Rabha W Ibrahim1, Hamid A Jalab2, Faten Khalid Karim3, Eatedal Alabdulkreem3, Mohamad Nizam Ayub2. 1. Institute of Electrical and Electronics Engineers (IEEE: 94086547), Kuala Lumpur, Malaysia. 2. Department of Computer System and Technology, Faculty of Computer Science and Information Technology, Universiti Malaya, Kuala Lumpur, Malaysia. 3. Department of Computer Science, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.
Abstract
BACKGROUND: The interest in using fractional calculus operators has grown in the field of image processing. Image enhancement is one of image processing tools that aims to improve the details of an image. The enhancement of medical images is a challenging task due to the unforeseeable variation in the quality of the captured images. METHODS: In this study, we present a mathematical model based on the class of fractional partial differential equations (FPDEs). The class is formulated by the proportional-Caputo hybrid operator (PCHO). Moreover, some properties of the geometric functions in the unit disk are applied to determine the upper bound solutions for this class of FPDEs. The upper bound solution is indicated in the relations of the general hypergeometric functions. The main advantage of FPDE lies in its capability to enhance the low contrast intensities through the proposed fractional enhanced operator. RESULTS: The proposed image enhancement algorithm is tested against brain and lungs computed tomography (CT) scans datasets of different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, Piqe, SSEQ, and SAMGVG were 40.93%, 41.13%, 66.09%, and 31.04%, respectively for brain magnetic resonance imaging (MRI) images and 39.07, 41.33, 30.97, and 159.24 respectively for the CT lungs images. The comparative results show that the proposed image enhancement model achieves the best image quality assessments. CONCLUSIONS: Overall, this model significantly improves the details of the given datasets, and could potentially help the medical staff during the diagnosis process. 2022 Quantitative Imaging in Medicine and Surgery. All rights reserved.
BACKGROUND: The interest in using fractional calculus operators has grown in the field of image processing. Image enhancement is one of image processing tools that aims to improve the details of an image. The enhancement of medical images is a challenging task due to the unforeseeable variation in the quality of the captured images. METHODS: In this study, we present a mathematical model based on the class of fractional partial differential equations (FPDEs). The class is formulated by the proportional-Caputo hybrid operator (PCHO). Moreover, some properties of the geometric functions in the unit disk are applied to determine the upper bound solutions for this class of FPDEs. The upper bound solution is indicated in the relations of the general hypergeometric functions. The main advantage of FPDE lies in its capability to enhance the low contrast intensities through the proposed fractional enhanced operator. RESULTS: The proposed image enhancement algorithm is tested against brain and lungs computed tomography (CT) scans datasets of different qualities to show that it is robust and can withstand dramatic variations in quality. The quantitative results of Brisque, Piqe, SSEQ, and SAMGVG were 40.93%, 41.13%, 66.09%, and 31.04%, respectively for brain magnetic resonance imaging (MRI) images and 39.07, 41.33, 30.97, and 159.24 respectively for the CT lungs images. The comparative results show that the proposed image enhancement model achieves the best image quality assessments. CONCLUSIONS: Overall, this model significantly improves the details of the given datasets, and could potentially help the medical staff during the diagnosis process. 2022 Quantitative Imaging in Medicine and Surgery. All rights reserved.
Entities:
Keywords:
Fractional calculus; analytic function; differential operator; image enhancement; image processing; medical images; univalent function
Authors: Bjoern H Menze; Andras Jakab; Stefan Bauer; Jayashree Kalpathy-Cramer; Keyvan Farahani; Justin Kirby; Yuliya Burren; Nicole Porz; Johannes Slotboom; Roland Wiest; Levente Lanczi; Elizabeth Gerstner; Marc-André Weber; Tal Arbel; Brian B Avants; Nicholas Ayache; Patricia Buendia; D Louis Collins; Nicolas Cordier; Jason J Corso; Antonio Criminisi; Tilak Das; Hervé Delingette; Çağatay Demiralp; Christopher R Durst; Michel Dojat; Senan Doyle; Joana Festa; Florence Forbes; Ezequiel Geremia; Ben Glocker; Polina Golland; Xiaotao Guo; Andac Hamamci; Khan M Iftekharuddin; Raj Jena; Nigel M John; Ender Konukoglu; Danial Lashkari; José Antonió Mariz; Raphael Meier; Sérgio Pereira; Doina Precup; Stephen J Price; Tammy Riklin Raviv; Syed M S Reza; Michael Ryan; Duygu Sarikaya; Lawrence Schwartz; Hoo-Chang Shin; Jamie Shotton; Carlos A Silva; Nuno Sousa; Nagesh K Subbanna; Gabor Szekely; Thomas J Taylor; Owen M Thomas; Nicholas J Tustison; Gozde Unal; Flor Vasseur; Max Wintermark; Dong Hye Ye; Liang Zhao; Binsheng Zhao; Darko Zikic; Marcel Prastawa; Mauricio Reyes; Koen Van Leemput Journal: IEEE Trans Med Imaging Date: 2014-12-04 Impact factor: 10.048