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A Novel Secure and Robust Image Watermarking Method Based on Decorrelation of Channels, Singular Vectors, and Values.

I. INTRODUCTION

The information available online as digital books, photos, videos, audios, etc. can easily be accessed from across the globe. A vast number of pirated copies of such information once accessed and downloaded can be made. This pirated data can then be redistributed either freely or at very low cost. Additionally, for an end user, the original and pirated data look alike. As a result, the economy suffers and the industries must bear loss every year [1]. To cater these problems, watermarking is suggested as a prominent solution [2-5].

Watermarking is simply a process of concealing some sort of data (watermark) into either of the same kind or of different type data (host) [3]. In case if host data is an image then watermarking is said to be image watermarking and the image obtained because of watermark embedding is called watermarked-image. A good watermarking technique must full fill four essential conditions; capacity, robustness, imperceptibility, and security, simultaneously [2, 6, 7]. Whenever an image is added with watermark, its perceptual quality degrades (known as imperceptibility [8]), and keeping the quality intact is a challenge in the field of watermarking. Furthermore, watermarking techniques for color images [2, 4-6] must meet one additional challenge as compared to their counterparts [7]. That challenge is that the three-color channels, Red (R), Green (G) and Blue (B), are extremely depended on each other [9]. Modifying any one of them has adverse effects on other two channels, which in turn destroy the quality of original image. However, this dependency can be avoided if the three channels are decorrelated. To do so, different approaches were proposed. Such as YIQ color model [5], Y[C.sub.b][C.sub.r] color model [9] were used to decorrelate these dependent color channels. In contrast, few researchers tried to embed a watermark in original color channels (R, G, and B), without going to any other color-model. For example, in [4], modified RGB channels were used and a very bad perceptual quality of watermarked-image resulted. On the other hand, the presented watermarking technique utilized Principal Component Analysis (PCA) to decorrelate these three dependent channels, and attained improved imperceptibility as compared to [4] and [5], as evident from results in Section V.

Getting a perceptually good watermarked-image is a challenge, but once achieved, watermarking may be subjected to other challenges, like, to destroy or to remove the watermark, the watermarked-image may be attacked. Therefore, the watermarking scheme must be designed in such a way that despite being attacked, the watermark should be extractable and recognizable so that it can be used to prove ownership. This property is called robustness of watermarking scheme [7]. In the presented technique, Singular Value Decomposition (SVD) is used to get satisfactory results of robustness. There are certain properties of SVD which make their use in image watermarking schemes ideal [5, 10-12]. For instance, alteration in singular values does not affect the original image significantly and same is true otherwise [7]. Additionally, singular values and vectors possess luminance and geometric information respectively [8].

Though using SVDs gives satisfactory results in respect of robustness, but it is inefficient to provide security (the property of a watermarking scheme to nullify the chances of watermark extraction completely, is referred as security [2, 7]). For instance, in 2002, a spatial watermarking scheme [10] was proposed. In [10], the singular values of an original image are modified to embed watermark, without modifying the singular vectors. The singular vectors were saved as security key and utilized when watermark was to be extracted. Later, it is found that using entirely different singular vectors can lead to the extraction of a watermark, that was not even embedded [13, 14]. That means unauthorized users with their choice of singular vectors can extract watermark of their own, and in turn, they can claim ownership. As a result, the main objective of any watermarking scheme (ensuring copyright protection) is completely ruined. An advanced version of [10] was presented in 2010, utilizing Discrete Wavelet Transform (DWT) in addition to SVD [11]. Nevertheless, the flaw that was with scheme [10] was also present in [11]. A slightly modified technique [15], was also vulnerable to these kinds of flaws [13,16]. In [4], a different approach is adapted to cater above-mentioned flaw. For that purpose, instead of singular values, first and second values of singular vectors were chosen for watermark embedding. Although, this scheme somehow was successful against that flaw, but unable to provide security. As the locations of watermarking bits are known, anyone can extract and therefore destroy the watermark. To meet all these challenges, in the presented technique, to reject the false positive extraction of watermark both right and left singular vectors are employed in watermark embedding procedure, which in turn, improved the robustness. For the detailed explanation, Appendix A can be referred. Furthermore, security is ensured by opting elements with least correlation with each other to embed the watermark. While keeping the location of those elements secret and needed when the watermark is to be extracted. Thereby, ensuring the security, which is also evident from results. The last requisite is capacity (the information a host image can conceal without being degraded in quality). Involving right and left singular vectors enhanced the capacity of the presented technique, which can also be seen from results in Section V. The presented technique is analyzed in following sections.

