Application of a novel image moment computation in X‐ray and MRI image watermarking

IET Image ProcessingVolume 15, Issue 3 p. 666-682 ORIGINAL RESEARCH PAPEROpen Access Application of a novel image moment computation in X-ray and MRI image watermarking Manoj K. Singh, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, IndiaSearch for more papers by this authorSanoj Kumar, Corresponding Author sanoj.kumar@ddn.upes.ac.in orcid.org/0000-0002-0476-4783 Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India Correspondence Sanoj Kumar, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun 248007, Uttarakhand, India. Email: sanoj.kumar@ddn.upes.ac.inSearch for more papers by this authorMusrrat Ali, Department of Basic Sciences, PYD, King Faisal University, Al Ahsa, Kingdom of Saudi ArabiaSearch for more papers by this authorDeepika Saini, Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun, Uttarakhand, IndiaSearch for more papers by this author Manoj K. Singh, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, IndiaSearch for more papers by this authorSanoj Kumar, Corresponding Author sanoj.kumar@ddn.upes.ac.in orcid.org/0000-0002-0476-4783 Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, India Correspondence Sanoj Kumar, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun 248007, Uttarakhand, India. Email: sanoj.kumar@ddn.upes.ac.inSearch for more papers by this authorMusrrat Ali, Department of Basic Sciences, PYD, King Faisal University, Al Ahsa, Kingdom of Saudi ArabiaSearch for more papers by this authorDeepika Saini, Department of Mathematics, Graphic Era (Deemed to be) University, Dehradun, Uttarakhand, IndiaSearch for more papers by this author First published: 19 December 2020 https://doi.org/10.1049/ipr2.12052Citations: 1AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat Abstract Orthogonal polar image moments which are defined over a unit disk, are used often in watermarking applications. One such image moment is polar harmonic Fourier transformation (PHFT). The quality of the extracted watermark depends on the accuracy of the computed image moments. Various methods have already been used for the computation of the moments with varying degrees of accuracy. This study proposes application of a novel image moments computation method which is a synergy of analytic, and numerical techniques, to image watermarking. The computed moment results in a robust watermark extraction. The PHFT have rotation, and scaling invariance property, which allows the watermark to resist various geometric attacks. In addition to the geometric attacks the watermark has the capability to resist various signal processing attacks. The performance of the proposed watermarking scheme is performed with the methods used in recently published articles. The experimental results show that the proposed method has the better performance compared to other techniques, and has better capability to resist various attacks. 1 INTRODUCTION With growing speed of internet accessibility and ever increasing internet speed, the amount of data transfer has increased [1, 2]. The transfer of data involved in many fields including medical, satellite data and internet of things applications [3-7]. Medical images are frequently transferred, uploaded and downloaded over the internet in telemedicine. In some cases, images are compromised and we just don't know if the images are attacked. Therefore, to identify the copyright of the image, often watermarks are inserted into the medical images [8-12]. Over the years, many state of the art techniques have been proposed in the literature, to insert watermarks in medical images and retrieve the watermarks. Many of these algorithms are robust against various attacks including addition of noise, JPEG compression, cropping and flipping [8, 13-15]. However, these algorithms are not very effective against geometric attacks such as rotation and scaling. For geometric invariant watermarking, the algorithm must use geometric invariant image descriptors. The family of orthogonal moments defined over a unit disk is used frequently in rotational and scaling invariant watermarking. The authors in [16] used Zernike moments (ZM) and pseudo Zernike moments (PZM) for watermarking. It was shown that the watermarking algorithm was robust against various attacks including rotation, scaling and flipping. The authors in [17] used polar harmonic transformation (PHT) for watermarking. PHT moments too are capable of attaining rotational and scaling invariance watermarking. However, the PHTs have higher capacity to embed watermark than the ZM and PZM. Radial harmonic