Fractal Dimension and Entropy Analysis of Medical Images for KNN-Based Disease Classification
DOI:
https://doi.org/10.21123/bsj.2024.10835Keywords:
CT scan, Fractal Dimension, K-Nearest Neighbors, Machine Learning, Magnetic Resonance Imaging, Medical Image Analysis, Shannon Entropy, Statistical AnalysisAbstract
The study of medical image-based disease detection has witnessed a notable surge in interest and success with computational methods. This work proposes a novel framework to detect diseases at earlier stages from medical images, using mathematical model and Machine Learning. Introduce two new quantitative measures for COVID-19 and Tumor disease detection: image uncertainty based on Shannon entropy and image complexity based on fractal dimension. Our result demonstrated that in COVID-19 positive images exhibited skewed pixel distribution due to the hazy regions resulting in lower entropy values for diseased cases compared to healthy ones. The second quantity, fractal dimension was measured by box counting method determines the image's complexity. The outcomes of both techniques were applied to the classification of images using the Machine Learning (ML) model k-NN (k-nearest neighbor). This complete framework provides a new and unique approach to identify and classify diverse types of images with a classification accuracy of 90% for Covid and 70% for Tumor achieved. Our work shows that Entropy and fractal dimensions can distinguish between COVID-19 and healthy patients, making them promise for early diagnosis. This manuscript presents a novel, computationally efficient and explainable methodology for disease classification that provides early-stage disease detection.
Received 31/01/2024
Revised 07/07/2024
Accepted 09/07/2024
Published Online First 20/10/2024
References
Ibrahim A, Mohamed HK, Maher A, Zhang B. A Survey on Human Cancer Categorization Based on Deep Learning. Front Artif Intell .2022 Jun 27; 5: 884749. https://doi.org/10.3389/frai.2022.884749
Dormer JD, Halicek M, Ma L, Reilly CM, Fei B, Schreibmann E. Convolutional neural networks for the detection of diseased hearts using CT images and left atrium patches. In SPIE-Intl Soc Optical Eng. 2018 Feb; 10575: 107. https://doi.org/10.1117/12.2293548
Swapna G, Soman KP, Vinayakumar R. Automated detection of diabetes using CNN and CNN-LSTM network and heart rate signals. Procedia Comput Sci. Elsevier B.V. 2018; 132: 1253–62. https://doi.org/10.1016/j.procs.2018.05.041
Ebrahimi A, Luo S, Disease Neuroimaging Initiative for the A. Convolutional neural networks for Alzheimer’s disease detection on MRI images. J Med Imaging . 2021 Apr 29; 8(02): 024503. https://doi.org/10.1117/1.jmi.8.2.024503
Khare SK, Bajaj V, Acharya UR. SPWVD-CNN for Automated Detection of Schizophrenia Patients Using EEG Signals. IEEE Trans Instrum Meas. 2021 Apr 2; 70: 1-9. https://doi.org/10.1109/TIM.2021.3070608
Vaz JM, Balaji S. Convolutional neural networks (CNNs): concepts and applications in pharmacogenomics. Mol Divers. 2021 Aug 1; 25(3): 1569–84. https://doi.org/10.1007/s11030-021-10225-3
He K, Sun J. Convolutional Neural Networks at Constrained Time Cost, InProceedings of the IEEE conference on computer vision and pattern recognition 2015; 5353-5360: https://doi.org/10.1109/CVPR.2015.7299173
Naser EF, Zeki SM. Using Fuzzy Clustering to Detect the Tumor Area in Stomach Medical Images. Baghdad Sci J. 2021 Apr 30; 18(4): 1294–302. https://doi.org/10.21123/BSJ.2021.18.4.1294
9. Hanif F, Muzaffar K, Perveen K, Malhi SM, Simjee SU. Glioblastoma multiforme: A review of its epidemiology and pathogenesis through clinical presentation and treatment, Asian Pac J Cancer Prev. 2017; 18(1): 3–9.https://doi.org/10.22034/APJCP.2017.18.1.3
Villanueva-Meyer JE, Mabray MC, Cha S. Current clinical brain tumor imaging. Clin Neurosurg. 2017 Sep 1; 81(3): 397–415. https://doi.org/10.1093/neuros/nyx103
Sanai N, Berger MS. Mapping the Horizon: Techniques to Optimize Tumor Resection Before and During Surgery. Clin Neurosurg. 2008 Jan 1; 55: 14-9.