II. PROPOSED TECHNIQUE

In the presented watermarking scheme, the three mutually dependent channels of a color image are first decorrelated, so that alteration in any one of them has no adverse effects on others. Hence, the perceptual quality of watermarked-image is improved drastically. The advantage of decorrelation of color channels resulted in terms of extremely improved imperceptibility, especially over [5]. (based on YIQ color model) and over [4]. In [4], values of left singular vectors are changed without changing singular values or right singular vectors. The data embedded in left singular vectors are distributed among singular values and right singular vectors, during the reconstruction of the image. Which results in the form of information loss when again SVD is used to obtain singular vectors and values. This phenomenon is discussed in detail in Appendix A. To overcome this challenge of loss of information along with other requirements mentioned-above, not only left but right singular vectors are employed in a unique and novel way (mentioned in section III), to ensure that no significant information is lost and the correct watermark is extracted. Additionally, in [4], the location where the watermark is embedded is known, which means anyone can extract and hence destroy the watermark. To meet this challenge a novel approach (see Appendix A) is adapted to select elements for watermark embedding and the location is kept confidential and needed when watermark needs to be extracted. Consequently, security is ensured, and it is evident from results. This novel procedure of elements selection provides better results in respect of imperceptibility and robustness, that can further be ensured from results in section V. Involving right and left singular vectors in the novel way is presented in this paper also doubles the capacity than those techniques proposed in [4] and [5]. The detailed explanation of embedding and extraction of the watermark is discussed in subsequent sections.

III. WATERMARK EMBEDDING

1. The watermark ([W.sub.mxn]) is decomposed into its constituents, as shown below

[mathematical expression not reproducible]. (1)

2. Host image ([I.sub.MxN]), such that M [greater than or equal to] 16 x m and N [greater than or equal to] 16 x n, is broken down into its constituents, where,

[mathematical expression not reproducible]. (2)

3. The covariance matrix C is computed as follows for a given matrix B,

C = 1/MN([BB.sup.T]) = Q[LAMBDA][Q.sup.-1], (3)

where,

[mathematical expression not reproducible].

4. The covariance matrix C is decomposed into three principal components using PCA [17] as shown below

[mathematical expression not reproducible].

Comment 1: Altering one color channel causes degradation in other two-color channels, and as a result when three channels are combined the quality of the original image is ruined [18]. It indicated that three color channels are extremely corelated and hence if uncorrected properly, this flaw can be overcome [19].

5. The matrices [[delta].sub.rn], [[delta].sub.gn] and [[delta].sub.bn] are obtained from [[delta].sub.r], [[delta].sub.g], and [[delta].sub.b] respectively, as shown below

[mathematical expression not reproducible]. (4)

Since [[delta].sub.rn], [[delta].sub.gn] and [[delta].sub.bn] are un-correlated representations of the three-color channels, and therefore, modifying any one of them for watermark embedding will not cause any other channel to suffer. As a consequence, the quality of the watermarked image will not be ruined.

6. Let [W.sub.r] is broken down into 8-bit planes [BP.sub.0], [BP.sub.1], ..., [BP.sub.7], where [BP.sub.0] carries least information and [BP.sub.7] possesses most information [20]. As a consequence, 8 x m x n bits are created, where, m and n denote the dimensions of [W.sub.r].

7. Distinct blocks, [A.sub.b] where, b [member of] [1,MN/16] of sizes 4 x 4 are created by dividing [[delta].sub.rn].

8. One-half that is (MN/32) blocks of total created blocks (MN/16) are randomly selected, and their locations are saved as secret keys [Z.sub.e] and needed when the watermark is to be extracted. Afterwards, chosen blocks are broken down into singular vectors and values as shown below

[A.sub.k] = [U.sub.k][S.sub.k][V.sup.T.sub.k], k = [Z.sub.e](1), [Z.sub.e](1), ..., [Z.sub.e] (MN/32). (5)

9. For each block [A.sub.k] two least co-related values are found for watermark embedding. The locations of those values are again saved as keys and used when watermark needs to be extracted. For example, [Z.sub.h](k) and [Z.sub.q](k) denote the location of two least co-related element, from least correlated column [Z.sub.r](k), chosen from block 'k', where, k [member of] [1,MN/32] It should be ensured that [Z.sub.h](k)>[Z.sub.q](k).

