the watermark can not be extracted correctly from the channel. 4.3 Resiliency to Image compression: Here we consider ‘Vegetable’ image of size 256 256 pixels with 256 gray levels (0 to 255) typically, such an image is represented using 8 bits pixel. These would require total 524288 bits to represent the image. The image compression or coding problem is concerned with finding ways of reducing the total number of bits required to represent the image while keeping the accompanying degradation in image quality as small as possible. Suppose the given image goes through one level of wavelet decomposition then we will have low resolution representation and three detail images each of the size 128 x 128 pixels. If we use 8 bits per pixel for each of these images, we would still be using a total of 524288 bits. However, it is not necessary to use 256 gray levels to represent each of these images. Most images have the property that their detail images have most values close to zero. Consequently, rather than allocating 256 levels to represent the detail images, we can have fewer levels and yet an acceptable representation of detail images. Suppose we represent HH1 image with 1 bit and LH1, HL1 images with 2 bits then the original image can be represented by total 212 992 bits which is less than half as many bits as before. Again if we go for more levels of decomposition then more number of bits can be reduced. After reducing, still our watermark image remains there. 4.4 Resiliency to median filtering: Here we have used 3 x 3 masks for median filtering the watermarked image. This process gives smooth watermark embedded image with preservation of major edges. After median filtering still we can regain our watermark. The robustness is directly proportional to the thickness of the watermark for median filtering attack. We have tested our thin watermark and several other watermarks with different thickness. 4.5 Resiliency to image cropping: Here we cropped watermarked image of size 128 x 128 pixels which is 1/4th of its original size. Then we regain the original size by assigning all the remaining pixels to be zero and then extracted the watermark. We observe that the watermark is still present.
5. CONCLUSION: We have presented a relationship between the area of watermark inserted in the channel and the area of the image affected. The details of this correspondence are given in figure 1(b), Table of correspondence. We have presented the more number of choices of the regions in the channel and the partitions of the channel. Here we can choose any partition of the channel and embed the watermark. If we use proper security keys i.e. wavelet filter, scaling factor, channel and watermark size then we are easily able to extract the watermark after different attacks like median filter, image compression, cropping. Here we have given an idea of partitioning the channel as we wish. We can have the different partitions of the channel .This also increases the security of our watermark. Robustness of watermark image increases with increase in thickness.
6. ACKNOWLEDGEMENTS: We are thankful to Mr. Uday Shende, Director, R. A. I. T. and our Principal, Dr. S. R. Devane for their valuable support throughout the work.
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Mr. Narendrakumar R. Dasre has received B. Sc. Degree with Mathematics in 2001 and M. Sc. Degree with specialization in Computational Mathematics in 2003 from North Maharashtra University , Jalgaon. Currently, he is a Lecturer in Applied Mathematics at Department of Engineering Sciences. His interest includes Image Processing, Cloud Computing, Number Theory, Numerical Analysis and Geometric Constructions.
Mr. Hemraj R. Patil has received B. E. Degree with Electronics in 1996 from Dr. B. A. Marathwada University, Aurangabad and M. E. Degree in Electronics in 2002 from Mumbai University, Mumbai. Currently, he is a Lecturer in Electronics and Telecommunication Engineering. His interest includes Image processing, Signal Processing and Communication Engineering.
