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Rough set based effective technique of image watermarking
Accepted Manuscript Title: Rough Set Based Effective Technique of Image Watermarking Author: Shishir Kumar Neha Jain Steven Lawrence Fernandes PII: DOI: Reference:
S1877-7503(16)30385-4 http://dx.doi.org/doi:10.1016/j.jocs.2016.11.009 JOCS 579
To appear in: Received date: Revised date: Accepted date:
20-7-2016 26-10-2016 21-11-2016
Please cite this article as: Shishir Kumar, Neha Jain, Steven Lawrence Fernandes, Rough Set Based Effective Technique of Image Watermarking, Journal of Computational Science http://dx.doi.org/10.1016/j.jocs.2016.11.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Rough Set Based Effective Technique of Image Watermarking
Shishir Kumar1, Neha Jain2, Steven Lawrence Fernandes3
1,2
Department of Computer Science & Engineering
Jaypee University of Engineering & Guna (M.P.), India 3
Dept of Electronics & Communication Engineering
Sahyadri College of Engineering & Management, Mangalore, Karnataka, India 1
[email protected],[email protected],
3
[email protected]
HIGHLIGHTS
A novel rough set based image-adaptive reference watermarking scheme based on DWT and SVD has been presented.
An attempt has been made to solve the problem of image ambiguity and statically redundant wavelet coefficients .
Lower and upper approximation of wavelet sub-bands has been computed by considering the threshold wavelet coefficients.
Graphical illustration of relative performance with existing reference watermarking routines has been presented.
Abstract: This paper presents rough set based image-adaptive reference watermarking technique based on Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD). A novel method has been proposed through this paper for solving the problem of image ambiguity and statistically redundant wavelet coefficients occurs during removal of shift-invariance problem. To deal with these redundant wavelet coefficients, the concept of rough set based approximation set has been used for watermarking. Rough sets is a mathematical tool which provides an approach to approximate a given image matrix in approximation sets. Lower and upper approximation of wavelet sub-bands has been used to generate the reference image. This method is based on embedding the singular values of watermark image into singular values of rough sets based reference image. The proposed reference image watermarking algorithm provides better-quality watermarked image than other contemporary reference watermarking scheme while holding the robustness.
Keywords: Rough Sets, Discrete wavelet transform (DWT), Reference Watermarking, Singular value decomposition (SVD)
1. Introduction Internet technologies and its associated services are facing the problem of rightful ownership, copyright protection, illegitimate coping and tampering the digital media from the decade. Digital watermarking has an extensive application in the domains resembling to communication content validation, content monitoring, owner recognition and detection, defense and intelligence [1,2]. These watermarking methods are classified into transform-domain and spatial-domain methods. In spatial domain algorithms, grayscale values of the host image has been modified straightforwardly whereas during transformed domain watermarking, its coefficients have been modified to implant the watermarks. Robustness of watermark is a major issue with spatial domain based
watermarking techniques; however it’s easier to implement. Watermarking based on Transform domain is consistent and vigorous to image based attacks such as DCT and DWT based techniques [3- 5]. DWT based watermarking uses various sub-bands composite of low and high frequency, to embed watermark images [5-7]. DCT and DWT have been used as a background mathematical transformation from the decade. In 2002, a novel transform for watermarking scheme has been introduced by Liu et al. [8] and named as Singular Value Decomposition (SVD). SVD inherits the feature of stability for singular values and various geometrical invariant characteristic. Furthermore, SVD has been applied to the consequential modified singular values to get the watermarked singular values. These watermarked singular values used further to get the watermarked image. Ganic and Eskicioglu[9] have suggested the collective use of DWT and SVD and recommended a technique based on hybridization of DWT-SVD watermarking algorithm. In this proposed technique, singular values of every sub-band have been used to embed the watermark. In view of the fact that, all one-level DWT sub-bands of host image has been modified. The proposed technique obtains excellent robustness against multiple image processing attacks. Lai et al. [10] recommended a hybrid watermarking method based on DWT-SVD. In this hybrid technique watermark has been divided into two halves. These halves correspondingly embedded into the two singular value matrices of mid- frequency sub-bands of host image. This watermarking technique provide enhancement over the other watermarking schemes under multiple attacks. Joo et al. [11] proposed a robust reference watermarking technique in which low frequency sub bands of n-level DWT decomposition has been used for watermarking purpose. Furthermore, this low frequency sub bands undergo to one more level DWT decomposition and then reference image has been framed by incorporating all high frequency sub bands to zero. It is well known fact that low-frequency wavelet sub bands persevere most of image energy and at the same very sensitive to human eyes. Due to this nature of low-frequency wavelet sub bands, this particular watermarking scheme do not provide a good perceptual quality of watermarked image. Liu et al. [12] have given a new watermarking scheme based on self-reference image after modification in Joo et al. [11] reference watermarking. In order to construct the reference image, original image has been changed by means of 1-level DWT decomposition and then substitute zero in all high frequency sub bands.Liu et al.[12] proposed a reference watermarking technique which shows robustness against multiple image processing manipulations such as scaling ,filtering, JPEG compression while suffering from imperceptibility problem. Bhatnagar et al. [13] presents a wavelet domain grayscale logo reference watermarking technique in which robust blocks of wavelet sub-bands has been used for embedding the watermark logo. Bhatnagar et al. [14] presents a novel watermarking technique to overcome the issue of imperceptibility occurred in Joo et al. [11] and Liu et al. [12].In this technique, sub-image has been formed using directive contrast of wavelet coefficients. Directive contrast used to represent the relation of high frequency sub bands with its corresponding low frequency sub bands. However this particular scheme provides a good perceptual quality of watermarked image but it does not
provide adaptive nature and suffers from robustness against multiple image processing attacks specifically filtering, rotation and Gaussian noise. The DWT based reference watermarking and its parallel variation which deals with robustness and impeccability. [11-14,33]. These all reported reference watermarking scheme does not depict the image-adaptive behavior due to the use of fixed embedding strength, hence be deficient in providing good perceptual quality of watermarked image. Rough set theory (RST) provides a prevailing tool for uncertainty problem, data redundancy, feature reduction, rule extraction and granularity computation [18-28]. The main contribution of Rough Set is to diminish the number redundant features thereby enhancing the performance of image dispensation considering the aspects of perceptual quality, noise removal, object extraction and image classification. This paper presents a novel robust Rough sets based reference watermarking technique based DWT and SVD. The first aim is to diminish the statistical redundancies among the wavelet coefficients of host image and the second aim is to provide the perceptual perfection to the watermarked image based on image adaptive watermarking threshold. The proposed approach in this paper is the hybridization of techniques such as DWT, Rough Sets and SVD for image watermarking. Initially, the host image has been segregated by means of discrete wavelet transform and then Rough Set classification has been performed on selected sub bands to divide into upper and lower approximation set. The upper and lower approximation of wavelet sub-bands has been computed by considering the threshold wavelet coefficients. Furthermore, these approximations are used to generate a reference image by applying inverse DWT. Now SVD is applied to reference image for modification of singular value of a logo watermark. The idea of Rough entropy has been exploited, in order to make an image-adaptive reference watermarking scheme. The proposed scheme for watermarking is efficient because of use of Rough entropy as embedding strength and rough set based classification for reduction of statistical redundancies between wavelet coefficients.
2. Preliminaries This section presents various terminologies used in the proposed algorithm for better understanding. These terminologies are given below: 2.1 Discrete Wavelet Transform(DWT) DWT is an important tool for various image processing applications such as in engineering, science and mathematics and computer science because to its highly energy compaction properties. DWT split an image into four parts or sub bands ( LL, LH, HL and HH ) using single level decomposition. Figure 1 has shown the two level decomposition of discrete wavelet transform [2, 4, 11,23,27]. High pass and Low pass filters are used in multiple directions for obtaining sub-bands. The general process of DWT-based watermarking schemes follow
transformation of the image into its transform domain and corresponding watermark has been embedded in subbands. Watermarks inserted in LL or LH sub-bands are better against multiple types of attacks. The perceptual quality of image degrades if watermarks inserted in LL or LH sub-bands. The mid frequency sub-bands are suitable for improving perceptual quality of host image and these sub-band are superior and robust against image processing attacks.
2.2 Singular Value Decomposition (SVD) SVD has emerged as a popular tool in all scientific fields because of its geometric and translation properties. A rectangular matrix “A” may be represented into an orthogonal matrix U, diagonal matrix 𝜎, and the transpose of an orthogonal matrix V [2,7,9,10,15,16,17,23,24,29,30] after applying SVD. Given image A of size M×N is decomposes by SVD as 𝐴𝑀𝑁 = 𝑈𝑀𝑀 𝜎𝑀𝑁 𝑉𝑁𝑁 𝑇 = 𝑈1 𝜎1 𝑉1 𝑇 + 𝑈2 𝜎2 𝑉2 𝑇 + 𝑈3 𝜎3 𝑉3 𝑇 + ⋯ … … … . . +𝑈𝑟 𝜎𝑟 𝑉𝑟 𝑇 It can be represented as 𝑈𝑀𝑀 𝜎𝑀𝑁 𝑉𝑁𝑁 𝑇 = 𝐴𝑀𝑁 𝑈1 𝜎1 𝑉1 𝑇 + 𝑈2 𝜎2 𝑉2 𝑇 + 𝑈3 𝜎3 𝑉3 𝑇 + ⋯ … … … . . +𝑈𝑟 𝜎𝑟 𝑉𝑟 𝑇 = 𝐴𝑀𝑁 Where r is the rank, U and V are orthogonal matrices of size M x M and N x N. Diagonal matrix S of size M x N having singular values and which satisfy the property, 𝜎,,1 > 𝜎2,2 > 𝜎3,3 > ⋯ … … > 𝜎𝑚,𝑛 SVD exhibits common geometric distortion attacks such as rotation transpose, flip, translation invariance and scale. These geometric invariance properties make SVD a very favorable tool for reference watermarking. 2.3. DWT-SVD based Reference Image Watermarking Joo et al. [11] presents a novel and robust scheme for reference watermarking based on DWT-SVD and further it has been extended by Liu et al. [12] by adopting the concept of self reference image. These watermarking schemes use the low frequency sub-bands to generate the reference image and provide better resist against various image processing attacks. Bhatnagar & Raman [14] introduced a new concept of directive contrast for watermarked images in order to provide high perceptual quality. Directive contrast of wavelet sub bands provides namely Horizontal contrast, Vertical contrast and Diagonal contrast used to represent the relative nature in
comparison to low frequency sub bands. Suppose one level DWT decomposition has been applied on image A to get four sub-bands {𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻} then corresponding directive contrast [14] may be defined as 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐿𝐻 𝐴(𝑖,𝑗)
(1)
𝐿𝐿𝐴(𝑖,𝑗)
𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐻𝐿𝐴 (𝑖,𝑗) 𝐿𝐿𝐴 (𝑖,𝑗)
𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐻𝐻 𝐴(𝑖,𝑗) 𝐿𝐿𝐴 (𝑖,𝑗)
(2) (3)
For extraction of the vertical, horizontal and diagonal details of wavelet coefficients, directive contrast can be explored equations (1), (2) and (3) as 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐿𝐻 𝐴 (𝑖, 𝑗) 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐻𝐿𝐴 (𝑖, 𝑗) 𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐻𝐻 𝐴 (𝑖, 𝑗)
Consequently, watermark embedding has been performed on the reference image generated by using directive contrast. The singular value of watermark logo image has been used for further embedding with the singular value of the reference image. Figure 2 has been provided in order to represent the block diagram of directive contrast based reference watermark embedding scheme proposed by Bhatnagar & Raman [14].
3. Problem of Image Ambiguity and Statistical Redundancy Gray Scale images are intrinsically surrounded with different types of ambiguities because of imprecision of grayscale values. Therefore an appropriate technique is required that integrate the ambiguities of images in order to perform image processing tasks. Grayscale ambiguity can be classified as grayness ambiguity and spatial ambiguity [19, 23]. The grayscale values around the pixels are deemed to be inexact primarily in terms of the gray level. It represents that a gray value of a pixel may not vary from its neighboring pixels up to definite extents and at the same time it may be observed that a gray value may depict in close proximity of gray levels to certain extents. Furthermore, the pixel values of nearby region have imperfect discernibility due to the scantiness of contrast. Figure 3 has been supplied to depict that an exact boundary cannot be represented due to steadily changing gray values. These ill defined boundaries and vagueness of grayscale values majorly affect the contrast of the image and degrade the perceptual quality of image. Consequently, if watermarking has been performed on ambiguous gray scale values, distress the imperceptibility of watermarked image.