10. Using the location of least-correlated elements found in Step 9, the values at same locations from [U.sub.k], [S.sub.k], and [V.sub.k.sup.T] (computed in Step 8) are opted for watermark-embedding. The watermark bits are embedded in the chosen values according to the way defined below.

Case 1: For watermark-embedding bit 1. ([W.sub.k] = 1)

[mathematical expression not reproducible].

Case 2: For watermark-embedding bit is 0 ([W.sub.k] = 0)

[mathematical expression not reproducible],

where,

[mathematical expression not reproducible].

Where [gamma] defines the amount of change that can be introduced without degrading the quality of the watermarked image, and w represents the addition of the watermark.

The least-correlated elements are chosen for watermark embedding to improve imperceptibility and that is enhanced extremely as evident from results in Section V. Furthermore, to ensure security random blocks were chosen and again least-correlated elements form those random blocks are selected for watermark embedding. The location of those random blocks and the location of those least-correlated elements are saved as secret keys. This novel approach indeed improved security drastically, which is experimentally demonstrated in results' section. In the end, right singular vectors ([V.sup.T]) and left singular vectors (U) are opted for modification, to boost robustness and capacity. The detailed explanation is given in Appendix A and verified from experimental results as well.

11. The watermark added singular vectors and values are used to reconstruct respective blocks,

[A.sub.wk] = [U.sub.wk][S.sub.wk][V.sup.T.sub.wk], k = [Z.sub.e](1),[Z.sub.e](1), ..., [Z.sub.e](MN/32). (6)

12. The watermark-added blocks and unchanged blocks are used to construct the watermark-added first principal component [[delta].sub.rnw], where,

[[delta].sub.rnw] = [[[delta].sub.rw](i,j)] 1 [less than or equal to] (i, j) [less than or equal to] M, N.

13. To embed [W.sub.g] and [W.sub.b] into [[delta].sub.gn] and [[delta].sub.bn] respectively, follow Step-6 through Step-12. Simply replace Wr with [W.sub.g], [[delta].sub.rn] with [[delta].sub.gn], [W.sub.r] with [W.sub.b], and [[delta].sub.rn] with [[delta].sub.bn] from Step-6 to Step-12. As a consequence, watermark-added principal components [[delta].sub.gnw] and [[delta].sub.bnw] are created, where,

[[delta].sub.gnw] = [[[delta].sub.gw](i,j)] [[delta].sub.bnw] = [[[delta].sub.gw](i,j)] 1[less than or equal to](i,j) [less than or equal to] M,N. (7)

14. The [[delta].sub.w] is obtained by combing all three watermarkadded principal components; [[delta].sub.rnw], [[delta].sub.gnw], and [[delta].sub.bnw].

[mathematical expression not reproducible].

where, [[delta].sub.rw], [[delta].sub.gw] and [[delta].sub.bw] are obtained from [[delta].sub.rnw], [[delta].sub.gnw] and [[delta].sub.bnw] respectively.

15. The matrix is obtained as

[mathematical expression not reproducible].

16. Finally, the watermarked image [I.sub.w] is obtained by combining the three watermark-added channels; [I.sub.rw], [I.sub.gw] and [I.sub.bw], where

[mathematical expression not reproducible]. (8)

IV. WATERMARK EXTRACTION

1. Let [[??].sub.w] (possibly attacked watermarked-image) is broken down into its constituents [[??].sub.rw] [[??].sub.gw] and [[??].sub.bw], where,

[mathematical expression not reproducible]. (9)

2. The covariance matrix [??] is computed as follows for a given matrix [??]

[mathematical expression not reproducible], (10)

where,

[mathematical expression not reproducible].

3. The covariance matrix [??] is decomposed into its principal components as shown below.

[mathematical expression not reproducible].