Kirschen MP, Jaworska A, Illes J. Subjects’ expectations in neuroimaging research. J Magn Reason Imaging. 2006 Feb; 23(2): 205–9. https://doi.org/10.1002/jmri.20499
Hasan AM, Qasim AF, Jalab HA, Ibrahim RW. Breast Cancer MRI Classification Based on Fractional Entropy Image Enhancement and Deep Feature Extraction. Baghdad Sci J. 2023; 20(1): 221–34. https://doi.org/10.21123/bsj.2022.6782
Nabaa A. RN. Assessment of image quality of cervical spine complications using Three Magnetic Resonance Imaging Sequences. Baghdad Sci J.2023; 20(3): 1155–63. https://doi.org/10.21123/bsj.2023.8244
Rong G, Zheng Y, Chen Y, Zhang Y, Zhu P, Sawan M. COVID-19 Diagnostic Methods and Detection Techniques. In: Encyclopedia of Sensors and Biosensors, First Edition. Elsevier. 2022; 1-4: 17–32. https://doi.org/10.1016/B978-0-12-822548-6.00080-7
Zaki SM, Jaber MM, Kashmoola MA. Diagnosing COVID-19 Infection in Chest X-Ray Images Using Neural Network. Baghdad Sci J. 2022; 19(6): 1356–61. https://doi.org/10.21123/bsj.2022.5965
Bhalla AS, Das A, Naranje P, Irodi A, Raj V, Goyal A. Imaging protocols for CT chest: A recommendation. Indian J Radiol Imaging. 2019 Jul; 29(03): 236–46. https://doi.org/10.4103/ijri.ijri3419
18. Kwee TC, Kwee RM. Chest ct in covid-19: What the radiologist needs to know. Radiographics. 2020 Nov 1; 40(7): 1848–65. https://doi.org/10.1148/rg.2020200159
Dumakude A, Ezugwu AE. Automated COVID-19 detection with convolutional neural networks. Sci Rep. 2023 Dec 1; 13(1): 10607. https://doi.org/10.1038/s41598-023-37743-4
Shi D, Zhang H, Wang G, Yao X, Li Y, Wang S, et al. Neuroimaging biomarkers for detecting schizophrenia: A resting-state functional MRI-based radiomics analysis. Heliyon. 2022 Dec 1; 8(12) pages =e12276, https://doi.org/10.1016/j.heliyon.2022.e12276
Shi D, Li Y, Zhang H, Yao X, Wang S, Wang G, et al. Machine Learning of Schizophrenia Detection with Structural and Functional Neuroimaging. Dis Markers. 2021; 2021(1): 9963824. https://doi.org/10.1155/2021/9963824
Ghazwani H, Nadeem MF, Ishfaq F, Koam ANA. On Entropy of Some Fractal Structures. Fractal Fract. 2023 May 1; 7(5): pages=378, https://doi.org/10.3390/fractalfract7050378
Hayashi T, Cimr D, Fujita H, Cimler R. Image entropy equalization: A novel preprocessing technique for image recognition tasks. Inf Sci (N Y). 2023 Nov 1; 647: 119539. https://doi.org/10.1016/j.ins.2023.119539
Zmeskal O, Dzik P, Vesely M. Entropy of fractal systems. Computers and Mathematics with Applications. 2013 Aug; 66(2): 135–46. https://doi.org/10.1016/j.camwa.2013.01.017
Čukić M, Pokrajac D, Stokić M, Simić S, Radivojević V, Ljubisavljević M. EEG machine learning with Higuchi’s fractal dimension and Sample Entropy as features for successful detection of depression, arXiv preprint arXiv: 1803.05985. 2018 Mar 15. https://doi.org/10.1007/s11571-020-09581-x
Uddin S, Haque I, Lu H, Moni MA, Gide E. Comparative performance analysis of K-nearest neighbour (KNN) algorithm and its different variants for disease prediction. Sci Rep. 2022 Dec 1; 12(1): 6256. https://doi.org/10.1038/s41598-022-10358-x
Zhang T, Han L, Chen W, Shahabi H. Hybrid integration approach of entropy with logistic regression and support vector machine for landslide susceptibility modeling. Entropy. 2018 Nov 1; 20(11): 884. https://doi.org/10.3390/e20110884
Sheth V, Tripathi U, Sharma A. A Comparative Analysis of Machine Learning Algorithms for Classification Purpose. Procedia Comput Sci. Elsevier B.V. 2022 Jan 1; 215: 422-31. https://doi.org/10.1016/j.procs.2022.12.044