Statistical redundancy of values is another problem that may find in DWT coefficients. The problem related to change in wavelet coefficients is due to shift invariance problem. In order to overcome the shift invariance problem, a problem of statistical redundancy introduced in all sub bands. The deficiency and the unpredictability in sensitivity intrinsic to the Human Visual System (HVS) permit the perceptual redundancies cause the poor quality of watermarked image. Rough set concept has been used because of its ability to deal with uncertain grayscale pixel values and statistical redundancy. RST has been emerged as a technique to control uncertainty, to assess the significance of attributes, to reduce redundancies, and classify objects into required classes [19]. In this paper RST has been used to generate the reference image while removing the redundancy of coefficient value and at the same time removing the uncertainty of grayscale values.
4. Rough Sets Based Image Representation 4.1 Rough Sets Rough set theory (RST) [22] established by Pawlak during 1980s, presents a way to describe knowledge and to approximation of sets. In recent times, RST has turned out to be a popular mathematical technique for the reduction of the ambiguity in grayscale images. The principal contribution of rough set theory is classification of information granules into outer and inner approximations and furthermore makes it eventual for image processing, image classification, feature selection, object extraction. An information system can be represented as a pair (U, A) where U (universe) stand for a non-empty finite set of information and A stands for a non-empty finite set of attributes. Suppose F ⊆ A and 𝑦 ∈ 𝑈 then it may be written as 𝑦~𝐵 = {𝑥 ∈ 𝑈 ∖ ∀𝜙 ∈ 𝐹, 𝜙(𝑦) = 𝜙(𝑥)
(4)
Equation (4) has been used to represent that description of y matches with description of x. An indiscernibility relation (R), in view of the universe generally means for the similarities of elements present in the universe. U/R is represented as the family of all granules consequently, the set A can be approximately by two definable set RA(u) and RA(u) which can be defined as 𝑈
𝑅𝐴(𝑢) = ⋃𝑖 (𝑋𝑖 | : 𝑋𝑖 ∈ 𝐴) 𝑅 𝑈
𝑅𝐴(𝑢) = ⋃𝑖 (𝑋𝑖 | 𝑅 : 𝑋𝑖 ∩ 𝐴 ≠ ∅)
(5)
(6)
RA(u) and RA(u) repectively known as lower and upper approximation sets. All three regions or equivalent classes induced by the feature values as depicted through Figure 4.
4.2 Rough Set for Image classification The gray scale values around the boundaries of object regions are generally vague because of spatial ambiguities subsist in grayscale images [18,19,20,21,22,32,35]. This ambiguity of grayscale values can be efficiently handled by classifying the grayscale images with upper and lower approximations. DWT also suffers from the shift variance problem. The lack of shift invariance nature of wavelet coefficients makes watermarked image vulnerable to geometrical attacks. The shift variance problem can be solved by the usage of un-decimated filters suggested by several authors and at the same time it introduces redundancy. In order to deal with the above problem, idea of rough set based approximation has been exploited. Considering the universe U as an image which consist various gray scale values at each pixels then U can be categorized into an assortment of non-overlapping windows of size x × y. Furthermore each window should be treated as a granule G and within this Object region in the image which is approximated by RST. An image of size M x N has been further classified into two different classes of lower approximation and upper approximation by considering of gray scale value. Let I(u) and I(l) represents the upper and lower approximation set of two images consequently. I (u) and I (l) may be further classified into two sets of gray scale values by considering a specific threshold value T. The upper and lower approximation set of an image I (u) and I (l) is defined as ̅̅̅̅̅̅ 𝐼 (𝑢) = {⋃𝑖 (𝐵𝑖 |𝐺𝑗 < 𝑇, ∀𝑗 = 1, … … … 𝑚𝑛) and Gj depicts the pixels value belongs to granule Bi }
(7)
𝐼(𝑙) = {⋃𝑖(𝐵𝑖 |𝐺𝑗 > 𝑇, ∀𝑗 = 1, … … … 𝑚𝑛) and Gj depicts the pixels value belongs to granule Bi }
(8)
Threshold T used for classifying the image into upper and lower approximation can be decided based upon the roughness and rough entropy of the image. Furthermore, from the equation (7) and equation (8) it may be observed that classifying the grayscale image into upper and lower approximations fully dependent on a threshold value. Roughness and Rough Entropy [20,23] of an image has been given as |𝐼(𝑙)|
𝑅𝐼 = 1 − |𝐼(𝑢)| Where, roughness of image R I ∈ {0,1}. 𝑒
𝑅𝐸𝐼 = − [𝐼(𝑙) 𝑙𝑜𝑔𝑒 𝐼(𝑙) + 𝐼(𝑢) 𝑙𝑜𝑔𝑒 𝐼(𝑢)] 2
(9)
Roughness and Rough Entropy of an image are contradictory to each other, when maximizing the rough entropy basically minimizing the roughness of the image. Rough Entropy of an image also ∈ {0,1} and further may be used as a watermarking strength because of its dependency on the roughness of the image. Suppose maximum_grayscale and minimum_grayscale depicts the corresponding grayscale values of an image, then with the help of below mentioned procedure a threshold value can be calculated. Decompose a given image into desired number of granule Bi
Where i ∈ {0,1 … … P} , P represents total number of granule 𝐺𝑗 ∈ {0,1 … … 𝑇, 𝑇 + 1, 𝑇 + 2 … … . .255} Symbolize the gray scale values. max_ Bi = maximum grayscale value of pixels in granule Bi min_ Bi = minimum grayscale value of pixels in granule Bi 𝑇=
𝑚𝑎𝑥{ 𝑚𝑎𝑥_ 𝐵𝑖 }+ 𝑚𝑖𝑛 {𝑚𝑖𝑛_ 𝐵𝑖 } 2
Figure 5 has been used to depict the (a) Lena image (b) lower approximation of lena image and (c) upper approximation of lena image respectively.
5. Rough Set based Reference Image Watermarking The proposed Reference watermarking scheme has been used to exploit the concept of rough set in view of image processing. The general understanding related to DWT-SVD based reference watermarking methods is that it provides the high perceptual quality of watermarked image but less resistive to multiple image processing attacks. In the literature, presented watermarking techniques are not adaptive due to the use of explicit embedding strength value and the same time suffers from the motion blur, filtering attack, and other attacks in the same domain. In the proposed approach the host image are classified into upper and lower approximation set using its wavelet coefficients for generating reference image.
The singular value used for generating a reference image has been utilized for embedding the logo watermark. Rough set has been used to enhance the perceptual quality while SVD provide robustness. DWT suffers from the redundancy problem that introduces while dealing with the shift invariance problem. To overcome the redundancy in wavelet coefficient during reference watermarking, the idea of rough set based image representation has been adopted. In order to provide a Rough Set based adaptive Reference Image Watermarking scheme, the idea of Rough Entropy of upper and lower approximation set has been considered. Furthermore it depends on that which approximation set has been considered for generation of the reference image and roughness will be used accordingly. Figure 6 and 7 has been consequently used to represent the rough set based reference watermark embedding and extraction scheme .If 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) and 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) consequently represents a lower and upper approximation of selected sub bands 𝐴
𝑙_𝑠𝑒𝑙𝑒𝑐𝑡
𝑛+1 (𝑖, 𝑗)
and further it has been used during reference image
generation for watermark embedding then Rough entropy for these approximation set is given as 𝑒
𝑅𝐸𝑙𝑜𝑤𝑒𝑟 = − 2 [𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑙𝑜𝑔𝑒 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) ]
(10)
𝑒
𝑅𝐸𝑢𝑝𝑝𝑒𝑟 = − 2 [𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑙𝑜𝑔𝑒 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) ]
(11)
These RElower and REupper has been used as watermarking embedding strength, makes it adaptive reference watermarking algorithm. The Rough set based image classification has been used to classify the wavelet coefficients into lower and upper approximation sets. Further these approximation sets has been used to generate the reference image. In order to generate the reference image 1-level DWT has been applied to selected sub bands and classify into lower and upper approximation sets described through Section 5.1.
5.1 Algorithm for classification of lower and upper approximations
𝑙_𝑠𝑒𝑙𝑒𝑐𝑡
𝐼𝑛𝑝𝑢𝑡:
𝐴 𝑛+1 (𝑖, 𝑗) = selected sub bands for reference image generation max_gray = maximum grayscale value of selected sub bands 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗)
min_gray = minimum grayscale value of selected sub bands 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑂𝑢𝑡𝑝𝑢𝑡: 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) = 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) = 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 RElower = Rough entropy of 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 = Rough entropy of 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑺𝒕𝒆𝒑𝟏. 𝐷𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑒 𝑎 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑖𝑛𝑡𝑜 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝐵𝑖 𝑤ℎ𝑒𝑟𝑒 𝑖 ∈ {0,1 … … 𝑃} 𝑎𝑛𝑑 𝑃 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝑺𝒕𝒆𝒑𝟐. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑇 𝑎𝑠 max{ max_ Bi (i, j)} + min{min_ Bi (i, j)} 𝑇(𝑖, 𝑗) = 2 𝑺𝒕𝒆𝒑𝟑. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗)𝑎𝑛𝑑 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑜𝑓 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑎𝑠 𝑓𝑜𝑟 𝑖 = 1: 1: 𝑃 (𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒) 𝑓𝑜𝑟 𝑗 = 1: 1: 𝑃 (𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒) 𝑖𝑓( 𝐵𝑖 (𝑖, 𝑗) < 𝑇(𝑖, 𝑗)) 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 𝐵𝑖 (𝑖, 𝑗); 𝑢𝑝𝑝𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 0; 𝑒𝑙𝑠𝑒 𝑢𝑝𝑝𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 𝐵𝑖 (𝑖, 𝑗); 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 0; 𝑒𝑛𝑑; 𝑺𝒕𝒆𝒑𝟒. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 RElower and REupper
𝑒𝑛𝑑; 𝑒𝑛𝑑;
e RElower = − [𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) log e 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) ] 2 e REupper = − [𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) log e 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) ] 2
The Lower and upper approximation sets of selected sub bands have been used further for reference image generation. We can use either lower approximation 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) or 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) of selected sub bands during production of reference image. Furthermore section 5.2 has been provided to depict the watermarking embedding algorithm by using 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) or 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) . 5.2 Watermark Embedding Algorithm
𝐼𝑛𝑝𝑢𝑡:
𝐴(𝑖, 𝑗) = 𝐻𝑜𝑠𝑡 𝐼𝑚𝑎𝑔𝑒 𝑊(𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝐼𝑚𝑎𝑔𝑒
𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) = 𝐿𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑅𝐸𝑙𝑜𝑤𝑒𝑟 𝑎𝑠 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) = 𝑈𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 and 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 𝑎𝑠 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑂𝑢𝑡𝑝𝑢𝑡:
𝐴𝑤 (𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝐼𝑚𝑎𝑔𝑒
𝑺𝒕𝒆𝒑𝟏:
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑛 𝑙𝑒𝑣𝑒𝑙 ℎ𝑎𝑎𝑟 𝑤𝑎𝑣𝑒𝑙𝑒𝑡 𝑑𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 ℎ𝑜𝑠𝑡 𝑖𝑚𝑎𝑔𝑒 𝐴𝑙 (𝑖, 𝑗) 𝑎𝑛𝑑 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑖𝑚𝑎𝑔𝑒 𝑊^𝑙 (𝑖, 𝑗) 𝑤ℎ𝑒𝑟𝑒 𝑙 ∈ {𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻}
𝑺𝒕𝒆𝒑 𝟐:
𝑆𝑒𝑙𝑒𝑐𝑡 𝑎𝑛𝑦 𝐴𝑙 𝑛 (𝑖, 𝑗 ) 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑙 𝑎𝑛𝑑 𝑛 ∈ {𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑙𝑒𝑣𝑒𝑙}
𝑺𝒕𝒆𝒑 𝟑:
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 1 − 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑜𝑛 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑑𝑒𝑛𝑜𝑡𝑒𝑑 𝑏𝑦 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 +1 (𝑖, 𝑗 )
𝑺𝒕𝒆𝒑 𝟒.