4. The 1st, 2nd, and 3rd rows of [[??].sub.w] are converted into matrices [[delta].sub.rnw], [[??].sub.grw] and [[??].sub.bnw] respectively, each of size M x N.

[mathematical expression not reproducible]. (11)

5. Distinct blocks, [[??].sub.b] where, b [member of] [1,MN/16] of sizes 4 x 4 are created by dividing [[??].sub.rnw].

6. Based on key Ze, the watermark-added blocks are found and then decomposed as follows

[mathematical expression not reproducible]. (12)

7. Afterwards, using keys; , the locations of watermark-added elements are found, and watermarking bits form those elements are extracted using following conditions:

[mathematical expression not reproducible] otherwise.

The bits are extracted using [PHI], [GAMMA], and [DELTA] as shown below

[mathematical expression not reproducible]. (13)

where,

[PSI] = Mode{[PHI], [GAMMA], [DELTA]}. (14)

8. Eight m x n , 8-bit planes are formed by arranging the bits calculated in last step (a total of 8 x m x n bits). Afterwards, those eight planes are used to create the 1st color channel of extracted watermark ([[??].sub.r]), where, [mathematical expression not reproducible]

9. To extract other two channels ([[??].sub.g] and [[??].sub.b]), follow Step-5 to Step-8, just replace [[??].sub.rnw] with [[??].sub.gnw] for [[??].sub.g], and replace [[??].sub.rnw] with [[??].sub.bnw] for [[??].sub.b], as shown below

[mathematical expression not reproducible]. (15)

10. Finally, the extracted color watermark ([??]) is obtained from three color channels; [[??].sub.r], [[??].sub.g] and [[??].sub.b].

V. EXPERIMENTAL RESULTS

A number of experimentations were conducted to measure the performance of the presented technique. To do so, six images (shown in Fig. 1) of dimensions (1024 x 1024) were utilized as host images. The average running time to embed a watermark into an image on a computer with specifications: i7 3.8 GHz processor, 8 GB RAM, and 64-bit operating system is 8.23 seconds. While for extracting the watermark from a watermarked image it takes 4.25 seconds. Likewise, two different watermarks (shown in Fig. 2) of dimensions (64 x 64) were used. The databank [21] was used to obtain these images.

The working of presented watermarking technique regarding capacity, robustness, security, and imperceptibility, is examined. The detailed discussion is in the subsequent sections.

A. Imperceptibility

The visual quality of watermarked-image is called imperceptibility [8, 22] and to examine the imperceptibility quantitatively, Peak-Signal-to-Noise-Ratio (PSNR), shown in (16), is used [7, 22]. The higher the PSNR value, the better is the imperceptibility.

The PNSR (measured in decibels) values of the presented technique for a range of scaling factor, which is used to control the amount of information embedded into the host image, is shown in Table I.

[mathematical expression not reproducible]. (16)

The PNSR values of the presented technique for a range of scaling factor is shown in Table I.

On contrary, to analyze the imperceptibility of presented scheme qualitatively, the original host images shown in Fig. 1 and their respective watermarked images are shown in Fig. 3.

It is clear that human eye cannot see any dissimilarity between original images (Fig. 1) and watermarked images (Fig. 3). Moreover, the comparison of the presented scheme with [4, 5] in respect of PSNR values (shown in Table II), shows significant improvement of proposed scheme over the existing techniques.

B. Robustness

Robustness (ability to withstand against attacks applied to destroy or remove the watermark [7]) is also an important requisite any good watermarking scheme must meet. Again, to measure the robustness quantitatively, normalized corelation (NC), shown in (17), where, W and W represent original and extracted watermarks respectively, used [29]. Higher the NC values, better the robustness. Normally, NC values lay between 0 and 1.

[mathematical expression not reproducible]. (17)

To examine the robustness of presented technique many attacks such as average filtering (AVGFL), Joint Photographic Expert Group (PEG) compression (JPEGC) rotation (ROT), simple blurring (SPBL), Y-Shearing (YSHR), motion blurring (MOBL), scaling (SCAL), salt & pepper noise (S&PNO), Cropping (CROP), affine transformation (AFTRA), Gaussian noise (GANO), X-shearing (XSHR), histogram equalization (HEQ) and, translation (TRL), were used to destroy the watermarks. The NC values for different scaling factors against all above-mentioned attacks are shown in Table III.