Vahid M. Ehsan Soleimanfar Mehrzad Navabakhsh Identification of Patterns and Factors Affecting the Health of Employees Based on Datamining of Occupational Examinations with the Purpose of Promoting Occupational Health. Iran J Health Educ Health Promot. 2019; 7(3): 295-305. https://doi.org/10.30699/ijhehp.7.3.295
Sarker IH. Machine Learning: Algorithms, Real-World Applications and Research Directions, SN Comput Sci. Springer.2021 May; 2(3):160. https://doi.org/10.1007/s42979-021-00592-x
Maity T, Balachandran AK, Krishnamurthy LP, Nagar KL, Upadhyayula RS, Sengupta S, et al. Data-Driven Approaches to Predict Dendrimer Cytotoxicity. ACS Omega 2024; 23: 24899–24906. https://doi.org/10.1021/acsomega.4c01775
Syriopoulos PK, Kalampalikis NG, Kotsiantis SB, Vrahatis MN. kNN Classification: a review. Ann Math Artif Intell. 2023 Sep; 1: 1-33; https://doi.org/10.1007/s10472-023-09882-x
Ali N, Neagu D, Trundle P. Evaluation of k-nearest neighbour classifier performance for heterogeneous data sets. SN Appl Sci. 2019 Dec 1; 1(12): 1-5. https://doi.org/10.1007/s42452-019-1356-9
Lal U, Chikkankod AV, Longo L. Fractal dimensions and machine learning for detection of Parkinson’s disease in resting-state electroencephalography. Neural Comput Appl. 2024 May 1; 36(15): 8257–80. https://doi.org/10.1007/s00521-024-09521-4
M R, R L. Multiocular disease detection using a generic framework based on handcrafted and deep learned feature analysis. Intell Syst Appl. 2023 Feb 1; 17: 200184. https://doi.org/10.1016/j.iswa.2023.200184
Swain M, Kisan S, Chatterjee JM, Supramaniam M, Mohanty SN, Jhanjhi NZ, et al. Hybridized Machine Learning based Fractal Analysis Techniques for Breast Cancer Classification. Int J Adv Comput Sci Appl. 2020; 11(10): 179-84.https://doi.org/10.14569/IJACSA.2020.0111024
Battalapalli D, Vidyadharan S, Prabhakar Rao BVVSN, Yogeeswari P, Kesavadas C, Rajagopalan V. Fractal dimension: analyzing its potential as a neuroimaging biomarker for brain tumor diagnosis using machine learning. Front Physiol. 2023 Jul 17; 14 :1201617. https://doi.org/10.3389/fphys.2023.1201617
Rebinth A, Kumar SM, Kumanan T, Varaprasad G. Glaucoma Image Classification Using Entropy Feature and Maximum Likelihood Classifier. In: J Phys Conf Ser. 2021 Jul 1; 1964(4) :042075. https://doi.org/10.1088/1742-6596/1964/4/042075
Ortiz-Vilchis P, Ramirez-Arellano A. An Entropy-Based Measure of Complexity: An Application in Lung-Damage. Entropy. 2022 Aug 14; 24(8): 1119. https://doi.org/10.3390/e24081119
Renjini A, Swapna MNS, Raj V, Sreejyothi S, Sankararaman SI. Fractal and Time-series A nalyses based Rhonchi and Bronchial Auscultation: A Machine Learning Approach. Indian J Sci Technol. 2022 Jun 5; 15(21): 1041–51. https://doi.org/10.17485/IJST/v15i21.627
Sharma U, Sood M, Puthooran E, Kumar Y. A block-based arithmetic entropy encoding scheme for medical images Int. J Healthc Inf Syst Inform. 2020 Jul 1; 15(3): 65–81. https://doi.org/10.4018/IJHISI.2020070104
Hellman Z, Peretz R. A survey on entropy and economic behaviour. Entropy. 2020 Jan 29; 22(2): 157, https://doi.org/10.3390/e22020157
Sparavigna AC. Entropy in image analysis, Entropy. MDPI AG. 2019 May 17; 21(5): 502. https://doi.org/10.3390/e21050502
Taha TB, Nurtayeva T, Arif SA, Jamal AS. Partial Differential Equations and Digital Image Processing: A Review. In: 8th IEC 2022 - International Engineering Conference: Towards Engineering Innovations and Sustainability. Institute of Electrical and Electronics Engineers Inc. 2022; 235–40. https://doi.org/10.1109/IEC54822.2022.9807553
Jeon G, Chehri A. Entropy-based algorithms for signal processing, Entropy. MDPI AG. 2020 Jun 4; 22(6): 621. https://doi.org/10.3390/E22060621