𝐷𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑒 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗 ) 𝑖𝑛𝑡𝑜 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝐵𝑖 𝑎𝑛𝑑 𝑒𝑥𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑜𝑟 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑓𝑟𝑜𝑚 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗 ) 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑎𝑐𝑐𝑜𝑟𝑑𝑖𝑛𝑔 𝑎𝑙𝑔𝑜𝑟𝑖𝑡ℎ𝑚 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 3.1
𝑺𝒕𝒆𝒑 𝟓.
𝑁𝑜𝑤 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑜𝑟 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑢𝑠𝑒𝑑 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡踘 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑏𝑦 𝑎𝑝𝑝𝑙𝑦𝑖𝑛𝑔 1 − 𝑙𝑒𝑣𝑒𝑙 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑤𝑎𝑣𝑒𝑙𝑒𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ).
𝑺𝒕𝒆𝒑 𝟔.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑆𝑉𝐷 𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑎𝑠 𝑤𝑒𝑙𝑙 𝑎𝑠 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑊 𝑡𝑜 𝑔𝑒𝑡, 𝑇
𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) W(𝑖, 𝑗 ) = 𝑊𝑈(i, j)𝑊𝑆(i, j)𝑊𝑉 𝑇 (i, j) 𝑺𝒕𝒆𝒑 𝟕.
𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑎𝑠 𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑏𝑦 𝑚𝑜𝑑𝑖𝑓𝑦𝑖𝑛𝑔 𝑡ℎ𝑒 𝑠𝑖𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑎𝑙𝑢𝑒𝑠
𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) + RElower ∗ 𝑊𝑆(i, j) if 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑢𝑠𝑒𝑑 𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) + 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 ∗ 𝑊𝑆(𝑖, 𝑗 ) 𝑖𝑓 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑢𝑠𝑒𝑑 𝑇
𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑤ℎ𝑒𝑟𝑒 RElower 𝑎𝑛𝑑 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ. 𝑺𝒕𝒆𝒑 𝟖.
𝐶𝑎𝑟𝑟𝑦 𝑜𝑢𝑡 𝐼𝐷𝑊𝑇𝑜𝑛 𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑡𝑜 𝑜𝑏𝑡𝑎𝑖𝑛 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒, 𝐴𝑤 (i, j)
5.3 Watermark Extraction Algorithm
𝐼𝑛𝑝𝑢𝑡:
𝐴𝑤 ∗ (𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝐼𝑚𝑎𝑔𝑒(𝐷𝑖𝑠𝑡𝑜𝑟𝑡𝑒𝑑 ) 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒
𝑂𝑢𝑡𝑝𝑢𝑡:
∗(
𝑊 i, j) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝐼𝑚𝑎𝑔𝑒 𝑺𝒕𝒆𝒑𝟏.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑜𝑛𝑒 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑜𝑛 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝐴𝑤 ∗ (𝑖, 𝑗 )𝑡𝑜 𝑔𝑒𝑡 𝑡ℎ𝑒 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠
𝑺𝒕𝒆𝒑 𝟐:
𝐸𝑥𝑡𝑟𝑎𝑐𝑡 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑓𝑜𝑟 𝑓𝑢𝑟𝑡ℎ𝑒𝑟 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑑𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑙𝑒𝑣𝑒𝑙}
𝑺𝒕𝒆𝒑𝟑.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑆𝑉𝐷 𝑜𝑛 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑎𝑛𝑑 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑇 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑇
𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑺𝒕𝒆𝒑𝟒.
𝐸𝑥𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑠𝑖𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑏𝑦 𝑐𝑜𝑚𝑝𝑢𝑡𝑖𝑛𝑔 𝑆 𝑟𝑒𝑓+ (𝑖, 𝑗 ) − 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑊 ∗ (i, j) = if 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑢𝑠𝑒𝑑 𝑑𝑢𝑟𝑖𝑛𝑔 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 RElower
𝑺𝒕𝒆𝒑𝟓.
𝑁𝑜𝑤 𝑓𝑜𝑟𝑚𝑢𝑙𝑎𝑡𝑒 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑎𝑠 𝑊 ∗ (i, j) = 𝑊𝑈(i, j)𝑊𝑆 ∗ (i, j)𝑊𝑉 𝑇 (i, j)
6. Results Analysis and Comparisons This section has been used to discuss the various evaluation parameters to quantify the effectiveness of proposed Rough set based Reference Watermarking, robustness of extracting watermark against a variety of attacks. A
detailed comparison with existing Reference watermarking scheme with proposed method has been presented latter in this section.
6.1 Experimental Environment In order to justify the performance evaluation of a proposed Rough set based Reference Watermarking algorithm, several experiments have been conducted on grayscale cover images “Barbara”, “Lena”, “Pirate”, “Livingroom” of size 512 × 512 and Watermark logo “JUET”,”JAYPEE” of size 64 x 64 depicted through Figure 8. All experiment has been performed on MATLAB platform version 7.1. For imperceptibility of the watermarked image, peak signal-to-noise ratio (PSNR) has been used and is given by following equations 𝐿
𝑚𝑎𝑥 𝑃𝑆𝑁𝑅(𝐴, 𝐴𝑤 ) = 10 ∗ 𝑙𝑜𝑔10 (𝑅𝑀𝑆𝐸 )
2
(12)
Where 𝐿𝑚𝑎𝑥 is maximum gray scale value and the root mean square error(RMSE) defined as 𝑅𝑀𝑆𝐸(𝐴, 𝐴𝑤 ) = √
𝑀 2 ∑𝑁 𝑖=1 ∑𝑗=1(𝐴(𝑖,𝑗)−𝐴𝑤 (𝑖,𝑗))
𝑁𝑥𝑀
(13)
Where 𝐴(𝑖, 𝑗) represents the luminance value of original image and 𝐴𝑤 (𝑖, 𝑗 ) is the luminance value of watermarked Image. The value of wPSNR is used to judge the quality of watermarked image which is given in Equation (14). 𝑤𝑃𝑆𝑁𝑅(𝐴, 𝐴𝑤 ) = 10 ∗ 𝑙𝑜𝑔10 (
𝐿𝑚𝑎𝑥 𝑅𝑀𝑆𝐸∗𝑁𝑉𝐹
)
2
(14)
Where (NVF) represents the Noise Visibility Function. Figure 9 and Table -1 presents the values of PSNR and wPSNR of test images.
Normalized Correlation Coefficient (NCorr) and Bit Error Rate (BER) has been used to justify the effectiveness of the proposed technique, which is defined as, 𝑁𝐶𝑜𝑟𝑟 (𝑊, 𝑊 ∗ ) =
𝐵𝐸𝑅 (𝑊, 𝑊 ∗ ) =
𝑀 ∗ ∗ ∑𝑁 𝑖=1 ∑𝑗=1(𝑊−𝑊)(𝑊 −𝑊 ) 𝑀 𝑁 𝑀 2 ∗ ∗ 2 √∑𝑁 𝑖=1 ∑𝑗=1(𝑊−𝑊) √∑𝑖=1 ∑𝑗=1(𝑊 −𝑊 )
100 𝐵
1 𝑖𝑓𝑊 ∗ (𝑛) ≠ 𝑊(𝑛) ∑𝐵−1 { 𝑛=0 0 𝑖𝑓𝑊 ∗ (𝑛) = 𝑊(𝑛)
(15)
(16)
Where W, W*,B,n consequently represents original watermark, extracted watermark from distorted image, total number of bits and location of bit . Normalized Correlation coefficient (NCorr) generally lies between [−1, 1]. It is a well known fact that NCorr and BER are of contradictory nature. If the value of NCorr is higher, then BER
should have to be lower and vice versa. Table -2 present normalized correlation coefficient value of extracted watermark from attacked watermarked Barbara, Lena, Livingroom and Pirate Images. 6.2 Experimental Results and Discussions The proposed Rough set based Reference Watermarking algorithm has been tested to check the robustness. Following are image processing attacks which are included for testing the robustness: Image Filtering, addition of Gaussian, Salt & Pepper, Speckle noise, Image Rotation, JPEG Compression and Scaling and Motion Blur [31].
6.2.1
Robustness against Image Filtering
Image filtering is a widely-used image processing technique and it has been used to remove the various types of noise, smooth the finer details while preserving the most important edges. In order to check the robustness of proposed watermarking algorithm, watermarked image passed through 13x13 average and median filter.
The attacked watermarked image and corresponding extracted watermark are depicted through Figure 10 and Figure 11 against average and median filtering attack.
6.2.2
Robustness against Gaussian, Salt & Pepper, Speckle Noise
Addition of channel noise is a very frequent and it can occur any time during image transmission. The quality images have been degraded mainly by Salt & Pepper noise, Gaussian noise and Speckle Noise. In our experiment watermarked image has been passed through additive Gaussian noise with variance density of 0.1. Figure 12 (a) & (c) has been used to represent the watermarked Pirate and Barbara Image after Gaussian noise and Figure 12 (b) & (d) consequently represents the extracted watermark. To test the effectiveness of a proposed watermarking scheme against salt & pepper and Speckle noise, the watermarked image has been covered by salt & pepper noise having a density of 50 % and Speckle noise of 50 %, consequently represented by Figure 13 and Figure 14.
6.2.3
Robustness against Rotation, Scaling and Cropping
To design reference watermarking embedding and detecting scheme, in order to survive against geometrical distortion is a challenging task. The Geometrical distortion of images is always a lossy operation and consequently removes some part of the image that may contain watermark information [34]. Due to the property and nature of survival of singular value decomposition against geometrical distortion such as rotation, cropping and resizing, the watermarking scheme proposed in this paper poses a high Normalized Correlation Coefficient
value. The influence of rotation is tested on the watermarked image up to 60 degrees and can be depicted through Figure 15. Figure 16 represents the watermarked image and corresponding extracted watermark after rescaling it to 512-128-512. Figure 17 presented cropping effect on watermarked image (25% left column) and corresponding equivalent extracted watermark. The watermark has been extracted and obtained NCC of JUET and Jaypee logo is 0.8822 and 0.7939 respectively.
6.2.4 Robustness against JPEG Compression and Motion Blur Any watermarking scheme has been robust against JPEG compression attacks. The experiment has been performed on a watermarked image by changing the JPEG compression quality factor that varies from (1-100). The value of Quality factor 100 represents a high quality image while degradation in quality factor represents the poor quality of image as in Figure 18 .Motion blur attack generally simulates the movement of the camera during image capturing. In our experiment the effectiveness of proposed watermarking methods has been tested against motion blur by considering 15 pixel movement of watermarked image. Figure 19 shows the watermarked image and corresponding extracted watermark after motion blur. Figure 18: (a) & (c) Watermarked image of Pirate and Barbara after JPEG compression on quality factor 50 (b) & (d) Extracted Watermark
6.3
Comparative Analysis
To verify the effectiveness of proposed Rough set based Reference watermarking technique with the other reported parallel Reference watermarking scheme (Bhatnagar & Raman[14] and Bhatnagar & Raman[13]) on various noise parameters has been compared. Figure 20 and Figure 21 depict the performance comparison of the proposed approach using NCorr and BER for average filtering attack by changing the filter size. The proposed algorithms against the average filtering attack are far better than Bhatnagar & Raman [14] Reference Watermarking. Furthermore in view of Figure 20 and 21, the extracted watermark correlation coefficient is quite good and at the same time representing low BER rather than Bhatnagar &Raman [14] Reference Watermarking scheme.
The influence of rotation has been compared by changing the degrees of rotation (10 to 50) in intervals of 5 and shown through Figure 22 and 23. It may be observed that the proposed technique is better restive against rotation
attack while comparing with Bhatnagar & Raman [14] Reference Watermarking scheme. The judgment has been made by considering the contradictory nature of NCorr and BER against rotation attack as represented by Figure 22 and Figure 23. In order to compare the performance proposed watermarking scheme for JPEG compression attack, quality factor of compresses has been varied. The robustness of extracted watermark have been tested by changing the quality factor values ( 10 to 100 in an interval of 5). From figure 24 and 25, It has been derived that the performance of Rough set based Reference Watermarking is inferior in comparison to Bhatnagar & Raman [14] Reference Watermarking scheme.