In contrast, to see the performance of presented scheme qualitatively, above-mentioned attacks were applied on watermarked images. Afterwards, the watermarks were extracted (shown in Fig. 4 and Fig. 5) from those attacked watermarked-images.

Every watermark is recognizable despite being extracted from attacked watermarked-images. This clearly means that the robustness of proposed scheme is satisfactory.

The comparison of the presented scheme with existing schemes [4, 5], in terms of NC values, shown in in Table IV, shows that presented scheme's improvement over the existing watermarking techniques.

C. Security

The third requirement in digital watermarking is that no one should be able to extract either false positive or true positive watermark with any fake key. This is known as security [7]. To examine the security of proposed scheme, several fake keys were applied and tried to extract the watermark. It is found that neither the true nor the false watermark was extracted. The extracted watermarks for fifteen false keys only are shown in Fig. 6. It is clear from Fig. 6, that none of the watermarks is recognizable, hence no recognizable watermark can be extracted.

D. Capacity

The fourth and last requirement is capacity, which refers to the capability of a watermarking scheme to accept any change with being degraded in quality. The capacity of the proposed scheme is two times more than [4, 5] and that is due to the involvement of both singular vectors and values in a novel and efficient way, as discussed in section III.

VI. CONCLUSION

A novel secure and blind dual watermarking scheme for color images based on decorrelation of channels, singular values, and vectors is proposed. Heretofore, the attention was given only to either one or two requirements, while other requirements were ignored altogether, in designing the watermarking scheme. However, in devising the proposed technique it was made sure that all requirements (security, robustness, capacity, and imperceptibility) are met simultaneously, and it is evident from experimental results. To do so, a novel approach is devised to get satisfactory results in respect of security, imperceptibility, capacity, and robustness. Several experiments were conducted to validate the performance of presented watermarking technique and the comparison of the presented scheme with the latest watermarking schemes shows significant improvement.

Digital Object Identifier 10.4316/AECE.2017.04013

APPENDIX A

Let a matrix A is broken down into its singular vectors (U, V) and singular values (S), as shown in (A.1).

[mathematical expression not reproducible]. (A.1)

A. Finding 1: Modifying elements of left singular vectors' columns results in the negligible distortion in original matrix A. On contrary, A suffers through sever distortion if the values of rows of left singular vectors (U) are changed [4].

Combining u, S and V can result in the reconstruction of A. The first and second row of A can be reconstructed as shown in (A.2) and (A. 3).

[mathematical expression not reproducible] (A.2)

[mathematical expression not reproducible] (A.3)

If 0 is put in place of the first row of U in (A.1) will reduce (A.2) to (A.4).

[[alpha].sub.1,1] = [[alpha].sub.1,2] = [[alpha].sub.1,3] = [[alpha].sub.1,4] = 0. (A.4)

On contrary, putting zero for the first column of u will reduce (A.2) and (A.3) to (A.5) and (A.6) respectively,

[mathematical expression not reproducible]. (A.5)

[mathematical expression not reproducible]. (A.6)

From (A.4)-(A.6) it is obvious that modifying rows of (U) has significant consequences on (A), whereas, modifying rows, instead, has a subtle effect on (A). The opposite holds true for V.

B. Finding 2: It is found that the robustness of a watermarking scheme further improves if both U and V are considered equally for watermark embedding.

To prove the Finding-2, let a matrix A is broken down to singular values and vectors, as shown below

A = [USV.sup.T], (A.7)

where,

[mathematical expression not reproducible].

Given that the watermarking bit is 0, modify second and third element from the first column of U using (4)-(7) in such a way that the second element of the first column of U becomes greater than the third element of the first column of U i.e. [U.sub.2,1] > [U.sub.3,1]. This condition is checked at watermark extracting stage to find out either bit-0 was embedded or bit-1. The new modified values of are as follows:

[mathematical expression not reproducible]

Here the condition [U.sub.w(2,1)] > [U.sub.w(3,1)] is satisfied, which indicates that bit 0 was embedded, and that is exactly the case. Now, modified [U.sub.w] is used to reconstruct contaminated (watermark added) A, i.e. [A.sub.w]

[mathematical expression not reproducible],

where,

[mathematical expression not reproducible].

