Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 AN APPROACH FOR IMAGE QUALITY ASSESSMENT USING INTUITIONISTIC FUZZY SETS A. Elaraby1,a , A. Nechaevskiy2 1 Department of Computer Science, South Valley University, Egypt. 2 LIT, Joint Institute for Nuclear Research, Dubna, Russia. E-mail: aa.elaraby87@gmail.com Image quality impact the ability of practitioners while they are using image information. In this work, we utilize Intuitionistic Fuzzy Sets (IFSs) theory for image quality assessment. In recent years, Intuitionistic Fuzzy Sets has increased much significance in various fields of signal and image processing as it considers the uncertainty in the assignment of membership called the hesitation degree. A reliable Image Quality Assessment is proposed based on generalized exponential intuitionistic fuzzy entropy. Keywords: Image Quality; Intuitionistic Fuzzy Sets; Exponential Entropy Ahmed Elaraby, Andrey Nechaevskiy Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0) 37 Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 1. Introduction Image quality assessment has been a topic of intense research over the last several decades. With each year come an increasing number of new quality assessment algorithms, extensions of existing quality assessment algorithms, and applications of quality assessment to other disciplines [1- 5]. Many applications in several topics of signal and image processing have been presented based on the theory of fuzzy set presented by Zadeh [6-12]. Similarity and distance measuring between IFSs is now being extensively used in various applications like pattern recognition [13], decision making and fuzzy clustering [14-15]. Handle imprecision and uncertainty is considered by using the theory of fuzzy set (FS) which characterized by a membership function between zero and one. Taking into consideration the hesitation or uncertainty about the membership degree, in real life situations the degree of non- membership is not always handle as in FS theory. To solve this task, Atanassov [16-18] proposed as an extension of FS called Intuitionistic Fuzzy Sets (IFSs). Since the appearance of intuitionistic fuzzy sets (IFSs), much research has been presented that measures the similarity and distance between IFSs. In [19] authors utilizing geometric interpretation to proposed four distance measures between IFSs. In [20] comprehensive overview of IFS distance and similarity measures is presented. In [21] author proposed IFSs distance metric that makes use of fuzzy implications and matrix norms. In [22] author used the convex combination of endpoints to present a new IFSs similarity measure and focusing on the property of min and max operators. In this paper, we present a reliable Image Quality Assessment based on the concept of generalized exponential intuitionistic fuzzy entropy. The novel measure considers membership degree, non-membership degree and hesitation degree. Recently, high-performance computing systems is necessary techniques for analysis of the large set of images. To use all the capabilities of such systems, it is necessary to develop parallel algorithms for already existing single threaded versions of algorithms