Figure 26 and Figure 27 have been used to show the performance of a proposed Rough set based Reference watermarking algorithm against Gaussian variance attack. It may be observed that proposed method NCorr value is in close proximity of Bahatnagar & Raman[14] Reference Watermarking as represented by Figure 26. When we compare our algorithm by using Bit Error Rate (BER) then it shows inferior performance in comparison to Bahatnagar & Raman [14] Reference Watermarking scheme. Proposed Rough Set based Reference watermarking has also been tested against Motion Blur. Motion Blur is a kind of attack that simulates the digital camera behavior and it occurs during image capturing. Performance of the proposed method has been evaluated by changing the pixel motion and observed that Rough set based Reference watermarking scheme is superior and the same represented through Figure 28 and Figure 29. Figure 30 and Figure 31 depict the performance of the proposed Rough set based Reference Watermarking scheme against median filtering attack by altering the filter size. The performance of proposed watermarking algorithms against the median filtering attack is better than Bhatnagar & Raman [14] Reference Watermarking Scheme. Consequently by looking at Figure 30 and 31, the extracted watermark correlation coefficient is higher and at the same time representing low BER in comparison to Bhatnagar & Raman [14].
The comparison of the PSNR, wPSNR values and NCorr of proposed Rough set based Reference watermarking algorithm with Bhatnagar &Raman Reference watermarking [14] and Bhatnagar & Raman [ 13] has been presented in Table-4 and Table-5.
7. Conclusion A novel Rough set based approach for Reference Watermarking technique has been presented in this paper to provide a better imperceptibility. In these scheme singular values of watermark signal is embedded in the singular
values of the reference image generated after rough set classification of DWT sub bands coefficients. The concept of Rough set has been used due to its capability of confiscating the statistical redundancies between wavelet coefficients. This concept is also used for removal of grayscale pixel uncertainties and providing improved perceptual perfection to the target watermarked images. This algorithm evades the drawback of fixed embedding strength value that adopted by multiple wavelet based reference watermarking approaches, by using the Rough entropy concept and improves the imperceptibility. The validation of the effectiveness of a proposed watermarking technique has been tested with several experiments and the conclusions inferred. With the results obtained by the experiments it is validated that the proposed approach is robust against multiple Image Processing attacks. Its PSNR values mentioned in Table-4 and Table-5 validated theses conclusions. Various graphical comparisons are presented for justification of robustness of this technique in comparison to other reference watermarking techniques.
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Author Biography
Shishir Kumar in working as Professor the Department of Computer Science and Engineering at Jaypee University of Engineering and Technology, Guna, M.P., India. He has earned PhD in Computer Science in 2005. He has 14 years of teaching and research experience.
Neha Jain received his Bachelor’s Degree in 2009 from Rajiv Gandhi Proudyogiki Vishwavidyala, Bhopal, India and received his Master’s Degree from Jaypee University of Engineering and Technology, India in 2012. Now, he is pursuing his Ph.D. degree from Jaypee University of Engineering and Technology, Guna, M.P., India.
Mr. Steven Fernandes is member of Core Research Group, Karnataka Government Research Centre of Sahyadri College of Engineering and Management, Mangalore, Karnataka. He has received Young Scientist Award by Vision Group on Science and Technology, Government of Karnataka, India in the year 2014 and also received grant from The Institution of Engineers (India), Kolkata, India. He completed his B.E (Electronics and Communication Engineering) with Distinction from Visvesvaraya Technological University, Belagavi, Karnataka and M.Tech (Microelectronics) with Distinction from Manipal University, Manipal, Karnataka. His Ph.D work “Match Composite Sketch with Drone Images” has received patent notification (Patent Application Number: 2983/CHE/2015) from Government of India, Controller General of Patents, Designs & Trade Marks. He has 5 years of industry experience working at STMicroelectronics Pvt. Ltd and Perform Group Pvt. Ltd. He has published several papers in peer-reviewed International Journals having Thomson Reuters Web of Science Impact Factor and IEEE, Springer, Elsevier International Conferences. He is also serving has reviewer and guest editor for several Science Citation Indexed and Scopus Indexed International Journals.
LL2
LH2
HL2
HH2
HL1
LH1
HH1
Figure 1: Two-level DWT decomposition
n- Level DWT
Select Wavelet Coefficients from
1-level DWT
{𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻}
Calculate directive contrast and Threshold
Modify selected sub bands by directive contrast
Host Image
IDWT
SVD
Watermark
Reference image from modified sub bands
SVD Watermarked Image
Inverse DWT
Watermarked Reference Image
Figure 2: Block diagram of directive contrast based reference watermark scheme
Modify Singular Values
Figure 3: ill defined boundary and ambiguity in grayscale values of Lena Image
Lower Approximation Information Granule
Set
Upper Approximation Universe
Figure 4: Basic perception of Rough Set
(a)
(b)
(c)
Figure 5: (a) Original Lena Image (b) Rough set based lower approximation of lena image (c) Rough set based upper approximation of lena image
n- Level DWT
Selected Wavelet Coefficients of HH sub bands
Rough set Classification
Lower and Upper approximation of HH sub bands
IDWT
Embedding Strength
Roughness of HH band
SVD
Watermarked Image
Inverse DWT
Watermarked Reference Image
Figure 6: Block diagram of proposed reference watermark embedding scheme
Reference image from HH sub bands
SVD Modify Singular Values
Watermarked Image
One Level DWT
Selected Wavelet Coefficients of LH and HL sub bands
Divisive Normalization Transform
DNT Coefficients of LH and HL sub bands
SVD U and V matrix of Watermark
Extracted Singular Values
Extracted Watermark Figure 7: Proposed watermark extraction scheme
Figure 8: Host image and their corresponding Watermark
Figure 9: Watermarked Image
(a)
(b)
(c)
(d)
Figure 10: (a) & (c) Watermarked images of Pirate and Barbara after Average Filtering (13x13) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 11: (a) & (c) Watermarked images of Pirate and Barbara Image after Median Filtering ((13x13) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 12: (a) & (c) Watermarked images of Pirate and Barbara after addition of Gaussian noise (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 13: (a) & (c) Watermarked image of Pirate and Barbara after addition of salt & pepper noise (b) & (d) Extracted Watermark
(a)
Watermark
(b)
(c)
(d)
Figure 14: (a) & (c) Watermarked images of Pirate and Barbara after speckle noise (b) & (d) Extracted
(a)
(b)
(c)
(d)
Figure 15: (a) & (c) Watermarked images of Pirate and Barbara after rotation (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 16: (a) &(c) Watermarked images of Pirate and Barbara after Resizing ((512-128-512) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 17: (a) & (c) Watermarked images of Pirate and Barbara Image after 25% cropping (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 18: (a) & (c) Watermarked image of Pirate and Barbara after JPEG compression on quality factor 50 (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 19: (a) & (c) Watermarked image of Pirate and Barbara after Motion Blur (15 pixel movement) (b) & (d) Extracted Watermark
Figure 20: Performance of proposed watermarking method for various average filter size by using NCorr
Figure 21: Performance analysis of average filter size by using BER
Figure 22: Performance of proposed technique at various degrees of rotation by using NCorr
Figure 23: Performance of the proposed technique at various degrees of rotation by using BER
Figure 24: Performance against JPEG compression by using NCorr
Figure 25: Performance against JPEG compression by using BER
Figure 26: Performance against Gaussian noise by using NCorr
Figure 27: Performance against Gaussian noise by using BER
Figure 28: Performance against Motion blur by using NCorr
Figure 29: Performance against Motion blur by using BER
Figure 30: Performance against Median Filtering attack by using NCorr
Figure 31: Performance against Median Filtering attack by using BER
Table 1: PSNR and wPSNR values of each test image
Test Images
Barbra
Lena
Pirate
Livingroom
PSNR
68.79
52.69
69.52
46.55
wPSNR
73.25
61.86
71.85
54.45
Table 2: NCorr of extracted watermark
Attacks
Median Filter(13x13) Average Filter(13x13) Rotation(60) Resizing(512-128-512) Gaussian Noise Cropping(1/4) JPEG Compression (50:1) Salt & Pepper (50%) Motion Blur Speckle(50%)
Jaypee
JUET
Barbra
Lena
Pirate
Livingroom
0.5762 0.7944 0.4529 0.6084 0.3879 0.7939 0.5520 0.3845 0.8248 0.3865
-0.1883 -0.1912 -0.2159 0.4439 0.6543 0.9098 0.5892 0.4649 -0.1905 0.4850
0.8692 0.9520 0.7351 0.8728 0.6684 0.8822 0.7937 0.6573 0.8644 0.6743
-0.2648 -0.2670 0.6726 -0.2426 0.9177 0.9744 0.9195 0.7476 -0.2675 0.7733
Table 3: Comparisons of Proposed Rough set based Reference watermarking with Bhatnagar &Raman Reference watermarking [14]
Attacks Extraction Technique Embedding Domain Embedding Strength Size of Watermark Size of Host Image Time Complexity Median Filter Rotation Average Filter Gaussian Noise JPEG Compression Cropping Salt & Pepper Speckle Motion Blur QF = Quality Factor
Proposed Rough set based Reference watermarking
Bhatnagar & Raman[14] Reference watermarking
Semi-Blind DWT+Rough Set+SVD Adaptive 64x64 512x512 O(MN2) 13x13 60 degree 13x13 Up to 50% QF = 1 to 100 25% Up to 50% Up to 50% Tested
Semi-Blind DWT+Directive Contrast+SVD Not Adaptive 64x64 512x512 O(MN2) 13x13 50 degree 13x13 Up to 100% QF = 1 to 100 25% Up to 50% Not applied Tested
Table-4: Comparisons of PSNR and wPSNR with Bhatnagar & Raman Reference Watermarking
Test Images
Barbara Lena Pirate Livingroom
Proposed Method
Bhatnagar &Raman [14]
PSNR
wPSNR
PSNR
wPSNR
68.79 52.69 69.52 46.55
73.25 61.86 71.85 54.45
59.26 54.03 44.43 47.10
68.49 63.71 51.18 54.25
Table-5: Comparisons of NCorr with existing method
Attacks
Proposed Method
Bhatnagar &Raman [14]
Bhatnagar& Raman [13 ]
Median Filter(13x13) Average Filter(13x13) Rotation(60) Resizing(512-128-512) Gaussian Noise Cropping(1/4) JPEG Compression (50:1) Salt & Pepper (50%) Motion Blur Speckle(50%)
0.8692 0.9520 0.7351 0.8728 0.6684 0.8822 0.7937 0.6573 0.8644 0.6743
0.7326 0.7406 0.6841 0.7619 0.6644 0.3369 0.9138 0.6512 0.8083 0.6644
0.4573 0.3072 Not Tested 0.2297 0.2575 -0.9925 0.9360 0.3557 Not Tested Not Tested
S1877-7503(16)30385-4 http://dx.doi.org/doi:10.1016/j.jocs.2016.11.009 JOCS 579
To appear in: Received date: Revised date: Accepted date:
20-7-2016 26-10-2016 21-11-2016
Please cite this article as: Shishir Kumar, Neha Jain, Steven Lawrence Fernandes, Rough Set Based Effective Technique of Image Watermarking, Journal of Computational Science http://dx.doi.org/10.1016/j.jocs.2016.11.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Rough Set Based Effective Technique of Image Watermarking
Shishir Kumar1, Neha Jain2, Steven Lawrence Fernandes3
1,2
Department of Computer Science & Engineering
Jaypee University of Engineering & Guna (M.P.), India 3
Dept of Electronics & Communication Engineering
Sahyadri College of Engineering & Management, Mangalore, Karnataka, India 1
[email protected],[email protected],
3
[email protected]
HIGHLIGHTS
A novel rough set based image-adaptive reference watermarking scheme based on DWT and SVD has been presented.
An attempt has been made to solve the problem of image ambiguity and statically redundant wavelet coefficients .
Lower and upper approximation of wavelet sub-bands has been computed by considering the threshold wavelet coefficients.
Graphical illustration of relative performance with existing reference watermarking routines has been presented.
