Abstract
Type II fuzzy sets consider the uncertainties involved in the membership function of classical fuzzy set theory. The membership function of a Type II fuzzy set is obtained by blurring the boundaries of the original fuzzy set membership function. The interval-based modified Type II fuzzy set method is presented in this paper to measure the fuzziness present in medical images. Using Hamacher T-conorm as the aggregation operator, the membership functions of the upper and lower intervals have been combined to obtain the contrast-enhanced image. For experimental analysis, quantitative and qualitative metrics have been evaluated for different kinds of medical data sets. To test the efficiency of the proposed technique, the computed results are compared with state-of-the-art techniques. The qualitative and quantitative results clearly demonstrate that the performance of the proposed techniques is much better than the existing techniques for almost all the image data sets. The results evaluated for average values with standard deviation for all the datasets bear witness to the performance of the proposed technique. The mean opinion score and the processing time also support the efficacy of the proposed technique, which is much better than most state-of-the-art techniques except at some of the cases.
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig1_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig2_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig3_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig4_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig5_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig6_HTML.png)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig7_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig8_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig9_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig10_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig11_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig12_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig13_HTML.jpg)
![](http://media.springernature.com/m312/springer-static/image/art%3A10.1007%2Fs00500-023-09535-5/MediaObjects/500_2023_9535_Fig14_HTML.png)
Similar content being viewed by others
Availability of data and material
The images that are used for preparing the manuscript are available online, and they can be downloaded from the suggested reference. Further, it may be provided on personal request.
References
Bloch I (2015) Fuzzy sets for image processing and understanding. Fuzzy Sets Syst 281:280–291
Boixader D, Recasens J (2022) Vague and fuzzy t-norms and t-conorms. Fuzzy Sets Syst 433:156–175
Bora DJ, Thakur RS (2018) An efficient technique for medical image enhancement based on interval type-2 fuzzy set logic. Adv Intell Syst Comput 710:667–678
Butnariu D, Klement EP (2002) CHAPTER 23—triangular norm-based measures, handbook of measure theory, pp 947–1010
Chaira T (2014) An improved medical image enhancement scheme using Type II fuzzy set. Appl Soft Comput 25:293–308
Chen SD, Ramli AR (2003) Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation. IEEE Trans Consum Electron 49:1301–1309
Gandhamal A, Talbar S, Gajre S, Hani AFM, Kumar D (2017) Local gray level S-curve transformation—a generalized contrast enhancement technique for medical images. Comput Biol Med 83:1220–2133
Gonzalez RC, Woods RE (2002) Digital image processing, 3rd edn. Pearson Education International
Ibrahim H, Kong NSP (2007) Brightness preserving dynamic histogram equalization for image contrast enhancement. IEEE Trans Consum Electron 53:1752–1758
Islam SM, Mondal HS (2019) Image enhancement based medical image analysis. In: 10th International Conference on Computing, Communication and Networking Technologies (ICCCNT), pp 1–5
Joseph J, Periyasamy R (2018) A fully customized enhancement scheme for controlling brightness error and contrast in magnetic resonance images. Biomed Signal Process Control 39:271–283
Khan MF, Khan E, Abbasi ZA (2014) Segment selective dynamic histogram equalization for brightness preserving contrast enhancement of images. Optik 125:1385–1389
Li B, **e W (2016) Image denoising and enhancement based on adaptive fractional calculus of small probability strategy. Neurocomputing 175:704–714
Minaee S, Kafieh R, Sonka M, Yazdani S, Soufi GJ (2020) Deep-COVID: predicting COVID-19 from chest X-ray images using deep transfer learning. Med Image Anal 65:101794
Murahira K, Kawakami T, Taguchi A (2010) Modified histogram equalization for image contrast enhancement. In: 4th International Symposium on Communications, Control and Signal Processing (ISCCSP), IEEE, pp 1–5
Raju G, Nair MS (2014) A fast and efficient colour image enhancement method based on fuzzy-logic and histogram. Int J Electron Commun (AEU) 68(3):237–243
Rao BS (2020) Dynamic Histogram Equalization for contrast enhancement for digital images. Appl Soft Comput J 89:106114
Salem N, Malik H, Shams A (2019) Medical image enhancement based on histogram algorithms. Proc Comput Sci 163:300–311
Soundrapandiyan R, Satapathy SC, PVSSR CM, Nhu NG (2022) A comprehensive survey on image enhancement techniques with special emphasis on infrared images. Multimed Tools Appl 81:9045–9077
Subramani B, Veluchamy M (2018) MRI brain image enhancement using brightness preserving adaptive fuzzy histogram equalization. Int J Imaging Syst Technol 28(3):217–222
Tang JR, Isa NAM (2017) Bi-histogram equalization using modified histogram bins. Appl Soft Comput 55:31–43
Tang X, Fu C, Xu DL, Yang S (2017) Analysis of fuzzy Hamacher aggregation functions for uncertain multiple attribute decision making. Inf Sci 387:19–33
Tizhoosh HR, Krell G, Michaelis B (1997) Locally adaptive fuzzy image enhancement. In: Reusch B (ed) Computational intelligence theory and applications, vol 1226. Springer, pp 272–276
Tizhoosh HR (1998) Fuzzy image processing: potentials and state of the art. In: International Conference on soft computing, vol. 1, pp 321–324
Tizhoosh HR (2000), Fuzzy image enhancement: an overview, fuzzy techniques in image processing, pp 137–171
Veluchamy M, Subramani B (2019) Image contrast and color enhancement using adaptive gamma correction and histogram equalization. Optik 183:329–337
Veluchamy M, Subramani B (2020) Fuzzy dissimilarity color histogram equalization for contrast enhancement and color correction. Appl Soft Comput J 89:106077
Wadhwa A, Bhardwaj A (2021) Contrast enhancement of MRI images using morphological transforms and PSO. Multimed Tools Appl 80:21595–21613
**ao L, Li C, Wu Z, Wang T (2016) An enhancement method for X-ray image via fuzzy noise removal and homomorphic filtering. Neurocomputing 195:56–64
Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353
Zarandi MHF, Zarinbal M, Izadi M (2011) Systematic image processing for diagnosing brain tumours: a Type-II fuzzy expert system approach. Appl Soft Comput 11:285–294
Funding
There is no funding source for this study.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors of this manuscript declare that they have no conflict of interest.
Ethical approval
All the images are taken from the open source, which is already included in the reference and compliance with ethical standards.
Informed consent
Informed consent was obtained from all participants involved in this study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Chandra, N., Bhardwaj, A. Medical image enhancement using modified type II fuzzy membership function generated by Hamacher T-conorm. Soft Comput 28, 6753–6774 (2024). https://doi.org/10.1007/s00500-023-09535-5
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-023-09535-5