Fourier moments (RHFMs) are also used in watermarking applications [18]. The authors in [18] shown that RHFMs provide more robust watermarking than the ZMs and PZMs. Orthogonal Fourier–Mellin moments can also used in image watermarking [19]. The authors in [20] used PHT moments for geometric invariant watermarking. The robustness of the watermark depends on the accuracy of the computed image moments. The authors in [20], have computed the PHT moments on a polar grid, and it was shown that the accuracy of the computed moments was improved significantly. It was also shown by the authors that the improved accuracy of the moments have contributed in more robust watermarking algorithm against various attacks when compared with PHT watermarking algorithm in [17]. [21] used polar harmonic Fourier moments (PHFM) for image watermarking and shown that their watermarking scheme is more robust than the ZMs, PZMs, PHTs and RHFMs. In image moment based watermarking, the watermark bits are embedded into the image moments. Watermarked image is reconstructed using the modified moments. The watermarked bits are extracted at the destination by recomputing the image moments from the watermarked image. Therefore, the quality of the extracted watermark depends on the accuracy of the computed moments. For example, the authors in [17] and [20], both used PHT moments for watermark embedding. Since, the accuracy of the moments was better in [20], the watermarking in [20] is more robust than the watermarking in [17]. The moment computation involve integration over a unit disk. The domain of the image function is mapped to the unit disk. There are two approaches to map an image function over the unit disk. In one approach the image is completely inscribed into a square and in the other approach unit circle is inscribed into a square. In watermarking applications the later approach is adopted often as the former is not rotational invariant. In this approach, integration is performed over each pixel falling within and on the unit circle. Since image function is discrete in nature, only an approximation of the integration can be found. Therefore, the accuracy of the moment reduced to the approximation of the integration. The authors in [16] and [17], have reduced the integration to just a value at centre of the pixel lying inside the unit circle. This method is known as zeroth order approximation. This method has many shortcomings. In this method, the image function remain constant over a pixel, but the kernel function varies over a pixel. Therefore, the computed moment will not be very accurate. The pixels partially intersecting with the unit circle and their centres falling outside the unit circle are completely ignored. In addition, the pixels partially intersecting with the unit circle and their centres falling inside the unit circle are treated similar to pixels completely falling inside. Therefore, the moments computed using the zeroth order approximation are not accurate and therefore, not robust for watermarking. The authors in [20], have computed the moments in polar coordinate system and their accuracy was better than the zeroth order approximation. However, in the watermarking algorithm the image function is interpolated two times in the watermark embedding and extraction process. Therefore, there is still an scope for the further improvement in the moment computation and their applications in the watermarking. The authors in [21] have used Gaussian quadrature numerical integration method [22] as an approximation to the integration. This method improved the robustness of the watermarking techniques as their results show that the watermarking robustness is better than the ZMs, PZMs, PHTs and RHFMs. Their method uses weights computed from the Legendre polynomials roots and the weights, but the sum of weights is not always sum to two. One of the properties of the Gaussian quadrature integration is that the weights must sum to two. In addition, this method also does not take into account the whole unit disk. Therefore, there is a requirement for an algorithm which takes into account the whole unit disk and improves the accuracy of the moments and hence improves the robustness of the watermarking algorithm. In this paper, we have utilised an integration technique proposed by the authors in another study, which uses the entire unit disk and improves accuracy of the PHFT moments. Watermark bits are embedded into this improved moments. The improved moments contribute considerably in improving the robustness of the watermarking technique. The orthogonal moments are not explored much in the medical images. In additional, the accurately computed PHFT moment is not used in watermarking. Therefore, the novelty of this work is the application of the improved accurate PHFT moments in the medical images. We have also tested the robustness of the watermarking with various attacks. We have compared the results with the ZM, PZM [16], PHT [17, 20] and PHFT [21]. In the next section we will define the PHFT and the watermarking algorithm is constructed. The results are discussed in Section 3, finally we conclude with a conclusion section. 