Abstract: This paper presents rough set based image-adaptive reference watermarking technique based on Discrete Wavelet Transform (DWT) and Singular Value Decomposition (SVD). A novel method has been proposed through this paper for solving the problem of image ambiguity and statistically redundant wavelet coefficients occurs during removal of shift-invariance problem. To deal with these redundant wavelet coefficients, the concept of rough set based approximation set has been used for watermarking. Rough sets is a mathematical tool which provides an approach to approximate a given image matrix in approximation sets. Lower and upper approximation of wavelet sub-bands has been used to generate the reference image. This method is based on embedding the singular values of watermark image into singular values of rough sets based reference image. The proposed reference image watermarking algorithm provides better-quality watermarked image than other contemporary reference watermarking scheme while holding the robustness.
Keywords: Rough Sets, Discrete wavelet transform (DWT), Reference Watermarking, Singular value decomposition (SVD)
1. Introduction Internet technologies and its associated services are facing the problem of rightful ownership, copyright protection, illegitimate coping and tampering the digital media from the decade. Digital watermarking has an extensive application in the domains resembling to communication content validation, content monitoring, owner recognition and detection, defense and intelligence [1,2]. These watermarking methods are classified into transform-domain and spatial-domain methods. In spatial domain algorithms, grayscale values of the host image has been modified straightforwardly whereas during transformed domain watermarking, its coefficients have been modified to implant the watermarks. Robustness of watermark is a major issue with spatial domain based
watermarking techniques; however it’s easier to implement. Watermarking based on Transform domain is consistent and vigorous to image based attacks such as DCT and DWT based techniques [3- 5]. DWT based watermarking uses various sub-bands composite of low and high frequency, to embed watermark images [5-7]. DCT and DWT have been used as a background mathematical transformation from the decade. In 2002, a novel transform for watermarking scheme has been introduced by Liu et al. [8] and named as Singular Value Decomposition (SVD). SVD inherits the feature of stability for singular values and various geometrical invariant characteristic. Furthermore, SVD has been applied to the consequential modified singular values to get the watermarked singular values. These watermarked singular values used further to get the watermarked image. Ganic and Eskicioglu[9] have suggested the collective use of DWT and SVD and recommended a technique based on hybridization of DWT-SVD watermarking algorithm. In this proposed technique, singular values of every sub-band have been used to embed the watermark. In view of the fact that, all one-level DWT sub-bands of host image has been modified. The proposed technique obtains excellent robustness against multiple image processing attacks. Lai et al. [10] recommended a hybrid watermarking method based on DWT-SVD. In this hybrid technique watermark has been divided into two halves. These halves correspondingly embedded into the two singular value matrices of mid- frequency sub-bands of host image. This watermarking technique provide enhancement over the other watermarking schemes under multiple attacks. Joo et al. [11] proposed a robust reference watermarking technique in which low frequency sub bands of n-level DWT decomposition has been used for watermarking purpose. Furthermore, this low frequency sub bands undergo to one more level DWT decomposition and then reference image has been framed by incorporating all high frequency sub bands to zero. It is well known fact that low-frequency wavelet sub bands persevere most of image energy and at the same very sensitive to human eyes. Due to this nature of low-frequency wavelet sub bands, this particular watermarking scheme do not provide a good perceptual quality of watermarked image. Liu et al. [12] have given a new watermarking scheme based on self-reference image after modification in Joo et al. [11] reference watermarking. In order to construct the reference image, original image has been changed by means of 1-level DWT decomposition and then substitute zero in all high frequency sub bands.Liu et al.[12] proposed a reference watermarking technique which shows robustness against multiple image processing manipulations such as scaling ,filtering, JPEG compression while suffering from imperceptibility problem. Bhatnagar et al. [13] presents a wavelet domain grayscale logo reference watermarking technique in which robust blocks of wavelet sub-bands has been used for embedding the watermark logo. Bhatnagar et al. [14] presents a novel watermarking technique to overcome the issue of imperceptibility occurred in Joo et al. [11] and Liu et al. [12].In this technique, sub-image has been formed using directive contrast of wavelet coefficients. Directive contrast used to represent the relation of high frequency sub bands with its corresponding low frequency sub bands. However this particular scheme provides a good perceptual quality of watermarked image but it does not
provide adaptive nature and suffers from robustness against multiple image processing attacks specifically filtering, rotation and Gaussian noise. The DWT based reference watermarking and its parallel variation which deals with robustness and impeccability. [11-14,33]. These all reported reference watermarking scheme does not depict the image-adaptive behavior due to the use of fixed embedding strength, hence be deficient in providing good perceptual quality of watermarked image. Rough set theory (RST) provides a prevailing tool for uncertainty problem, data redundancy, feature reduction, rule extraction and granularity computation [18-28]. The main contribution of Rough Set is to diminish the number redundant features thereby enhancing the performance of image dispensation considering the aspects of perceptual quality, noise removal, object extraction and image classification. This paper presents a novel robust Rough sets based reference watermarking technique based DWT and SVD. The first aim is to diminish the statistical redundancies among the wavelet coefficients of host image and the second aim is to provide the perceptual perfection to the watermarked image based on image adaptive watermarking threshold. The proposed approach in this paper is the hybridization of techniques such as DWT, Rough Sets and SVD for image watermarking. Initially, the host image has been segregated by means of discrete wavelet transform and then Rough Set classification has been performed on selected sub bands to divide into upper and lower approximation set. The upper and lower approximation of wavelet sub-bands has been computed by considering the threshold wavelet coefficients. Furthermore, these approximations are used to generate a reference image by applying inverse DWT. Now SVD is applied to reference image for modification of singular value of a logo watermark. The idea of Rough entropy has been exploited, in order to make an image-adaptive reference watermarking scheme. The proposed scheme for watermarking is efficient because of use of Rough entropy as embedding strength and rough set based classification for reduction of statistical redundancies between wavelet coefficients.
2. Preliminaries This section presents various terminologies used in the proposed algorithm for better understanding. These terminologies are given below: 2.1 Discrete Wavelet Transform(DWT) DWT is an important tool for various image processing applications such as in engineering, science and mathematics and computer science because to its highly energy compaction properties. DWT split an image into four parts or sub bands ( LL, LH, HL and HH ) using single level decomposition. Figure 1 has shown the two level decomposition of discrete wavelet transform [2, 4, 11,23,27]. High pass and Low pass filters are used in multiple directions for obtaining sub-bands. The general process of DWT-based watermarking schemes follow
transformation of the image into its transform domain and corresponding watermark has been embedded in subbands. Watermarks inserted in LL or LH sub-bands are better against multiple types of attacks. The perceptual quality of image degrades if watermarks inserted in LL or LH sub-bands. The mid frequency sub-bands are suitable for improving perceptual quality of host image and these sub-band are superior and robust against image processing attacks.
2.2 Singular Value Decomposition (SVD) SVD has emerged as a popular tool in all scientific fields because of its geometric and translation properties. A rectangular matrix “A” may be represented into an orthogonal matrix U, diagonal matrix 𝜎, and the transpose of an orthogonal matrix V [2,7,9,10,15,16,17,23,24,29,30] after applying SVD. Given image A of size M×N is decomposes by SVD as 𝐴𝑀𝑁 = 𝑈𝑀𝑀 𝜎𝑀𝑁 𝑉𝑁𝑁 𝑇 = 𝑈1 𝜎1 𝑉1 𝑇 + 𝑈2 𝜎2 𝑉2 𝑇 + 𝑈3 𝜎3 𝑉3 𝑇 + ⋯ … … … . . +𝑈𝑟 𝜎𝑟 𝑉𝑟 𝑇 It can be represented as 𝑈𝑀𝑀 𝜎𝑀𝑁 𝑉𝑁𝑁 𝑇 = 𝐴𝑀𝑁 𝑈1 𝜎1 𝑉1 𝑇 + 𝑈2 𝜎2 𝑉2 𝑇 + 𝑈3 𝜎3 𝑉3 𝑇 + ⋯ … … … . . +𝑈𝑟 𝜎𝑟 𝑉𝑟 𝑇 = 𝐴𝑀𝑁 Where r is the rank, U and V are orthogonal matrices of size M x M and N x N. Diagonal matrix S of size M x N having singular values and which satisfy the property, 𝜎,,1 > 𝜎2,2 > 𝜎3,3 > ⋯ … … > 𝜎𝑚,𝑛 SVD exhibits common geometric distortion attacks such as rotation transpose, flip, translation invariance and scale. These geometric invariance properties make SVD a very favorable tool for reference watermarking. 2.3. DWT-SVD based Reference Image Watermarking Joo et al. [11] presents a novel and robust scheme for reference watermarking based on DWT-SVD and further it has been extended by Liu et al. [12] by adopting the concept of self reference image. These watermarking schemes use the low frequency sub-bands to generate the reference image and provide better resist against various image processing attacks. Bhatnagar & Raman [14] introduced a new concept of directive contrast for watermarked images in order to provide high perceptual quality. Directive contrast of wavelet sub bands provides namely Horizontal contrast, Vertical contrast and Diagonal contrast used to represent the relative nature in
comparison to low frequency sub bands. Suppose one level DWT decomposition has been applied on image A to get four sub-bands {𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻} then corresponding directive contrast [14] may be defined as 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐿𝐻 𝐴(𝑖,𝑗)
(1)
𝐿𝐿𝐴(𝑖,𝑗)
𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐻𝐿𝐴 (𝑖,𝑗) 𝐿𝐿𝐴 (𝑖,𝑗)
𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 =
𝐻𝐻 𝐴(𝑖,𝑗) 𝐿𝐿𝐴 (𝑖,𝑗)
(2) (3)
For extraction of the vertical, horizontal and diagonal details of wavelet coefficients, directive contrast can be explored equations (1), (2) and (3) as 𝐻𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐿𝐻 𝐴 (𝑖, 𝑗) 𝑉𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐻𝐿𝐴 (𝑖, 𝑗) 𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙 𝐶𝑜𝑛𝑡𝑟𝑎𝑠𝑡 ∗ 𝐿𝐿𝐴 (𝑖, 𝑗) = 𝐻𝐻 𝐴 (𝑖, 𝑗)
Consequently, watermark embedding has been performed on the reference image generated by using directive contrast. The singular value of watermark logo image has been used for further embedding with the singular value of the reference image. Figure 2 has been provided in order to represent the block diagram of directive contrast based reference watermark embedding scheme proposed by Bhatnagar & Raman [14].
3. Problem of Image Ambiguity and Statistical Redundancy Gray Scale images are intrinsically surrounded with different types of ambiguities because of imprecision of grayscale values. Therefore an appropriate technique is required that integrate the ambiguities of images in order to perform image processing tasks. Grayscale ambiguity can be classified as grayness ambiguity and spatial ambiguity [19, 23]. The grayscale values around the pixels are deemed to be inexact primarily in terms of the gray level. It represents that a gray value of a pixel may not vary from its neighboring pixels up to definite extents and at the same time it may be observed that a gray value may depict in close proximity of gray levels to certain extents. Furthermore, the pixel values of nearby region have imperfect discernibility due to the scantiness of contrast. Figure 3 has been supplied to depict that an exact boundary cannot be represented due to steadily changing gray values. These ill defined boundaries and vagueness of grayscale values majorly affect the contrast of the image and degrade the perceptual quality of image. Consequently, if watermarking has been performed on ambiguous gray scale values, distress the imperceptibility of watermarked image.
Statistical redundancy of values is another problem that may find in DWT coefficients. The problem related to change in wavelet coefficients is due to shift invariance problem. In order to overcome the shift invariance problem, a problem of statistical redundancy introduced in all sub bands. The deficiency and the unpredictability in sensitivity intrinsic to the Human Visual System (HVS) permit the perceptual redundancies cause the poor quality of watermarked image. Rough set concept has been used because of its ability to deal with uncertain grayscale pixel values and statistical redundancy. RST has been emerged as a technique to control uncertainty, to assess the significance of attributes, to reduce redundancies, and classify objects into required classes [19]. In this paper RST has been used to generate the reference image while removing the redundancy of coefficient value and at the same time removing the uncertainty of grayscale values.