Based on the relationship between two elements of u, the receiver decides regarding extracting bit information.

[mathematical expression not reproducible].

The receiver decomposed [A.sub.w] to extract the hidden information; [mathematical expression not reproducible]. Here, [[??].sub.w(2,1)] > [[??].sub.w(31)], that is the indication that embedded bit is 1, however, in reality, the embedded bit was 0. The reason for this false detection is that the changes introduced between elements of U is divided among other elements of S, and V as well, during construction and reconstruction of [A.sub.w]. The fragility of watermark embedding can extraction can be avoided if the same amount of change that was introduced between two elements of U, is also introduced between two elements of V as shown below

[mathematical expression not reproducible].

Now, using both modified singular vectors [U.sub.w] and [V.sub.w] to get the modified image A, i.e. [A.sub.w1], as shown below

[mathematical expression not reproducible].

The receiver decomposes [A.sub.w1] to extract the hidden information, i.e. [mathematical expression not reproducible]. This time [[??].sub.w(2,1)] > [[??].sub.w(3,1)], indicating extracting bit is 0 and which is correct. It is hence proved that employing right singular vectors (V), in addition to left singular vector (U), improves the robustness significantly.

C. Finding 3: Modification of two elements from a column of U with lowest covariance value results in minor degradation in A as compared to modification in any other two elements of U.

It has been shown in observation 1 that changing column of left singular vectors (U) results in terms of negligible distortion in A, in contrast, altering rows of U makes significant changing in A. The next task is to select the column. For this reason, three cases are analyzed and the case with the good result is adapted in watermark embedding process.

1) Case 1: Two elements (2nd and 3rd) from the first column of U are selected for modification.

2) Case 2: A column with lowest covariance value is selected, and then two elements with lowest covariance values within the selected column are chosen for modification.

3) Case 3: Any two elements with lowest covariance values from the first column of U are selected for modification.

Let the image I is decomposed into blocks of size 4 x 4 . Based on the covariance matrix of each block, two elements for each case discussed above are modified, then reconstruct the blocks from modified values for each case. In Fig. A.1, the PSNR of first 200 blocks are calculated and plotted. From Fig. A.1, it is clear, that the PSNR for Case 2 is better as compared to other two cases. Therefore, Case 2 was adopted in this paper for watermark embedding.

Caption: Figure A.1: Graphical illustration of Finding 3

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[22] C. S. Chang, J. J. Shen, "Feature classification forest: A novel development that is adaptable to robust blind watermarking techniques," IEEE Transaction on Image Processing, vol. 26, no. 8, pp. 3921-3935, 2017. doi: 10.1109/TIP.2017.2706502.

Muhammad IMRAN, Bruce A. HARVEY

Department of Computer & Electrical Engineering, College of Engineering

Florida State University, Tallahassee, Florida, USA

iimran@fsu.edu

Caption: Figure 1. Test images (1024 x 1024) (i). people, (ii). church, (iii). mountains, (iv). sea, (v). building, (vi). sunset

Caption: Figure 2: Watermarks (64 x 64) (a). Butterfly, (b). Log

Caption: Figure 3: Watermarked Images (1024 x 1024) (a). People, (b). Church, (c). Mountains, (d). Sea, (e). Building, (f). Sunset

Caption: Figure 4. Watermarks (butterfly) extracted from watermarked-image attacked by: (i). ROT (ii). TRL (iii) XSHR (iv) YSHR (v) AFTRA (vi) SCAL (vii) CROP (viii) GANO (ix) S&PNO (x) SPNO (xi) SPBL (xii) MOBL (xiii) HEQ (xiv) JPEGC (xv) AVGFL.

Caption: Figure 5. Watermarks (butterfly) extracted from watermarked-image attacked by: (i). ROT (ii). TRL (iii) XSHR (iv) YSHR (v) AFTRA (vi) SCAL (vii) CROP (viii) GANO (ix) S&PNO (x) SPNO (xi) SPBL (xii) MOBL (xiii) HEQ (xiv) JPEGC (xv) AVGFL.