implementations. The transition to advanced digital technology, such as high-performance hybrid computing technologies (parallel computing technologies on a cluster, on a graphic cards, etc.), for solution of a similar class of problems, allows in a short time to obtain physically significant world-class results. Thus, the research work presented in this paper can be extended to parallelization considering its features. A good computing platform available through JINR can be used for extension of this work, as JINR actively participates in different international projects which are relied on advanced computing technologies. A unique computer infrastructure has been created at LIT JINR, which makes it possible to use a supercomputer, a hybrid cluster, and cloud computing for research. The Heterogeneous platform “HybriLIT” is the part of the JINR Multifunctional Information and Computing Complex [MICC] for high-performance computing. The HybriLIT platform consists of two elements, i.e. the education and testing polygon and the “Govorun” supercomputer, combined by a unified software and information environment [NEC2019]. The “Govorun” supercomputer commissioned in 2018, is aimed to cardinally accelerate complex theoretical and experimental studies in all projects underway at JINR. “HybriLIT” heterogeneous cluster is intended for performing computations with the use of parallel programming technologies. Heterogeneous structure of computational nodes allows developing parallel applications for the solution of a wide range of mathematical resource intensive tasks using the whole capacity of multicore component and computation accelerators [23]. The paper is organized as follows. In Section 2, describes the proposed measure. Section 3 describes the application of proposed measure in Image Quality Assessment and experimental results. The conclusion is presented in Section 4. 2. Proposed Intuitionistic Fuzzy Divergence In [24] authors proposed a new information measure for Atanassov’s intuitionistic fuzzy sets, calling it exponential intuitionistic fuzzy entropy. This measure based on the concept of exponential fuzzy entropy is defined in [25]. This approach is found particularly useful in situations where data is available in terms of intuitionistic fuzzy set values, but implementation requirements are only fuzzy. In the practice, the hesitation part is ignored. But it is possible to obtain a better result by not ignoring the hesitation; in fact, a better result is obtained if we merge the hesitation part suitably. The result is an approach that may help applications of IFS data in industry, where the tools used are those of fuzzy set theory. 38 Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 In this section, a novel measure is proposed based on the concept of generalized exponential intuitionistic fuzzy entropy, we called as New Intuitionistic Fuzzy Divergence (NIFD). Let 𝛼 = {(𝑥, 𝜇𝛼 (𝑥), 𝜐𝛼 (𝑥)│𝑥 ∈ 𝑋)} and 𝛽 = {(𝑥, 𝜇𝛽 (𝑥), 𝜐𝛽 (𝑥)|𝑥 ∈ 𝑋)} be two intuitionistic fuzzy sets. Considering the hesitation degree, the interval or range of the membership degree of the two intuitionistic fuzzy sets 𝛼 and 𝛽 may be given as {(𝜇𝛼 (𝑥), (𝜇𝛼 (𝑥) + 𝜋𝛼 (𝑥))}, {(𝜇𝛽 (𝑥), (𝜇𝛽 (𝑥) + 