4. Rough Sets Based Image Representation 4.1 Rough Sets Rough set theory (RST) [22] established by Pawlak during 1980s, presents a way to describe knowledge and to approximation of sets. In recent times, RST has turned out to be a popular mathematical technique for the reduction of the ambiguity in grayscale images. The principal contribution of rough set theory is classification of information granules into outer and inner approximations and furthermore makes it eventual for image processing, image classification, feature selection, object extraction. An information system can be represented as a pair (U, A) where U (universe) stand for a non-empty finite set of information and A stands for a non-empty finite set of attributes. Suppose F ⊆ A and 𝑦 ∈ 𝑈 then it may be written as 𝑦~𝐵 = {𝑥 ∈ 𝑈 ∖ ∀𝜙 ∈ 𝐹, 𝜙(𝑦) = 𝜙(𝑥)
(4)
Equation (4) has been used to represent that description of y matches with description of x. An indiscernibility relation (R), in view of the universe generally means for the similarities of elements present in the universe. U/R is represented as the family of all granules consequently, the set A can be approximately by two definable set RA(u) and RA(u) which can be defined as 𝑈
𝑅𝐴(𝑢) = ⋃𝑖 (𝑋𝑖 | : 𝑋𝑖 ∈ 𝐴) 𝑅 𝑈
𝑅𝐴(𝑢) = ⋃𝑖 (𝑋𝑖 | 𝑅 : 𝑋𝑖 ∩ 𝐴 ≠ ∅)
(5)
(6)
RA(u) and RA(u) repectively known as lower and upper approximation sets. All three regions or equivalent classes induced by the feature values as depicted through Figure 4.
4.2 Rough Set for Image classification The gray scale values around the boundaries of object regions are generally vague because of spatial ambiguities subsist in grayscale images [18,19,20,21,22,32,35]. This ambiguity of grayscale values can be efficiently handled by classifying the grayscale images with upper and lower approximations. DWT also suffers from the shift variance problem. The lack of shift invariance nature of wavelet coefficients makes watermarked image vulnerable to geometrical attacks. The shift variance problem can be solved by the usage of un-decimated filters suggested by several authors and at the same time it introduces redundancy. In order to deal with the above problem, idea of rough set based approximation has been exploited. Considering the universe U as an image which consist various gray scale values at each pixels then U can be categorized into an assortment of non-overlapping windows of size x × y. Furthermore each window should be treated as a granule G and within this Object region in the image which is approximated by RST. An image of size M x N has been further classified into two different classes of lower approximation and upper approximation by considering of gray scale value. Let I(u) and I(l) represents the upper and lower approximation set of two images consequently. I (u) and I (l) may be further classified into two sets of gray scale values by considering a specific threshold value T. The upper and lower approximation set of an image I (u) and I (l) is defined as ̅̅̅̅̅̅ 𝐼 (𝑢) = {⋃𝑖 (𝐵𝑖 |𝐺𝑗 < 𝑇, ∀𝑗 = 1, … … … 𝑚𝑛) and Gj depicts the pixels value belongs to granule Bi }
(7)
𝐼(𝑙) = {⋃𝑖(𝐵𝑖 |𝐺𝑗 > 𝑇, ∀𝑗 = 1, … … … 𝑚𝑛) and Gj depicts the pixels value belongs to granule Bi }
(8)
Threshold T used for classifying the image into upper and lower approximation can be decided based upon the roughness and rough entropy of the image. Furthermore, from the equation (7) and equation (8) it may be observed that classifying the grayscale image into upper and lower approximations fully dependent on a threshold value. Roughness and Rough Entropy [20,23] of an image has been given as |𝐼(𝑙)|
𝑅𝐼 = 1 − |𝐼(𝑢)| Where, roughness of image R I ∈ {0,1}. 𝑒
𝑅𝐸𝐼 = − [𝐼(𝑙) 𝑙𝑜𝑔𝑒 𝐼(𝑙) + 𝐼(𝑢) 𝑙𝑜𝑔𝑒 𝐼(𝑢)] 2
(9)
Roughness and Rough Entropy of an image are contradictory to each other, when maximizing the rough entropy basically minimizing the roughness of the image. Rough Entropy of an image also ∈ {0,1} and further may be used as a watermarking strength because of its dependency on the roughness of the image. Suppose maximum_grayscale and minimum_grayscale depicts the corresponding grayscale values of an image, then with the help of below mentioned procedure a threshold value can be calculated. Decompose a given image into desired number of granule Bi
Where i ∈ {0,1 … … P} , P represents total number of granule 𝐺𝑗 ∈ {0,1 … … 𝑇, 𝑇 + 1, 𝑇 + 2 … … . .255} Symbolize the gray scale values. max_ Bi = maximum grayscale value of pixels in granule Bi min_ Bi = minimum grayscale value of pixels in granule Bi 𝑇=
𝑚𝑎𝑥{ 𝑚𝑎𝑥_ 𝐵𝑖 }+ 𝑚𝑖𝑛 {𝑚𝑖𝑛_ 𝐵𝑖 } 2
Figure 5 has been used to depict the (a) Lena image (b) lower approximation of lena image and (c) upper approximation of lena image respectively.
5. Rough Set based Reference Image Watermarking The proposed Reference watermarking scheme has been used to exploit the concept of rough set in view of image processing. The general understanding related to DWT-SVD based reference watermarking methods is that it provides the high perceptual quality of watermarked image but less resistive to multiple image processing attacks. In the literature, presented watermarking techniques are not adaptive due to the use of explicit embedding strength value and the same time suffers from the motion blur, filtering attack, and other attacks in the same domain. In the proposed approach the host image are classified into upper and lower approximation set using its wavelet coefficients for generating reference image.
The singular value used for generating a reference image has been utilized for embedding the logo watermark. Rough set has been used to enhance the perceptual quality while SVD provide robustness. DWT suffers from the redundancy problem that introduces while dealing with the shift invariance problem. To overcome the redundancy in wavelet coefficient during reference watermarking, the idea of rough set based image representation has been adopted. In order to provide a Rough Set based adaptive Reference Image Watermarking scheme, the idea of Rough Entropy of upper and lower approximation set has been considered. Furthermore it depends on that which approximation set has been considered for generation of the reference image and roughness will be used accordingly. Figure 6 and 7 has been consequently used to represent the rough set based reference watermark embedding and extraction scheme .If 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) and 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) consequently represents a lower and upper approximation of selected sub bands 𝐴
𝑙_𝑠𝑒𝑙𝑒𝑐𝑡
𝑛+1 (𝑖, 𝑗)
and further it has been used during reference image
generation for watermark embedding then Rough entropy for these approximation set is given as 𝑒
𝑅𝐸𝑙𝑜𝑤𝑒𝑟 = − 2 [𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑙𝑜𝑔𝑒 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) ]
(10)
𝑒
𝑅𝐸𝑢𝑝𝑝𝑒𝑟 = − 2 [𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑙𝑜𝑔𝑒 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) ]
(11)
These RElower and REupper has been used as watermarking embedding strength, makes it adaptive reference watermarking algorithm. The Rough set based image classification has been used to classify the wavelet coefficients into lower and upper approximation sets. Further these approximation sets has been used to generate the reference image. In order to generate the reference image 1-level DWT has been applied to selected sub bands and classify into lower and upper approximation sets described through Section 5.1.
5.1 Algorithm for classification of lower and upper approximations
𝑙_𝑠𝑒𝑙𝑒𝑐𝑡
𝐼𝑛𝑝𝑢𝑡:
𝐴 𝑛+1 (𝑖, 𝑗) = selected sub bands for reference image generation max_gray = maximum grayscale value of selected sub bands 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗)
min_gray = minimum grayscale value of selected sub bands 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑂𝑢𝑡𝑝𝑢𝑡: 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) = 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) = 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 RElower = Rough entropy of 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 = Rough entropy of 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑠𝑒𝑡𝑠 𝑺𝒕𝒆𝒑𝟏. 𝐷𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑒 𝑎 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑖𝑛𝑡𝑜 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝐵𝑖 𝑤ℎ𝑒𝑟𝑒 𝑖 ∈ {0,1 … … 𝑃} 𝑎𝑛𝑑 𝑃 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝑺𝒕𝒆𝒑𝟐. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑇ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑 𝑇 𝑎𝑠 max{ max_ Bi (i, j)} + min{min_ Bi (i, j)} 𝑇(𝑖, 𝑗) = 2 𝑺𝒕𝒆𝒑𝟑. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗)𝑎𝑛𝑑 𝑢𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑜𝑓 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗) 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑎𝑠 𝑓𝑜𝑟 𝑖 = 1: 1: 𝑃 (𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒) 𝑓𝑜𝑟 𝑗 = 1: 1: 𝑃 (𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒) 𝑖𝑓( 𝐵𝑖 (𝑖, 𝑗) < 𝑇(𝑖, 𝑗)) 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 𝐵𝑖 (𝑖, 𝑗); 𝑢𝑝𝑝𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 0; 𝑒𝑙𝑠𝑒 𝑢𝑝𝑝𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 𝐵𝑖 (𝑖, 𝑗); 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) = 0; 𝑒𝑛𝑑; 𝑺𝒕𝒆𝒑𝟒. 𝐶𝑜𝑚𝑝𝑢𝑡𝑒 RElower and REupper
𝑒𝑛𝑑; 𝑒𝑛𝑑;
e RElower = − [𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) log e 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) ] 2 e REupper = − [𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) log e 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) ] 2
The Lower and upper approximation sets of selected sub bands have been used further for reference image generation. We can use either lower approximation 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) or 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) of selected sub bands during production of reference image. Furthermore section 5.2 has been provided to depict the watermarking embedding algorithm by using 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) or 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) . 5.2 Watermark Embedding Algorithm
𝐼𝑛𝑝𝑢𝑡:
𝐴(𝑖, 𝑗) = 𝐻𝑜𝑠𝑡 𝐼𝑚𝑎𝑔𝑒 𝑊(𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝐼𝑚𝑎𝑔𝑒
𝑙𝑜𝑤𝑒𝑟 𝐵𝑖 (𝑖,𝑗) = 𝐿𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑎𝑛𝑑 𝑅𝐸𝑙𝑜𝑤𝑒𝑟 𝑎𝑠 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) = 𝑈𝑝𝑝𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 and 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 𝑎𝑠 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑂𝑢𝑡𝑝𝑢𝑡:
𝐴𝑤 (𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝐼𝑚𝑎𝑔𝑒
𝑺𝒕𝒆𝒑𝟏:
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑛 𝑙𝑒𝑣𝑒𝑙 ℎ𝑎𝑎𝑟 𝑤𝑎𝑣𝑒𝑙𝑒𝑡 𝑑𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 ℎ𝑜𝑠𝑡 𝑖𝑚𝑎𝑔𝑒 𝐴𝑙 (𝑖, 𝑗) 𝑎𝑛𝑑 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑖𝑚𝑎𝑔𝑒 𝑊^𝑙 (𝑖, 𝑗) 𝑤ℎ𝑒𝑟𝑒 𝑙 ∈ {𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻}
𝑺𝒕𝒆𝒑 𝟐:
𝑆𝑒𝑙𝑒𝑐𝑡 𝑎𝑛𝑦 𝐴𝑙 𝑛 (𝑖, 𝑗 ) 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑙 𝑎𝑛𝑑 𝑛 ∈ {𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑙𝑒𝑣𝑒𝑙}
𝑺𝒕𝒆𝒑 𝟑:
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 1 − 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑜𝑛 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑑𝑒𝑛𝑜𝑡𝑒𝑑 𝑏𝑦 𝐴𝑙_𝑠𝑒𝑙𝑒𝑐𝑡 +1 (𝑖, 𝑗 )
𝑺𝒕𝒆𝒑 𝟒.
𝐷𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑒 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗 ) 𝑖𝑛𝑡𝑜 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑎𝑛𝑢𝑙𝑒 𝐵𝑖 𝑎𝑛𝑑 𝑒𝑥𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑢𝑝𝑝𝑒𝑟 𝑎𝑛𝑑 𝑙𝑜𝑤𝑒𝑟 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑙𝑜𝑤𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑜𝑟 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑓𝑟𝑜𝑚 𝐴𝑙𝑠𝑒𝑙𝑒𝑐𝑡 𝑛+1 (𝑖, 𝑗 ) 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠 𝑎𝑐𝑐𝑜𝑟𝑑𝑖𝑛𝑔 𝑎𝑙𝑔𝑜𝑟𝑖𝑡ℎ𝑚 𝑔𝑖𝑣𝑒𝑛 𝑖𝑛 𝑠𝑒𝑐𝑡𝑖𝑜𝑛 3.1
𝑺𝒕𝒆𝒑 𝟓.