Caption: Figure 6: Watermarks tried to extract using fake (false) keys
TABLE I. PSNR (IN DECIBELS) VALUES USING DIVERSE SCALING FACTORS

Test-                          ([gamma])
Images      0.02     0.04    0.06    0.08     0.1

People      45.49   44.50    43.48   42.51   41.59
Church      46.52   45.56    44.58   43.64   42.73
Mountains   46.37   45.49    44.61   43.77   42.96
Sea         60.34   57.32    54.83   52.79   51.15
Building    45.64   44.77    43.92   43.09   42.30
Sunset      56.44   54.304   52.18   50.37   48.78

TABLE II. PSNR (IN DECIBELS) VALUES FOR DIFFERENT TECHNIQUES FOR
SCALING FACTORS 0.06

Test        Proposed       Presented in
Images       Scheme      [4]       [5]

People      43.4878    35.8533   28.4232
Church      44.5871    35.1059   27.8682
Mountains   44.6116    35.4712   27.3109
Sea         54.8339    36.8526   29.4537
Building    43.9181    34.3124   26.5556
Sunset      52.1849    38.1190   30.0461

TABLE III: NC VALUES FOR DIVERSE VALUE OF [gamma]

  Attacks and their parameters                      [gamma]

Different                 Parameters           0.02       0.04
Types of Attacks

ROT                      [theta] = 45         0.9391     0.9383
                        [theta] = 125         0.9365     0.9345
TRL                    Displayed by 40%       0.9446     0.9443
                      Displayed by 120%       0.9351     0.9366
XSHR                Sheared by factor 0.4     0.9467     0.9465
                    Sheared by factor -0.5    0.9472     0.9464
YSHR                Sheared by factor -0.4    0.9398     0.9388
                    Sheared by factor 0.5     0.9331     0.9310
AFTRA                 Transformed by 0.4      0.9269     0.9272
                      Transformed by 0.5      0.9402     0.9405
SCAL                 Scaled up by3 times      0.9824     0.9838
                    Scaled down 0.5 times     0.9625     0.9637
CROP               10% cropping from center   0.9473     0.9475
                   25% cropping from sides    0.9479     0.9489
GANO                    Mean is 0.4 &         0.9453     0.9468
                        variance is .01
                        Mean is 0.5 &         0.9443     0.9433
                        variance is 0.5
S&PNO                    10% density          0.9501     0.9515
                         50% density          0.9452     0.9447
SPNO                     10% density          0.9511     0.9507
                         50% density          0.9439     0.9436
Blurring                     SPBL             0.9560     0.9563
                             MOBL             0.9523     0.9519
AVGFL                        5x5              0.9558     0.9557
                             7x7              0.9534     0.9520
HEQ                                           0.9741     0.9756
JPEGC                      QF = 50            0.9558     0.9560

  Attacks and their parameters                    [gamma]

Different                 Parameters            0.06       0.08
Types of Attacks

ROT                      [theta] = 45          0.9392     0.9384
                        [theta] = 125          0.9359     0.9340
TRL                    Displayed by 40%        0.9451     0.9444
                      Displayed by 120%        0.9355     0.9379
XSHR                Sheared by factor 0.4      0.9463     0.9457
                    Sheared by factor -0.5     0.9474     0.9463
YSHR                Sheared by factor -0.4     0.9389     0.9387
                    Sheared by factor 0.5      0.9328     0.9309
AFTRA                 Transformed by 0.4       0.9261     0.9268
                      Transformed by 0.5       0.9400     0.9403
SCAL                 Scaled up by3 times       0.9852     0.9853
                    Scaled down 0.5 times      0.9647     0.9649
CROP               10% cropping from center    0.9477     0.9487
                   25% cropping from sides     0.9494     0.9482
GANO                    Mean is 0.4 &          0.9472     0.9457
                        variance is .01
                        Mean is 0.5 &          0.9431     0.9446
                        variance is 0.5
S&PNO                    10% density           0.9515     0.9513
                         50% density           0.9444     0.9448
SPNO                     10% density           0.9515     0.9522
                         50% density           0.9434     0.9444
Blurring                     SPBL              0.9573     0.9560
                             MOBL              0.9518     0.9523
AVGFL                        5x5               0.9553     0.9562
                             7x7               0.9523     0.9534
HEQ                                            0.9759     0.9763
JPEGC                      QF = 50             0.9560     0.9555