2 METHODOLOGY This section has five subsections. First two subsections describe the definition of PHFT and its computations, the third section presents a image scrambling method used to provide an additional layer of security. The watermark embedding and watermark extraction procedure are described in the final two subsections. 2.1 Polar harmonic Fourier transform Let us denote Z as set of integers and Z + denotes the set of non negative integers. The PHFT with order u ∈ Z + and repetition v ∈ Z , of a function g ( r , ϕ ) is a complex function defined over a unit disk as [23]: C u v = 2 π ∫ 0 2 π ∫ 0 1 H u v ( r , ϕ ) ¯ g ( r , ϕ ) r d r d ϕ , (1)where H u v ( r , ϕ ) = T u ( r ) e i v ϕ , (2) T u ( r ) is known as the radial basis function and defined as T u ( r ) = 1 2 , if u = 0 . sin ( u + 1 ) π r 2 , if u is positive and odd . cos u π r 2 , if u is positive and even . (3) The kernel functions H u v ( r , ϕ ) are orthogonal to each other, i.e., 2 π ∫ 0 2 π ∫ 0 1 H u v ( r , ϕ ) H p q ( r , ϕ ) ¯ r d r d ϕ = δ u p δ v q . (4) The function g ( r , ϕ ) can be reconstructed using Equation (4) [23]: g ( r , ϕ ) = ∑ u = 0 u m a x ∑ v = − v m i n v m a x C u v H u v ( r , ϕ ) . (5) Here u m a x is the maximum order and v m a x is the maximum repetition used for the function reconstruction. To reconstruct and image f ( x , y ) the coordinates ( x , y ) are transformed to ( r , ϕ ) . 2.2 PHFT computation Let us consider a square image f ( i , j ) of size N × N . Let us consider a circle inscribed into the square image with the four boundaries as the tangent to circle. Let us give a coordinate system to the image by considering that the centre of the image as origin and the two axes parallel to the columns and rows. Assign the left boundary as x = − 1 and right boundary as x = 1 . Similarly, assign the lower boundary as y = − 1 and the upper boundary as y = 1 . With this configuration the radius of the inscribed circle will be 1 and width δ x along x-axis and δ y along y-axis are δ x = δ y = 2 N . Let us denote the centres of the image pixels as ( x i , y j ) , i , j = 0 , 1 , … , N . The PHFT moments for an image can be expressed by modifying Equation (1) as c u v = 2 π ∑ i ∑ j f ( i , j ) H u v ( r i , ϕ j ) ¯ δ x δ y , (6)where ( r i , ϕ j ) is the polar form of centres ( x i , y j ) of the pixels. If we restrict the index i , j in Equation (6) such that the centres ( x i , y j ) is within and on the unit circle, the corresponding approximation of the moments is known as zeroth order approximation. This method is used in [16] and [17]. The accuracy of the moments can be increased by refining the function H u v ( r i , ϕ j ) ¯ δ x δ y as H u v ( r i , ϕ j ) ¯ δ x δ y = ∫ ∫ H u v ( r , ϕ ) ¯ d x d y . (7)Here, ( r , ϕ ) is polar form for the points lying within the pixel with centre ( x i , y j ) and in unit disk domain. The domain of integration depends on the pixel location. If a pixel falls completely inside the circle, the domain of integration will be the square boundaries of the pixel. If the pixel falls completely outside the unit circle the integral in Equation (7) will be zero and contribution of the pixel in the moment will be zero. If the circle passes through a pixel, the limit of the integral will be circular boundary instead of the rectangular boundary. In earlier studies such circular boundary was not taken into account and therefore complete unit disk was not taken into consideration for the computation of moments. For example, Figure 1 shows the three different cases of the intersection of the circular boundary with pixel boundaries. In the following the difference between the proposed method and other methods. In the zeroth order approximation the first case will be neglected and approximated with zeros. The next two cases will be treated as equivalent and approximated with Equation (8) ∫ ∫ H u v ( r , ϕ ) ¯ d x d y = ∫ a b d y ∫ c d H u v ( r , ϕ ) ¯ d x , (8)where a , b are the lower and upper boundaries along the y-axis, respectively, and c , d are the left and right boundaries along the x-axis, respectively, of