𝑁𝑜𝑤 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑜𝑟 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖(𝑖,𝑗) 𝑢𝑠𝑒𝑑 𝑡𝑜 𝑔𝑒𝑛𝑒𝑟𝑎𝑡踘 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑏𝑦 𝑎𝑝𝑝𝑙𝑦𝑖𝑛𝑔 1 − 𝑙𝑒𝑣𝑒𝑙 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑤𝑎𝑣𝑒𝑙𝑒𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑜𝑟𝑚 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ).
𝑺𝒕𝒆𝒑 𝟔.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑆𝑉𝐷 𝑜𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑎𝑠 𝑤𝑒𝑙𝑙 𝑎𝑠 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑊 𝑡𝑜 𝑔𝑒𝑡, 𝑇
𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) W(𝑖, 𝑗 ) = 𝑊𝑈(i, j)𝑊𝑆(i, j)𝑊𝑉 𝑇 (i, j) 𝑺𝒕𝒆𝒑 𝟕.
𝐶𝑜𝑚𝑝𝑢𝑡𝑒 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑎𝑠 𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑏𝑦 𝑚𝑜𝑑𝑖𝑓𝑦𝑖𝑛𝑔 𝑡ℎ𝑒 𝑠𝑖𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑎𝑙𝑢𝑒𝑠
𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) + RElower ∗ 𝑊𝑆(i, j) if 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑢𝑠𝑒𝑑 𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) + 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 ∗ 𝑊𝑆(𝑖, 𝑗 ) 𝑖𝑓 𝑢𝑝𝑝𝑒𝑟 𝐵𝑖 (𝑖,𝑗) 𝑢𝑠𝑒𝑑 𝑇
𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑤ℎ𝑒𝑟𝑒 RElower 𝑎𝑛𝑑 𝑅𝐸𝑢𝑝𝑝𝑒𝑟 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ. 𝑺𝒕𝒆𝒑 𝟖.
𝐶𝑎𝑟𝑟𝑦 𝑜𝑢𝑡 𝐼𝐷𝑊𝑇𝑜𝑛 𝐴𝑟𝑒𝑓∗ (𝑖, 𝑗 ) 𝑡𝑜 𝑜𝑏𝑡𝑎𝑖𝑛 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒, 𝐴𝑤 (i, j)
5.3 Watermark Extraction Algorithm
𝐼𝑛𝑝𝑢𝑡:
𝐴𝑤 ∗ (𝑖, 𝑗) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝐼𝑚𝑎𝑔𝑒(𝐷𝑖𝑠𝑡𝑜𝑟𝑡𝑒𝑑 ) 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒
𝑂𝑢𝑡𝑝𝑢𝑡:
∗(
𝑊 i, j) = 𝑊𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝐼𝑚𝑎𝑔𝑒 𝑺𝒕𝒆𝒑𝟏.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑜𝑛𝑒 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑜𝑛 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝐴𝑤 ∗ (𝑖, 𝑗 )𝑡𝑜 𝑔𝑒𝑡 𝑡ℎ𝑒 𝑠𝑢𝑏 𝑏𝑎𝑛𝑑𝑠
𝑺𝒕𝒆𝒑 𝟐:
𝐸𝑥𝑡𝑟𝑎𝑐𝑡 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑓𝑜𝑟 𝑓𝑢𝑟𝑡ℎ𝑒𝑟 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑓𝑟𝑜𝑚 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑙𝑒𝑣𝑒𝑙 𝐷𝑊𝑇 𝑑𝑒𝑐𝑜𝑚𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑙𝑒𝑣𝑒𝑙}
𝑺𝒕𝒆𝒑𝟑.
𝑃𝑒𝑟𝑓𝑜𝑟𝑚 𝑡ℎ𝑒 𝑆𝑉𝐷 𝑜𝑛 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘𝑒𝑑 𝑖𝑚𝑎𝑔𝑒 𝑎𝑛𝑑 𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑚𝑎𝑔𝑒 𝑇 𝐴𝑟𝑒𝑓+ (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓+ (𝑖, 𝑗 ) 𝑇
𝐴𝑟𝑒𝑓 (𝑖, 𝑗 ) = 𝑈 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑉 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑺𝒕𝒆𝒑𝟒.
𝐸𝑥𝑡𝑟𝑎𝑐𝑡 𝑡ℎ𝑒 𝑠𝑖𝑛𝑔𝑢𝑙𝑎𝑟 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑏𝑦 𝑐𝑜𝑚𝑝𝑢𝑡𝑖𝑛𝑔 𝑆 𝑟𝑒𝑓+ (𝑖, 𝑗 ) − 𝑆 𝑟𝑒𝑓 (𝑖, 𝑗 ) 𝑊 ∗ (i, j) = if 𝑙𝑜𝑤𝑒𝑟_ 𝐵𝑖 (𝑖, 𝑗) 𝑢𝑠𝑒𝑑 𝑑𝑢𝑟𝑖𝑛𝑔 𝑒𝑚𝑏𝑒𝑑𝑑𝑖𝑛𝑔 RElower
𝑺𝒕𝒆𝒑𝟓.
𝑁𝑜𝑤 𝑓𝑜𝑟𝑚𝑢𝑙𝑎𝑡𝑒 𝑡ℎ𝑒 𝑤𝑎𝑡𝑒𝑟𝑚𝑎𝑟𝑘 𝑎𝑠 𝑊 ∗ (i, j) = 𝑊𝑈(i, j)𝑊𝑆 ∗ (i, j)𝑊𝑉 𝑇 (i, j)
6. Results Analysis and Comparisons This section has been used to discuss the various evaluation parameters to quantify the effectiveness of proposed Rough set based Reference Watermarking, robustness of extracting watermark against a variety of attacks. A
detailed comparison with existing Reference watermarking scheme with proposed method has been presented latter in this section.
6.1 Experimental Environment In order to justify the performance evaluation of a proposed Rough set based Reference Watermarking algorithm, several experiments have been conducted on grayscale cover images “Barbara”, “Lena”, “Pirate”, “Livingroom” of size 512 × 512 and Watermark logo “JUET”,”JAYPEE” of size 64 x 64 depicted through Figure 8. All experiment has been performed on MATLAB platform version 7.1. For imperceptibility of the watermarked image, peak signal-to-noise ratio (PSNR) has been used and is given by following equations 𝐿
𝑚𝑎𝑥 𝑃𝑆𝑁𝑅(𝐴, 𝐴𝑤 ) = 10 ∗ 𝑙𝑜𝑔10 (𝑅𝑀𝑆𝐸 )
2
(12)
Where 𝐿𝑚𝑎𝑥 is maximum gray scale value and the root mean square error(RMSE) defined as 𝑅𝑀𝑆𝐸(𝐴, 𝐴𝑤 ) = √
𝑀 2 ∑𝑁 𝑖=1 ∑𝑗=1(𝐴(𝑖,𝑗)−𝐴𝑤 (𝑖,𝑗))
𝑁𝑥𝑀
(13)
Where 𝐴(𝑖, 𝑗) represents the luminance value of original image and 𝐴𝑤 (𝑖, 𝑗 ) is the luminance value of watermarked Image. The value of wPSNR is used to judge the quality of watermarked image which is given in Equation (14). 𝑤𝑃𝑆𝑁𝑅(𝐴, 𝐴𝑤 ) = 10 ∗ 𝑙𝑜𝑔10 (
𝐿𝑚𝑎𝑥 𝑅𝑀𝑆𝐸∗𝑁𝑉𝐹
)
2
(14)
Where (NVF) represents the Noise Visibility Function. Figure 9 and Table -1 presents the values of PSNR and wPSNR of test images.
Normalized Correlation Coefficient (NCorr) and Bit Error Rate (BER) has been used to justify the effectiveness of the proposed technique, which is defined as, 𝑁𝐶𝑜𝑟𝑟 (𝑊, 𝑊 ∗ ) =
𝐵𝐸𝑅 (𝑊, 𝑊 ∗ ) =
𝑀 ∗ ∗ ∑𝑁 𝑖=1 ∑𝑗=1(𝑊−𝑊)(𝑊 −𝑊 ) 𝑀 𝑁 𝑀 2 ∗ ∗ 2 √∑𝑁 𝑖=1 ∑𝑗=1(𝑊−𝑊) √∑𝑖=1 ∑𝑗=1(𝑊 −𝑊 )
100 𝐵
1 𝑖𝑓𝑊 ∗ (𝑛) ≠ 𝑊(𝑛) ∑𝐵−1 { 𝑛=0 0 𝑖𝑓𝑊 ∗ (𝑛) = 𝑊(𝑛)
(15)
(16)
Where W, W*,B,n consequently represents original watermark, extracted watermark from distorted image, total number of bits and location of bit . Normalized Correlation coefficient (NCorr) generally lies between [−1, 1]. It is a well known fact that NCorr and BER are of contradictory nature. If the value of NCorr is higher, then BER
should have to be lower and vice versa. Table -2 present normalized correlation coefficient value of extracted watermark from attacked watermarked Barbara, Lena, Livingroom and Pirate Images. 6.2 Experimental Results and Discussions The proposed Rough set based Reference Watermarking algorithm has been tested to check the robustness. Following are image processing attacks which are included for testing the robustness: Image Filtering, addition of Gaussian, Salt & Pepper, Speckle noise, Image Rotation, JPEG Compression and Scaling and Motion Blur [31].
6.2.1
Robustness against Image Filtering
Image filtering is a widely-used image processing technique and it has been used to remove the various types of noise, smooth the finer details while preserving the most important edges. In order to check the robustness of proposed watermarking algorithm, watermarked image passed through 13x13 average and median filter.
The attacked watermarked image and corresponding extracted watermark are depicted through Figure 10 and Figure 11 against average and median filtering attack.
6.2.2
Robustness against Gaussian, Salt & Pepper, Speckle Noise
Addition of channel noise is a very frequent and it can occur any time during image transmission. The quality images have been degraded mainly by Salt & Pepper noise, Gaussian noise and Speckle Noise. In our experiment watermarked image has been passed through additive Gaussian noise with variance density of 0.1. Figure 12 (a) & (c) has been used to represent the watermarked Pirate and Barbara Image after Gaussian noise and Figure 12 (b) & (d) consequently represents the extracted watermark. To test the effectiveness of a proposed watermarking scheme against salt & pepper and Speckle noise, the watermarked image has been covered by salt & pepper noise having a density of 50 % and Speckle noise of 50 %, consequently represented by Figure 13 and Figure 14.
6.2.3
Robustness against Rotation, Scaling and Cropping
To design reference watermarking embedding and detecting scheme, in order to survive against geometrical distortion is a challenging task. The Geometrical distortion of images is always a lossy operation and consequently removes some part of the image that may contain watermark information [34]. Due to the property and nature of survival of singular value decomposition against geometrical distortion such as rotation, cropping and resizing, the watermarking scheme proposed in this paper poses a high Normalized Correlation Coefficient
value. The influence of rotation is tested on the watermarked image up to 60 degrees and can be depicted through Figure 15. Figure 16 represents the watermarked image and corresponding extracted watermark after rescaling it to 512-128-512. Figure 17 presented cropping effect on watermarked image (25% left column) and corresponding equivalent extracted watermark. The watermark has been extracted and obtained NCC of JUET and Jaypee logo is 0.8822 and 0.7939 respectively.
6.2.4 Robustness against JPEG Compression and Motion Blur Any watermarking scheme has been robust against JPEG compression attacks. The experiment has been performed on a watermarked image by changing the JPEG compression quality factor that varies from (1-100). The value of Quality factor 100 represents a high quality image while degradation in quality factor represents the poor quality of image as in Figure 18 .Motion blur attack generally simulates the movement of the camera during image capturing. In our experiment the effectiveness of proposed watermarking methods has been tested against motion blur by considering 15 pixel movement of watermarked image. Figure 19 shows the watermarked image and corresponding extracted watermark after motion blur. Figure 18: (a) & (c) Watermarked image of Pirate and Barbara after JPEG compression on quality factor 50 (b) & (d) Extracted Watermark
6.3
Comparative Analysis
To verify the effectiveness of proposed Rough set based Reference watermarking technique with the other reported parallel Reference watermarking scheme (Bhatnagar & Raman[14] and Bhatnagar & Raman[13]) on various noise parameters has been compared. Figure 20 and Figure 21 depict the performance comparison of the proposed approach using NCorr and BER for average filtering attack by changing the filter size. The proposed algorithms against the average filtering attack are far better than Bhatnagar & Raman [14] Reference Watermarking. Furthermore in view of Figure 20 and 21, the extracted watermark correlation coefficient is quite good and at the same time representing low BER rather than Bhatnagar &Raman [14] Reference Watermarking scheme.