  Attacks and their parameters                [gamma]

Different                 Parameters            0.1
Types of Attacks

ROT                      [theta] = 45         0.9360
                        [theta] = 125         0.9367
TRL                    Displayed by 40%       0.9444
                      Displayed by 120%       0.9367
XSHR                Sheared by factor 0.4     0.9456
                    Sheared by factor -0.5    0.9469
YSHR                Sheared by factor -0.4    0.9397
                    Sheared by factor 0.5     0.9296
AFTRA                 Transformed by 0.4      0.9274
                      Transformed by 0.5      0.9400
SCAL                 Scaled up by3 times      0.9863
                    Scaled down 0.5 times     0.9658
CROP               10% cropping from center   0.9471
                   25% cropping from sides    0.9477
GANO                    Mean is 0.4 &         0.9458
                        variance is .01
                        Mean is 0.5 &         0.9440
                        variance is 0.5
S&PNO                    10% density          0.9501
                         50% density          0.9443
SPNO                     10% density          0.9514
                         50% density          0.9447
Blurring                     SPBL             0.9565
                             MOBL             0.9517
AVGFL                        5x5              0.9560
                             7x7              0.9541
HEQ                                           0.9768
JPEGC                      QF = 50            0.9550

TABLE IV. NC VALUES FOR COMPARISON USING DIFFERENT IMAGES
FOR SCALING FACTOR 0.006

Different          Image: Church
Types of Attacks   Proposed    Presented in
                    Scheme      [4]      [5]

ROT                 0.9238     0.6725   0.6350
TRL                 0.9430     0.8059   0.7136
XSHR                0.9454     0.8212   0.6990
YSHR                0.9319     0.6758   0.7292
AFTRA               0.9239     0.6769   0.6943
SCAL                0.9850     0.8445   0.7540
CROP                0.9416     0.7312   0.6335
GANO                0.9433     0.7618   0.6332
S&PNO               0.9441     0.7482   0.6800
SPNO                0.9446     0.7572   0.6499
MOBL                0.9539     0.6695   0.5990
SPBL                0.9513     0.7024   0.6196
AVGFL               0.9642     0.7177   0.6650
HEQ                 0.9732     0.8458   0.7292
JPEGC               0.9539     0.7295   0.6746

Different          Image: Mountains
Types of Attacks   Proposed   Presented in
                    Scheme     [4]      [5]

ROT                 0.9016    0.6554   0.6405
TRL                 0.9427    0.7938   0.7282
XSHR                0.9375    0.8284   0.7050
YSHR                0.9195    0.6973   0.6861
AFTRA               0.9156    0.6685   0.6844
SCAL                0.9813    0.8430   0.7318
CROP                0.9431    0.7499   0.6459
GANO                0.9440    0.7570   0.6490
S&PNO               0.9447    0.7462   0.6814
SPNO                0.9457    0.7558   0.6899
MOBL                0.9518    0.6903   0.6034
SPBL                0.9529    0.6918   0.6133
AVGFL               0.9542    0.7223   0.6336
HEQ                 0.9651    0.8461   0.6989
JPEGC               0.9518    0.7271   0.6649

Different          Image: Sea
Types of Attacks   Proposed   Presented in
                   Scheme     [4]      [5]

ROT                0.9159     0.6320   0.5994
TRL                0.9429     0.8058   0.7444
XSHR               0.9434     0.8317   0.7398
YSHR               0.9218     0.6335   0.7202
AFTRA              0.9265     0.6939   0.6526
SCAL               0.9775     0.8481   0.7445
CROP               0.9453     0.7294   0.6488
GANO               0.9437     0.7623   0.6597
S&PNO              0.9443     0.7503   0.6537
SPNO               0.9440     0.7582   0.6944
MOBL               0.9553     0.5568   0.6389
SPBL               0.9366     0.6375   0.6255
AVGFL              0.9502     0.7187   0.6545
HEQ                0.9610     0.8434   0.7027
JPEGC              0.9261     0.7065   0.6324
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Author:Imran, Muhammad; Harvey, Bruce A.
Publication:Advances in Electrical and Computer Engineering
Article Type:Report
Date:Nov 1, 2017
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