𝜋𝛽 (𝑥))} where 𝜇𝛼 (𝑥), 𝜇𝛽 (𝑥) are the membership degrees and 𝜋𝛼 (𝑥), 𝜋𝛽 (𝑥) are the hesitation degrees in the respective sets, with 𝜋𝛼 (𝑥) = 1 − 𝜇𝛼 (𝑥) − 𝜐𝛼 (𝑥) and 𝜋𝐵 (𝑥) = 1 − 𝜇𝛽 (𝑥) − 𝜐𝛽 (𝑥). The interval is due to the hesitation or the lack of knowledge in assign membership values. The distance measure has been proposed here considering the hesitation degrees. In an image of size 𝑀 × 𝑀 with 𝐿 distinct gray levels having probabilities 𝑝0 , 𝑝1 , … … . , 𝑝𝐿−1 }, the exponential entropy is defined as: 𝐻 = ∑𝐿−1 𝑖=0 𝑝𝑖 𝑒 1−𝑝𝑖 . In fuzzy cases, an image 𝐴 of size 𝑀 × 𝑀 fuzzy entropy s [11] is: 𝑀−1 𝑀−1 1 𝐻(𝐴) = ∑ ∑ [(𝜇𝐴 (𝑎𝑖𝑗 )𝑒 1−𝜇𝐴 (𝑎𝑖𝑗) ) + (1 − (𝜇𝐴 (𝑎𝑖𝑗 )𝑒 𝜇𝐴 (𝑎𝑖𝑗) )) − 1] (1) 𝑛(√𝑒 − 1) 𝑖=0 𝑗=0 2 where 𝑛 = 𝑀 , 𝑖, 𝑗 = 0,1,2, … … . . , 𝑀 − 1, and 𝜇𝐴 (𝑎𝑖𝑗 ) membership degree of (𝑖, 𝑗)th pixels 𝑎𝑖𝑗 of an image 𝐴. For images 𝐴 and 𝐵, the amount of information between the membership degrees of images 𝐴 and 𝐵 is given in [11]: (i) due to 𝑚1 (𝐴) and 𝑚1 (𝐵) i.e., 𝜇𝐴 (𝑎𝑖𝑗 ) and 𝜇𝐵 (𝑏𝑖𝑗 ) of the (𝑖, 𝑗)th pixels: 𝑒 𝜇𝐴 (𝑎𝑖𝑗) / 𝑒 𝜇𝐵 (𝑏𝑖𝑗) or 𝑒 𝜇𝐴 (𝑎𝑖𝑗)−𝜇𝐵 (𝑏𝑖𝑗). (ii) due to 𝑚2 (𝐴) and 𝑚2 (𝐵) i.e., 𝜇𝐴 (𝑎𝑖𝑗 ) + 𝜋𝐴 (𝑎𝑖𝑗 ) and 𝜇𝐵 (𝑏𝑖𝑗 ) + 𝜋𝐵 (𝑏𝑖𝑗 ) of the (𝑖, 𝑗)th pixels: 𝜇𝐴 (𝑎𝑖𝑗 )+𝜋𝐴(𝑎𝑖𝑗 ) 𝜇𝐵 (𝑏𝑖𝑗 )+𝜋𝐵 (𝑏𝑖𝑗 ) 𝑒 /𝑒 . The Generalized Exponential Fuzzy Entropy [24]: 𝑀−1 𝑀−1 1 𝑒𝐻(𝐴) = ∑ ∑ [(𝑧𝐴 (𝑎𝑖𝑗 )𝑒 1−𝑧𝐴 (𝑎𝑖𝑗) ) + (1 − (𝑧𝐴 (𝑎𝑖𝑗 )𝑒 𝑧𝐴 (𝑎𝑖𝑗) )) − 1] (2) 𝑛(√𝑒 − 1) 𝑖=0 𝑗=0 𝜇𝐴 (𝑎𝑖𝑗 ) + 1 − 𝜐𝐴 (𝑎𝑖𝑗 ) 𝑧𝐴 (𝑎𝑖𝑗 ) = (3) 2 The divergence between images 𝐴 and 𝐵 by corresponding Generalized Exponential Fuzzy Entropy, is: 𝐷1 (𝐴, 𝐵) = ∑ ∑(1 − (1 − 𝑧𝐴 (𝑎𝑖𝑗 ))𝑒 𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗) − 𝑧𝐴 (𝑎𝑖𝑗 )𝑒 𝑧𝐵 (𝑏𝑖𝑗)−𝑧𝐴 (𝑎𝑖𝑗) ) (4) 𝑖 𝑗 Similarly, the divergence of 𝐵 against 𝐴 is: 𝐷1 (𝐵, 𝐴) = ∑ ∑(1 − (1 − 𝑧𝐵 (𝑏𝑖𝑗 ))𝑒 𝑧𝐵 (𝑏𝑖𝑗)−𝑧𝐴 (𝑎𝑖𝑗) − 𝑧𝐵 (𝑏𝑖𝑗 )𝑒 𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗) ) (5) 𝑖 𝑗 So, the total divergence as: 𝐷𝑖𝑣 − 𝑚1 (𝐴, 𝐵) = 𝐷1 (𝐴, 𝐵) + 𝐷1 (𝐵, 𝐴) = ∑ ∑ (2 − (1 − 𝑧𝐴 (𝑎𝑖𝑗 ) + 𝑧𝐵 (𝑏𝑖𝑗 ))𝑒 𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗 ) − (1 − 𝑧𝐵 (𝑏𝑖𝑗 ) 𝑖 𝑗 + 𝑧𝐴 (𝑎𝑖𝑗 )𝑒 𝑧𝐵 (𝑏𝑖𝑗)−𝑧𝐴 (𝑎𝑖𝑗) ) (6) 𝐷𝑖𝑣 − 𝑚2 (𝐴, 𝐵) = 𝐷1 (𝐴, 𝐵) + 𝐷1 (𝐵, 𝐴) 𝐷𝑖𝑣 − 𝑚2 (𝐴, 𝐵) = ∑ ∑(2 − [1 − 𝑧𝐴 (𝑎𝑖𝑗 ) − 𝑧𝐵 (𝑏𝑖𝑗 ) + 𝜋𝐵 (𝑏𝑖𝑗 ) 𝑖 𝑗 − 𝜋𝐴 (𝑎𝑖𝑗 )]𝑒 (𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗))−(𝜋𝐵 (𝑏𝑖𝑗 )−𝜋𝐴 (𝑎𝑖𝑗)) −[1 − (𝜋𝐵 (𝑏𝑖𝑗 ) − 𝜋𝐴 (𝑎𝑖𝑗 )) + 𝑧𝐴 (𝑎𝑖𝑗 ) − 𝑧𝐵 (𝑏𝑖𝑗 )]𝑒 (𝜋𝐵 (𝑏𝑖𝑗)−𝜋𝐴 (𝑎𝑖𝑗))−(𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗)) ) (7) Thus, the overall of NIFD between the images 𝐴 and 𝐵 by adding Eqs. (6) and (7) as: 𝑁𝐼𝐹𝐷(𝐴, 𝐵) = 𝐷𝑖𝑣 − 𝑚1 (𝐴, 𝐵) + 𝐷𝑖𝑣 − 𝑚2 (𝐴, 𝐵) 39 Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 𝑁𝐼𝐹𝐷(𝐴, 𝐵) = ∑𝑖 ∑𝑗 (2 − (1 − 𝑧𝐴 (𝑎𝑖𝑗 ) + 𝑧𝐵 (𝑏𝑖𝑗 ))𝑒 𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗 ) − (1 − 𝑧𝐵 (𝑏𝑖𝑗 )) + 𝑧𝐴 (𝑎𝑖𝑗 )𝑒 𝑧𝐵 (𝑏𝑖𝑗)−𝑧𝐴 (𝑎𝑖𝑗) ] + ∑𝑖 ∑𝑗( 2 − [1 − 𝑧𝐴 (𝑎𝑖𝑗 ) − 𝑧𝐵 (𝑏𝑖𝑗 ) + 𝜋𝐵 (𝑏𝑖𝑗 ) − 𝜋𝐴 (𝑎𝑖𝑗 )]𝑒 (𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗))−(𝜋𝐵 (𝑏𝑖𝑗)−𝜋𝐴 (𝑎𝑖𝑗)) − [1 − (𝜋𝐵 (𝑏𝑖𝑗 ) − 𝜋𝐴 (𝑎𝑖𝑗 )) + 𝑧𝐴 (𝑎𝑖𝑗 ) − 𝑧𝐵 (𝑏𝑖𝑗 )]𝑒 (𝜋𝐵 (𝑏𝑖𝑗)−𝜋𝐴 (𝑎𝑖𝑗))−(𝑧𝐴 (𝑎𝑖𝑗)−𝑧𝐵 (𝑏𝑖𝑗)) )) (8) 3. Application to Image Quality Assessment The 𝑁𝐼𝐹𝐷 at each pixel position (𝑖, 𝑗) of an image 𝑁𝐼𝐹𝐷(𝑖, 𝑗), is calculated between the reference image and the other image (same size as that of the reference image) as: 