the respective pixels. In the proposed method all the three cases are treated differently and the double integration is performed in the required region only, no region is omitted and no unnecessary regions are added. The first case of Figure 1 is computed by using Equation (9) ∫ ∫ H u v ( r , ϕ ) ¯ d x d y = ∫ a b 1 d y ∫ c 1 − y 2 H u v ( r , ϕ ) ¯ d x , (9)where b1 is the intersection of the left boundary with the unit circle. Note that the horizontal and vertical directions in Figure 1 are considered as the x-axis and y-axis, respectively. FIGURE 1Open in figure viewerPowerPoint Three conditions of the intersection between the unit circle and a rectangular region The second case of Figure 1 is computed by using Equation (10) ∫ ∫ H u v ( r , ϕ ) ¯ d x d y = ∫ a b d y ∫ c 1 − y 2 H u v ( r , ϕ ) ¯ d x . (10)The third case is computed by using Equation (11) ∫ ∫ H u v ( r , ϕ ) ¯ d x d y = ∫ a b d y ∫ c d H u v ( r , ϕ ) ¯ d x − ∫ a 1 b d y ∫ 1 − y 2 d H u v ( r , ϕ ) ¯ d x , (11)where a1 is the intersection of the right boundary with the circle. The method used in [21] uses Gaussian quadrature numerical integration method [22] as an approximation to the integration. As discussed in the introduction, the weights used in this method when applied in the three cases in Figure 1 do not sum to two. Figure 1 and Equations (9)–(11) illustrated that the proposed method takes the circular boundary into consideration for pixels intersecting the unit circle. Therefore, the limits of integration of such pixels in Equation (7) is no longer constant but a variable. Double integration of such integration is computed numerically. One of the popular methods for such integration is Quadpack [24] which is a subroutine package for automatic integration. Quadpack is part of the integrate module in python library scipy. Our method for computing Equation (7) consists of two steps. In first step, which is analytical part, we have found the boundary of each pixel. In the second step, which is numerical part, these boundaries are passed into the dblquad function of the integrate module. The image is reconstructed using Equation (12) f ( i , j ) = ∑ u = 0 u m a x ∑ v = − v m i n v m a x C u v H u v ( r i , ϕ j ) . (12) The computations are computationally intensive. However, as noted in Equation (6), the computationally intensive part which is the computation of Equation (7), is performed only once for each pixel. Then this computed value can be applied on any image to compute the image moments. We have used an Ubuntu laptop with 8GB RAM for our computations. 2.3 Imagel scrambling To provide an additional layer of security, we have scrambled the watermark before embedding. A chaotic sequence generated from three dimensional quadratic system is used for the scrambling of watermark. The system consists of three first order ordinary differential equations in variables x , y , z (shown below) with five constant parameters a , b , c , d , e [25] (Note that the parameters a , b , c , d are different from the parameters a , b , c , d used in the PHFT computation section as limits of integration). For description of the variables and parameter refer [25]. d x d t = a ( y − x ) + e y z , d y d t = c x + d y − z x , d z d t = − b x + x y . Recently [26] showed that chaotic sequence generated from such system of differential equations can be effectively used in image encryption. With initial condition x = y = z = 0.1 and values of parameters a = 14 , b = 43 , c = − 7.2 , d = 16 , e = 4 , we have generated 256 iterations of the variables x and y. Figure 2 shows the 256 iterations of the x and y variables. We have followed algorithm discussed in [26] for the scrambling of the watermark image (size as 16 × 16) using the sequence x and y of length 256 (=16 × 16). For complete description of the encryption and decryption algorithms refer [26]. Since the algorithm was primarily meant for gray scale image and our watermark is a binary image, we did a modification in the algorithm. In the algorithm of [26], the y-sequence between 0 and 255. We have changed the y-sequence as a binary sequence by replacing elements of the sequence by 0 for the non-negative elements and by 255 for positive elements. FIGURE 2Open in figure viewerPowerPoint Chaotic sequence generated from iteration of solution of the system of differential equations. Top plot shows x-sequence and the bottom plot shows y-sequence 2.4 Watermarking algorithm The watermark algorithm presented in this paper broadly function in three stages. In the first stage watermark bits are scrambled, in the second stage, the scrambled watermark bits