The influence of rotation has been compared by changing the degrees of rotation (10 to 50) in intervals of 5 and shown through Figure 22 and 23. It may be observed that the proposed technique is better restive against rotation
attack while comparing with Bhatnagar & Raman [14] Reference Watermarking scheme. The judgment has been made by considering the contradictory nature of NCorr and BER against rotation attack as represented by Figure 22 and Figure 23. In order to compare the performance proposed watermarking scheme for JPEG compression attack, quality factor of compresses has been varied. The robustness of extracted watermark have been tested by changing the quality factor values ( 10 to 100 in an interval of 5). From figure 24 and 25, It has been derived that the performance of Rough set based Reference Watermarking is inferior in comparison to Bhatnagar & Raman [14] Reference Watermarking scheme.
Figure 26 and Figure 27 have been used to show the performance of a proposed Rough set based Reference watermarking algorithm against Gaussian variance attack. It may be observed that proposed method NCorr value is in close proximity of Bahatnagar & Raman[14] Reference Watermarking as represented by Figure 26. When we compare our algorithm by using Bit Error Rate (BER) then it shows inferior performance in comparison to Bahatnagar & Raman [14] Reference Watermarking scheme. Proposed Rough Set based Reference watermarking has also been tested against Motion Blur. Motion Blur is a kind of attack that simulates the digital camera behavior and it occurs during image capturing. Performance of the proposed method has been evaluated by changing the pixel motion and observed that Rough set based Reference watermarking scheme is superior and the same represented through Figure 28 and Figure 29. Figure 30 and Figure 31 depict the performance of the proposed Rough set based Reference Watermarking scheme against median filtering attack by altering the filter size. The performance of proposed watermarking algorithms against the median filtering attack is better than Bhatnagar & Raman [14] Reference Watermarking Scheme. Consequently by looking at Figure 30 and 31, the extracted watermark correlation coefficient is higher and at the same time representing low BER in comparison to Bhatnagar & Raman [14].
The comparison of the PSNR, wPSNR values and NCorr of proposed Rough set based Reference watermarking algorithm with Bhatnagar &Raman Reference watermarking [14] and Bhatnagar & Raman [ 13] has been presented in Table-4 and Table-5.
7. Conclusion A novel Rough set based approach for Reference Watermarking technique has been presented in this paper to provide a better imperceptibility. In these scheme singular values of watermark signal is embedded in the singular
values of the reference image generated after rough set classification of DWT sub bands coefficients. The concept of Rough set has been used due to its capability of confiscating the statistical redundancies between wavelet coefficients. This concept is also used for removal of grayscale pixel uncertainties and providing improved perceptual perfection to the target watermarked images. This algorithm evades the drawback of fixed embedding strength value that adopted by multiple wavelet based reference watermarking approaches, by using the Rough entropy concept and improves the imperceptibility. The validation of the effectiveness of a proposed watermarking technique has been tested with several experiments and the conclusions inferred. With the results obtained by the experiments it is validated that the proposed approach is robust against multiple Image Processing attacks. Its PSNR values mentioned in Table-4 and Table-5 validated theses conclusions. Various graphical comparisons are presented for justification of robustness of this technique in comparison to other reference watermarking techniques.
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Author Biography
Shishir Kumar in working as Professor the Department of Computer Science and Engineering at Jaypee University of Engineering and Technology, Guna, M.P., India. He has earned PhD in Computer Science in 2005. He has 14 years of teaching and research experience.
Neha Jain received his Bachelor’s Degree in 2009 from Rajiv Gandhi Proudyogiki Vishwavidyala, Bhopal, India and received his Master’s Degree from Jaypee University of Engineering and Technology, India in 2012. Now, he is pursuing his Ph.D. degree from Jaypee University of Engineering and Technology, Guna, M.P., India.
Mr. Steven Fernandes is member of Core Research Group, Karnataka Government Research Centre of Sahyadri College of Engineering and Management, Mangalore, Karnataka. He has received Young Scientist Award by Vision Group on Science and Technology, Government of Karnataka, India in the year 2014 and also received grant from The Institution of Engineers (India), Kolkata, India. He completed his B.E (Electronics and Communication Engineering) with Distinction from Visvesvaraya Technological University, Belagavi, Karnataka and M.Tech (Microelectronics) with Distinction from Manipal University, Manipal, Karnataka. His Ph.D work “Match Composite Sketch with Drone Images” has received patent notification (Patent Application Number: 2983/CHE/2015) from Government of India, Controller General of Patents, Designs & Trade Marks. He has 5 years of industry experience working at STMicroelectronics Pvt. Ltd and Perform Group Pvt. Ltd. He has published several papers in peer-reviewed International Journals having Thomson Reuters Web of Science Impact Factor and IEEE, Springer, Elsevier International Conferences. He is also serving has reviewer and guest editor for several Science Citation Indexed and Scopus Indexed International Journals.
LL2
LH2
HL2
HH2
HL1
LH1
HH1
Figure 1: Two-level DWT decomposition
n- Level DWT
Select Wavelet Coefficients from
1-level DWT
{𝐿𝐿, 𝐿𝐻, 𝐻𝐿, 𝐻𝐻}
Calculate directive contrast and Threshold
Modify selected sub bands by directive contrast
Host Image
IDWT
SVD
Watermark
Reference image from modified sub bands
SVD Watermarked Image
Inverse DWT
Watermarked Reference Image
Figure 2: Block diagram of directive contrast based reference watermark scheme
Modify Singular Values
Figure 3: ill defined boundary and ambiguity in grayscale values of Lena Image
Lower Approximation Information Granule
Set
Upper Approximation Universe
Figure 4: Basic perception of Rough Set
(a)
(b)
(c)
Figure 5: (a) Original Lena Image (b) Rough set based lower approximation of lena image (c) Rough set based upper approximation of lena image
n- Level DWT
Selected Wavelet Coefficients of HH sub bands
Rough set Classification
Lower and Upper approximation of HH sub bands
IDWT
Embedding Strength
Roughness of HH band
SVD
Watermarked Image
Inverse DWT
Watermarked Reference Image
Figure 6: Block diagram of proposed reference watermark embedding scheme
Reference image from HH sub bands
SVD Modify Singular Values
Watermarked Image
One Level DWT
Selected Wavelet Coefficients of LH and HL sub bands
Divisive Normalization Transform
DNT Coefficients of LH and HL sub bands
SVD U and V matrix of Watermark
Extracted Singular Values
Extracted Watermark Figure 7: Proposed watermark extraction scheme
Figure 8: Host image and their corresponding Watermark
Figure 9: Watermarked Image
(a)
(b)
(c)
(d)
Figure 10: (a) & (c) Watermarked images of Pirate and Barbara after Average Filtering (13x13) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 11: (a) & (c) Watermarked images of Pirate and Barbara Image after Median Filtering ((13x13) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 12: (a) & (c) Watermarked images of Pirate and Barbara after addition of Gaussian noise (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 13: (a) & (c) Watermarked image of Pirate and Barbara after addition of salt & pepper noise (b) & (d) Extracted Watermark
(a)
Watermark
(b)
(c)
(d)
Figure 14: (a) & (c) Watermarked images of Pirate and Barbara after speckle noise (b) & (d) Extracted
(a)
(b)
(c)
(d)
Figure 15: (a) & (c) Watermarked images of Pirate and Barbara after rotation (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 16: (a) &(c) Watermarked images of Pirate and Barbara after Resizing ((512-128-512) (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 17: (a) & (c) Watermarked images of Pirate and Barbara Image after 25% cropping (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 18: (a) & (c) Watermarked image of Pirate and Barbara after JPEG compression on quality factor 50 (b) & (d) Extracted Watermark
(a)
(b)
(c)
(d)
Figure 19: (a) & (c) Watermarked image of Pirate and Barbara after Motion Blur (15 pixel movement) (b) & (d) Extracted Watermark
Figure 20: Performance of proposed watermarking method for various average filter size by using NCorr
Figure 21: Performance analysis of average filter size by using BER
Figure 22: Performance of proposed technique at various degrees of rotation by using NCorr
Figure 23: Performance of the proposed technique at various degrees of rotation by using BER
Figure 24: Performance against JPEG compression by using NCorr
Figure 25: Performance against JPEG compression by using BER
Figure 26: Performance against Gaussian noise by using NCorr
Figure 27: Performance against Gaussian noise by using BER
Figure 28: Performance against Motion blur by using NCorr
Figure 29: Performance against Motion blur by using BER
Figure 30: Performance against Median Filtering attack by using NCorr
Figure 31: Performance against Median Filtering attack by using BER
Table 1: PSNR and wPSNR values of each test image
Test Images
Barbra
Lena
Pirate
Livingroom
PSNR
68.79
52.69
69.52
46.55
wPSNR
73.25
61.86
71.85
54.45
Table 2: NCorr of extracted watermark
Attacks
Median Filter(13x13) Average Filter(13x13) Rotation(60) Resizing(512-128-512) Gaussian Noise Cropping(1/4) JPEG Compression (50:1) Salt & Pepper (50%) Motion Blur Speckle(50%)
Jaypee
JUET
Barbra
Lena
Pirate
Livingroom
0.5762 0.7944 0.4529 0.6084 0.3879 0.7939 0.5520 0.3845 0.8248 0.3865
-0.1883 -0.1912 -0.2159 0.4439 0.6543 0.9098 0.5892 0.4649 -0.1905 0.4850
0.8692 0.9520 0.7351 0.8728 0.6684 0.8822 0.7937 0.6573 0.8644 0.6743
-0.2648 -0.2670 0.6726 -0.2426 0.9177 0.9744 0.9195 0.7476 -0.2675 0.7733
Table 3: Comparisons of Proposed Rough set based Reference watermarking with Bhatnagar &Raman Reference watermarking [14]
Attacks Extraction Technique Embedding Domain Embedding Strength Size of Watermark Size of Host Image Time Complexity Median Filter Rotation Average Filter Gaussian Noise JPEG Compression Cropping Salt & Pepper Speckle Motion Blur QF = Quality Factor
Proposed Rough set based Reference watermarking
Bhatnagar & Raman[14] Reference watermarking
Semi-Blind DWT+Rough Set+SVD Adaptive 64x64 512x512 O(MN2) 13x13 60 degree 13x13 Up to 50% QF = 1 to 100 25% Up to 50% Up to 50% Tested
Semi-Blind DWT+Directive Contrast+SVD Not Adaptive 64x64 512x512 O(MN2) 13x13 50 degree 13x13 Up to 100% QF = 1 to 100 25% Up to 50% Not applied Tested
Table-4: Comparisons of PSNR and wPSNR with Bhatnagar & Raman Reference Watermarking
Test Images
Barbara Lena Pirate Livingroom
Proposed Method
Bhatnagar &Raman [14]
PSNR
wPSNR
PSNR
wPSNR
68.79 52.69 69.52 46.55
73.25 61.86 71.85 54.45
59.26 54.03 44.43 47.10
68.49 63.71 51.18 54.25
Table-5: Comparisons of NCorr with existing method
Attacks
Proposed Method
Bhatnagar &Raman [14]
Bhatnagar& Raman [13 ]
Median Filter(13x13) Average Filter(13x13) Rotation(60) Resizing(512-128-512) Gaussian Noise Cropping(1/4) JPEG Compression (50:1) Salt & Pepper (50%) Motion Blur Speckle(50%)
0.8692 0.9520 0.7351 0.8728 0.6684 0.8822 0.7937 0.6573 0.8644 0.6743
0.7326 0.7406 0.6841 0.7619 0.6644 0.3369 0.9138 0.6512 0.8083 0.6644
0.4573 0.3072 Not Tested 0.2297 0.2575 -0.9925 0.9360 0.3557 Not Tested Not Tested