𝑁𝐼𝐹𝐷(𝑖, 𝑗) = 𝑁𝐼𝐹𝐷(𝐴, 𝐵) (9) The 𝑁𝐼𝐹𝐷 between 𝐴 and𝐵,𝑁𝐼𝐹𝐷(𝐴, 𝐵), is calculated by finding the 𝑁𝐼𝐹𝐷 between each of the elements 𝑎𝑖𝑗 and 𝑏𝑖𝑗 of the reference image 𝐴 and image 𝐵 using Eq. (8). Finally, 𝑁𝐼𝐹𝐷 matrix, the same size as that of image, is formed with values of 𝑁𝐼𝐹𝐷(𝑖, 𝑗) at each point of the matrix. This 𝑁𝐼𝐹𝐷 matrix is indexed to get an image quality measure. To explore the performance of the new algorithm, the image is distorted by a wide variety of corruptions: Salt & pepper noise, Gaussian noise, Poisson noise, speckle noise, blurring, stretching and Compression. All the analyses were performed using MATLAB. To investigate the new algorithm effectiveness, we have compared it to SSIM that considered well known measure. Fig.1. Original CT brain image (a) Gaussian noise (b) salt & pepper noise (c) speckle noise (d) Blurring (e) Compression (f) stretching Fig.2. The CT brain test image is distorted by a wide variety of corruptions: (a) additive Gaussian noise, (b) impulsive salt-pepper noise, (c) multiplicative speckle noise, (d) blurring, (e) JPEG compression and (f) contrast stretching. 40 Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 Table 1. Evaluation of CT Brain Image with Different Types of Distortions Image Distortion Type Proposed IQM SSIM Fig. 2 (a) Additive gaussian noise 0.1609 0.2114 Fig. 2 (b) Impulsive salt-pepper noise 0.8071 0.2576 Fig. 2 (c) Multiplicative speckle noise 0.4329 0.8025 Fig. 2 (d) Blurring 0.2400 0.3747 Fig. 2 (e) JPEG compression 0.0864 0.4451 Fig. 2 (f) Contrast stretching 0.2729 0.9566 4. Conclusion In this paper, the novel application of Intuitionistic Fuzzy Set in image quality assessment is introduced. A new measure is proposed that utilize the Generalized Exponential Intuitionistic Fuzzy Entropy. This measure has been applied on images for the purpose of quality assessment. Experimental results for a wide variety of corruptions for image are presented. The proposed approach clearly measures the quality of images. In our view, the results are reliable due to uses the Intuitionistic Fuzzy Set to assign the membership degrees, in consideration of the uncertainty. Future research in taking the uncertainty into account will lead to even better performance. References [1] Xueyang Fu, Xiangyong Cao, Underwater image enhancement with global–local networks and compressed-histogram equalization, Signal Processing: Image Communication, Volume 86, 2020. [2] Liu Dun Nan , Hou Rui, Li Qiang, Zhao Ning Ning, Ge Ruid LuYi,, Research on fuzzy enhancement algorithms for infrared image recognition quality of power internet of things equipment based on membership function, Journal of Visual Communication and Image Representation, Volume 62, 2019. [3] A. Elaraby, A. Nechaevskiy: An Interval-Valued Image Based Approach to Detect Edges in Aerial images, Symposium on Nuclear Electronics and Computing – NEC, Montenegro, Budva, Becici, 2019. [4] A. Elaraby; David Moratal: A Generalized Entropy-Based Two-Phase Threshold Algorithm for Noisy Medical Image Edge Detection. Scientia Iranica, Vol. 24; 6, 2017. [5] A. Elaraby; Alain Bretto: Proposed Image Similarity Measurement Model Based on Hypergraph, International Journal of