are embedded into the moments of the image, in the third stage the modified moments are used for reconstruction of the watermarked image using Equation (12). Let us consider a watermark image of size n × n . Let us denote the n2 bits of the scrambled watermark image as W i , i = 1 , 2 , … , n 2 . Since one watermark bit is embedded per image moment, a total of n2 moments are required for embedding a n × n watermark image. The selection of proper moments are also an important task. It was shown in an earlier study by the authors that, the accuracy of the lower order moments are better than the accuracy of the higher order moments. Therefore, the moments order is restricted between 0 and 25 and repetition is restricted between −25 and (-25). Since, C u v = C u − v ¯ , that is the moment corresponding to the repetition v is complex conjugate of the moment corresponding to the repetition − v , only positive repetitions are considered as candidate for selection. Therefore, we have selected randomly n2 moments with a fixed seed from a total of 26 × 25 = 650 moments ( u > = 0 , v > 0 ) . Let us denote M i , i = 1 , 2 , … , n 2 , as the selected moments. Let A i represents the absolute values of the moments M i , that is, A i = | M i | and θ i represents the argument of the moments M i for i = 1 , 2 , … , n 2 . By division algorithm, there exists real numbers Q i and 0 ≤ R i < Δ , such that A i = Q i Δ + R i , where Δ is a quantisation step. The absolute values A i are modified as following equations A i ′ = ( Q i + 1.5 ) Δ , if W i + Q i is odd , ( Q i + 0.5 ) Δ , if W i + Q i is even, (13)for i = 1 , 2 , … , n 2 . Using the modified absolute values, the image moments M i are modified as, M i ′ = A i ′ e j θ i , i = 1 , 2 , … , n 2 , (14)here j = − 1 . To obtain the watermarked image from the modified moments, Equation (12) is adjusted as, g ( i , j ) = 2 Re ∑ k = 0 n 2 M k H k ( x i , y j ) . (15)Here 'Re' stands for real part of a complex number and the index k contains the information of u , v so that H k ( x i , y j ) can be computed from corresponding u and v. Let k is associated with u and v. If we make modification in the moment M k , then similar change will take place in the moment with order u and repetition − v . Sum of the corresponding two complex number in the right hand side of Equation (12) will be twice the real part any one of then, i.e., C u v H u v ( x i , y j ) + C u − v H u − v ( x i , y j ) = 2 Re ( C u v H u v ( x i , y j ) ) . Let f ( i , j ) denotes the original image and g ( i , j ) represents the reconstructed image using Equation (12). Let us define the error in the reconstructed image as e ( i , j ) = f ( i , j ) − g ( i , j ) , (16)where i , j = 0 , 1 , … , N − 1 . Let us denote by h ( i , j ) , the reconstructed image by replacing M k by M k ′ in Equation (12), that is, the reconstructed image with the modified moments. Then the watermarked image will be obtained by adding e ( i , j ) and h ( i , j ) . 2.5 Watermark extraction The seed is the only information required to extract the scrambled watermark. In this sense the watermarking algorithm is blind. The moments M k ′ of the watermarked image is computed and let us denote their absolute values as A k ′ , k = 1 , 2 , … n 2 . Then by division algorithm, there exist, Q k and 0 ≤ R i < Δ such that, A k ′ = Q k Δ + R k for k = 1 , 2 , … , n 2 . We can extract the scrambled watermarked bits W k ′ using the following rule. W k ′ = 1 , if Q k is odd , 0 , if Q k is even, (17)for k = 1 , 2 , … , n 2 . The watermark image W k can be restored by decrypting the W k ′ using the chaotic sequence method discussed earlier in the section. 3 EXPERIMENTAL RESULTS AND DISCUSSION We have selected an X-ray image and two MRI images both of size 256 × 256 (Figure 3). In addition, the performance of the proposed solution is also assessed by using two publicly available datasets. First database is, chest X-ray image database of Mendeley Data, V2, [27] available publicly. The database contains two types of labeled X-ray images, normal and Pneumonia. The database is primarily used for classification problem in machine learning. However, normal X-ray images of first category (total 69) are used for the validation of the watermarking technique discussed in this paper. The second database is the chest X-ray image database of ChestX-ray8 [28] available publicly. This database contains 108948 frontal-view X-ray images of 32717 unique patients with the eight different disease labels. This database, too, is primarily used for classification problem in machine learning. However, first 50 X-ray images from the fourth