Hao J, Ho TK. Machine Learning Made Easy: A Review of Scikit-learn Package in Python Programming Language. J Educ Behav Stat. SAGE Publications Inc. 2019 Jun; 44(3): 348-61. https://doi.org/10.3102/1076998619832248
Ferreira Júnior PE, Mello VM, Giraldi GA. Image thresholding through nonextensive entropies and long-range correlation. Multimed Tools Appl. 2023 Nov 1; 82(28): 43029–73. https://doi.org/10.1007/s11042-023-14978-x
Aljanabi MA, Hussain ZM, Lu SF. An Entropy-Histogram Approach for Image Similarity and Face Recognition. Math Probl Eng. 2018; 2018(1): 9801308. https://doi.org/10.1155/2018/9801308
Wu J, Yang S, Gou F, Zhou Z, Xie P, Xu N, et al. Intelligent Segmentation Medical Assistance System for MRI Images of Osteosarcoma in Developing Countries. Comput Math Methods Med. 2022; 2022(1): 7703583. https://doi.org/10.1155/2022/7703583
Delgado-Bonal A, Marshak A. Approximate entropy and sample entropy: A comprehensive tutorial. Entropy. MDPI AG. 2019 May 28; 21(6): pages= {541}, https://doi.org/10.3390/e21060541
Cannon-AmericanMathematicalMonthly-1984; 91(9), p. ebi. https://doi.org/10.1080/00029890.1984.11971488
Al-Kadi OS, Watson D. Texture analysis of aggressive and nonaggressive lung tumor CE CT images. IEEE Trans Biomed Eng. 2008 Jul; 55(7): 1822–30. https://doi.org/10.1109/TBME.2008.919735
Khalili M, Karamouzian M, Nasiri N, Javadi S, Mirzazadeh A, Sharifi H. Epidemiological Characteristics of COVID-19: A Systematic Review and Meta-Analysis. Epidemiol Infect. 2020 Jan; 148: e130; https://doi.org/10.1017/S0950268820001430
Waliszewski P. The quantitative criteria based on the fractal dimensions, entropy, and lacunarity for the spatial distribution of cancer cell nuclei enable identification of low or high aggressive prostate carcinomas. Front Physiol. 2016 Feb 11; 7:34, https://doi.org/10.3389/fphys.2016.00034
Wang H, Lei Z, Zhang X, Zhou B, Peng J. A review of deep learning for renewable energy forecasting, Energy Convers Manag. Elsevier Ltd; 2019 Oct 15; 198: 111799. https://doi.org/10.1016/j.enconman.2019.111799
Pinheiro W, Santos D, Santana M, Gomes J, Nematollahi MA, Marefat A, et al. CCTCOVID: COVID-19 detection from chest X-ray images using Compact Convolutional Transformers. Front Public Health. 2023 Feb 27; 11: 1025746, https://doi.org/10.3389/fpubh.2023.1025746
Wu Y, Zhou Y, Saveriades G, Agaian S, Noonan JP, Natarajan P. Local Shannon entropy measure with statistical tests for image randomness. Inf Sci (N Y). 2013 Feb 10; 222: 323–42. https://doi.org/10.1016/j.ins.2012.07.049
Yang D, Martinez C, Visuña L, Khandhar H, Bhatt C, Carretero J. Detection and analysis of COVID-19 in medical images using deep learning techniques. Sci Rep. 2021 Oct 4; 11(1): 19638. https://doi.org/10.1038/s41598-021-99015-3
El Hajjar S, Dornaika F, Abdallah F. Recognizing and detecting COVID-19 in chest X-ray images using constrained multi-view spectral clustering. Prog Artif Intell. 2024 Feb 9; 1-14; https://doi.org/10.1007/s13748-023-00312-x
Christie DC. Efficient estimation of directional wave buoy spectra using a reformulated Maximum Shannon Entropy Method: Analysis and comparisons for coastal wave datasets. Appl Ocean Res 2024 Jan 1; 142. https://doi.org/10.1016/j.apor.2023.103830
Mohammadi H, Gupta S, Sharma S. A large-scale performance study of entropy-based image thresholding techniques using new SAD metric. Pattern Anal and Appl. 2023 May 1; 26(2): 473–86. https://doi.org/10.1007/s10044-022-01121-z
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