Computer Applications, Vol.96; 21, 2014. [6] S. Mukherjee, B. P. Majumder, A. Piplai, S. Das, An Adaptive Differential Evolution Based Fuzzy Approach for Edge Detection in Color Grayscale Images. Lecture Notes in Computer Science. vol. 8297, pp. 260-273, 2013. [7] A. Khunteta D. Ghosh, Edge Detection via Edge-Strength Estimation Using Fuzzy Reasoning Optimal Threshold Selection Using Particle Swarm Optimization, Advances in Fuzzy Systems, vol. 2014, 2014. [8] J. Wu, Z. Yin, Y. Xiong, The fast multilevel fuzzy edge detection of blurry images, IEEE Signal Processing Letters, vol. 14, no. 5, pp. 344–347, 2007. [9] P. Melin, O. Mendoza, O. Castillo, An improved method for edge detection based on interval type- 2 fuzzy logic, Expert Systems with Applications, vol. 37, no. 12, pp. 8527–8535, 2010. 41 Proceedings of the Big data analysis tasks on the supercomputer GOVORUN Workshop (SCG2020) Dubna, Russia, September 16, 2020 [10] O. P. Verma, M. Hanmlu, A. Sultania, A. S. Parihar, A novel fuzzy system for edge detection in noisy image using bacterial foraging, Multidimensional Systems Signal Processing, vol. 24, no. 1, pp. 181–198, 2013. [11] T. Chaira, A. K. Ray, A new measure using intuitionistic fuzzy set theory its application to edge detection. Applied Soft Computing, vol. 8, pp. 919–927, 2008. [12] T. J. Ross, Fuzzy Logic with Engineering Applications, John Wiley& Sons, 3rd edition, 2010. [13] D. F. Li, C. T. Cheng, New similarity measures of intuitionistic fuzzy sets application to pattern recognitions. Pattern Recognition Letter, vol. 23, pp. 221–225, 2002. [14] N. Chen, Z. Xu, M. Xia, Correlation coefficients of hesitant fuzzy sets their applications to clustering analysis, Applied Mathematical Modelling, pp. 2197–2211, 2013. [15] R. Rodriguez, L. Martinez, F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems, vol. 20 pp. 109-119, 2012. [16] K. T. Atanassov, Intuitionistic Fuzzy Sets, Theory, Applications, Series in Fuzziness Soft Computing, Phisica-Verlag, 1999. [17] K. T. Atanassov, Intuitionistic fuzzy set, Fuzzy Sets Syst. pp. 87–97, 1986. [18] K. T. Atanassov, S. Stoeva, Intuitionistic fuzzy set, Polish Symposium on Interval Fuzzy Mathematics, Poznan, pp. 23–26, 1993. [19] E. Szmidt, J. Kacprzyk, Distance between intuitionistic fuzzy set. Fuzzy Sets Syst, vol. 114, pp. 505–518, 2000. [20] Z. S. Xu, J. Chen, An overview of distance similarity measures of intuitionistic fuzzy sets. Int. J. Uncertainty Fuzz. Knowl.-Based Syst. vol. 16, pp. 529–555, 2008. [21] A. G Hatzimichailidis, G. A Papakostas, V. G. Kaburlasos, A novel distance measure of intuitionistic fuzzy sets its application to pattern recognition problems. Int. J. Intell. Syst. vol. 27, pp. 396–409, 2012. [22] B. Farhadinia, An efficient similarity measure for intuitionistic fuzzy sets. Soft Comput. vol. 18, pp. 85–94, 2014. [23] Multifunctional Information and Computing Complex [Electronic resource]: https://miccom.jinr.ru/. [24] R. Verma, B. D. Sharma,. Exponential entropy on intuitionistic fuzzy sets. Kybernetika. vol. 49, pp. 114–127, 2013. [25] N. R Pal, S. K Pal, Object background segmentation using new definition of entropy. IEEE Proceeding, vol. 136, no. 4, pp. 284-295, 1989. 42