category are used for the validation of the watermarking technique discussed in this paper. The watermark image is a binary image of size 16 × 16 (Figure 3). The High values of the quantisation step Δ gives lower PSNR but high robustness against various attacks. The low values of the quantisation step gives high PSNR but less robustness against various attacks. Therefore, there is a trade-off between PSNR and robustness. We have selected experimentally the value of the quantisation step in such a way that the PSNR is above 40 and robustness is also not compromised. This way, the quantisation step Δ is set at 0.2. The maximum order of the PHFM is restricted to 25 as in [21]. The quality of the watermarked image is measured in terms of peak signal-to-noise ratio (PSNR). The quality of the extracted watermark is measured in term of bit error ratio (BER) defined as BER = b N 2 , (18)where b is the number of pixels in which the extracted and the original watermark do not match. Since, b and N2 are positive numbers and b ≤ N 2 , BER is always between 0 and 1. If the extracted and original watermark are similar, then b will be smaller and BER will be close to 0. Similarly, if the two watermark image are very different from each other, b will be higher and BER will be close to 1. The quality of the watermarked image is quantified using the peak signal-to-noise ratio (PSNR), which is defined as in Equation (19). PSNR = 10 log 10 255 2 MSE , (19)where MSE is the mean squared error between the original image and the watermarked image. FIGURE 3Open in figure viewerPowerPoint Host image and watermark used for the study. From left two images shown are host images. The rightmost image is selected as the watermark We have compared the watermark algorithm with ZM, PZM in [16], PHT in [17, 20] and PHFT in [21]. The robustness of the watermarking algorithm is compared using various attacks. Complete analysis is performed over an ubuntu machine with 8 GB RAM using Python 3. 3.1 Experimental results on X-ray and MRI images rotational invariance The ZM, PZM, PCET, PCT, PST and PHFT are theoretically invariant to rotation. When watermark bits are embedded into an image and the moments are computed accurately, the watermark will be extracted from the watermarked correctly. Due to rotational invariant property of the moments, when the watermarked image is rotated the moments will be similar to the original moments and watermark will be extracted without error. Figure 4 shows the watermarked images rotated counter clockwise with angles at 10 ∘ , 20 ∘ and 30 ∘ , 40 ∘ , 50 ∘ , 60 ∘ , 70 ∘ , 80 ∘ and 90° along with corresponding extracted watermark images. The visual results indicate the good robustness of the propose method. Table 1 shows the comparison of watermarking algorithms, when watermarked image (chest X-ray) is rotated counter clockwise at angles at 0 ∘ , 10 ∘ , 20 ∘ , 30 ∘ , 40 ∘ , 50 ∘ , 60 ∘ , 70 ∘ , 80 ∘ , 90 ∘ . It is observed that the PSNR of the ZM and PZM is above 50. However, their property to resist rotation is poor as they have higher BER close to 0.5 at each of the angles. The PCET, PCT and PST of [17] have smaller PSNR compared to ZM and PZM but their BER is much smaller that ZM and PZM. The BER of the PCET [20] has small BER across all angles but the PSNR is only 38.76. Since PSNR of PCET in [20] is smaller than 40, analysis involving PCET was not done. The BER of PCT [20] is comparable with our method, but PSNR is less than our method. The PSNR of PST [20] is comparable with PSNR of our method, their BER is higher than ours, however. The BER of PHFT in [21] is only smaller at 50° and 60°. TABLE 1. The first column represents the algorithms used for the comparison of the watermarking algorithms on the chest X-ray. The second column represents PSNR between the base image and the watermarked embedded image. The third column represents the BER of the extracted watermark. The next nine columns represent the of the BER of the extracted watermark when watermarked image is rotated counter clockwise at angles at 0 ∘ , 10 ∘ , 20 ∘ , 30 ∘ , 40 ∘ , 50 ∘ , 60 ∘ , 70 ∘ , 80 ∘ , 90 ∘ PSNR 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° Proposed 41.812 0.0000 0.0039 0.0039 0.0234 0.0859 0.0820 0.0312 0.0039 0.0000 0.0000 ZM [16] 53.399 0.4727 0.5508 0.5547 0.5469 0.5391 0.4844 0.4766 0.4648 0.5195 0.4727 PZM [16] 50.4086 0.4922 0.5703 0.5664 0.5195 0.4883 0.5312 0.5352 0.4453 0.5078 0.4922 PCET [17] 41.7634 0.0977 0.0977 0.1016 0.1055 0.1055 0.1172 0.1055 0.0977 0.0977 0.0977 PCT [17] 43.5683 0.0430 0.0469 0.0469 0.0586 0.1055 0.1055 0.0547 0.0508 0.0430 0.0430 PST [17] 44.