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A new proposed model for image enhancement using the coefficients obtained by a subclass of the Sakaguchi-type function

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Abstract

The identification of illnesses relating to the retina is greatly aided by retinal fundus imaging. Retinal image enhancement typically aids in the analysis of disorders connected to the retinal fundus image because the detailed information of the retinal fundus image, such as small vessels, microaneurysms and exudates, may be in low contrast. The false boundaries, rapid changes in colour levels and loss of visual detail can result from current image-enhancing techniques. In this study, we present a novel image enhancement approach utilizing the concept of geometric function theory (GFT). Initially, coefficient bounds were obtained by the subclass \( {\mathfrak {p}}-\Phi {\mathcal {S}}^*(t,\mu ,\nu ,J,K) \). Then, for the enhancement process these coefficients were subsequently convoluted with the input image. To assess the quality of the enhanced images, we employed a set of performance metrics, including peak signal-to-noise ratio, structured similarity indexing method, contrast improvement ratio and absolute mean brightness error. Comparative analysis against established state-of-the-art methods revealed that our GFT-based enhancement method consistently outperforms existing techniques.

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Data Availability

Source files of the test images are given below: Source file of “VIRAL PNEUMONIA”.Source file of “PEPPERS”.Source file of “YELLOWLILY”.Source file of “MOON”.Source file of “SATURN”.Source file of “RETINAL”.

References

  1. Agarwal, R.. P.: A propos d’une note de M. Pierre Humbert. C. R. Acad. Sci. Paris 236, 2031–2032 (1953)

    MathSciNet  Google Scholar 

  2. Alessa, N., et al.: A new subclass of analytic functions related to Mittag-Leffler type Poisson distribution series. J. Funct. Spaces 2021, 1–7 (2021)

    MathSciNet  Google Scholar 

  3. Khan, M. G. et al.: Applications of Mittag-Leffer type Poisson distribution to a subclass of analytic functions involving conic-type regions. J. Funct. Spaces 2021, Art. ID 4343163, pp. 9

  4. Kanas, S., Wisniowska, A.: Conic regions and \(k\)-uniform convexity. J. Comput. Appl. Math. 105(1–2), 327–336 (1999)

    Article  MathSciNet  Google Scholar 

  5. Kanas, S., Wiśniowska, A.: Conic domains and starlike functions. Rev. Roumaine Math. Pures Appl. 45(4), 647–657 (2001)

    MathSciNet  Google Scholar 

  6. Kanas, S., Srivastava, H.M.: Linear operators associated with \(k\)-uniformly convex functions. Integral Transform. Spec. Funct. 9(2), 121–132 (2000)

    Article  MathSciNet  Google Scholar 

  7. Kanas, S., Răducanu, D.: Some class of analytic functions related to conic domains. Math. Slovaca 64(5), 1183–1196 (2014)

    Article  MathSciNet  Google Scholar 

  8. Gour, M.M., Joshi, S., Goswami, P., Purohit, S.D.: New classes of bi-univalent functions. J. Interdiscip. Math. 23(2), 583–590 (2020). https://doi.org/10.1080/09720502.2020.1731978

    Article  MathSciNet  Google Scholar 

  9. Mittag-Leffler, G.M.: Une generalisation de I’integrale de Laplace-Abel. Comptes Rendus de I’Acadėmie des Sciences Sėrie II 37, 537–539 (1903)

    Google Scholar 

  10. Mittag-Leffler, G.M.: Sur la nouvelle fonction \(E_{\alpha }(x)\). Comptes Rendus de I’Acadėmie des Sciences Sėrie II 137, 554–558 (1903)

    Google Scholar 

  11. Mittag-Leffler, G.: Sur la représentation analytique d’une branche uniforme d’une fonction monogène. Acta Math. 29(1), 101–181 (1905)

    Article  MathSciNet  Google Scholar 

  12. Mahmood, T., et al.: A subclass of analytic functions defined by using Mittag-Leffler function. Honam Math. J. 42(3), 577–590 (2020)

    MathSciNet  Google Scholar 

  13. Noor, K.I., Malik, S.N.: On coefficient inequalities of functions associated with conic domains. Comput. Math. Appl. 62(5), 2209–2217 (2011)

    Article  MathSciNet  Google Scholar 

  14. Porwal, S., Dixit, K.K.: On Mittag-Leffler type Poisson distribution. Afr. Mat. 28(1–2), 29–34 (2017)

    Article  MathSciNet  Google Scholar 

  15. Wiman, A.: Über den Fundamentalsatz in der Teorie der Funktionen \(E_a(x)\). Acta Math. 29(1), 191–201 (1905)

    Article  MathSciNet  Google Scholar 

  16. Wiman, A.: Über die Nullstellen der Funktionen \(E_\alpha (x)\). Acta Math. 29(1), 217–234 (1905)

    Article  MathSciNet  Google Scholar 

  17. Wang, Z., Bovik, A.. C.: A universal image quality index. in IEEE Signal Process Lett 9(3), 81–84 (2002). https://doi.org/10.1109/97.995823

    Article  ADS  CAS  Google Scholar 

  18. Ibrahim, R.W., Jalab, H.A.: Image denoising based on approximate solution of fractional CauchyEuler equation by using complex-step method. Iranian J. Sci. Tech. 39(A3), 243 (2015)

    Google Scholar 

  19. Ibrahim, R.W., et al.: A medical image enhancement based on generalized class of fractional partial differential equations. Quant. Imag. Med. Surg. 12(1), 172 (2022)

    Article  Google Scholar 

  20. Sara, U., Morium, A., Mohammad, S.U.: Image quality assessment through FSIM, SSIM, MSE and PSNRa comparative study. J. Comput. Commun. 7(3), 8–18 (2019)

    Article  Google Scholar 

  21. Hor, A., Ziou, D.: Image quality metrics: PSNR vs. SSIM, 2010 20th International Conference on Pattern Recognition, 2010, pp. 2366-2369, https://doi.org/10.1109/ICPR.2010.579

  22. Karim, Faten Khalid, et al.: Mathematical model based on fractional trace operator for COVID-19 image enhancement. J. King Saud Univ. Sci. 34(7), 102254 (2022)

    Article  PubMed  PubMed Central  Google Scholar 

  23. Amoako-Yirenkyi, P., Appati, J.K., Dontwi, I.K.: A new construction of a fractional derivative mask for image edge analysis based on Riemann-Liouville fractional derivative. Adv. Differ. Equ 2016, 238 (2016). https://doi.org/10.1186/s13662-016-0946-8

    Article  MathSciNet  Google Scholar 

  24. Samajdar T, Quraishi MI.: Analysis and evaluation of image quality metrics, pp. 369–378. New Delhi, Information Systems Design and Intelligent Applications. Springer (2015)

  25. Ibrahim, R.W., et al.: Mathematical design enhancing medical images formulated by a fractal flame operator. Intell. Autom. Soft Comput. 32(2), 937–950 (2022)

    Article  MathSciNet  Google Scholar 

  26. Janan, F., Brady, M.: RICE: A method for quantitative mammographic image enhancement. Med. Image Anal. 71, 102043 (2021)

    Article  PubMed  Google Scholar 

  27. Agrawal, S., Panda, R., Mishro, P., Abraham, A.: A novel joint histogram equalization based image contrast enhancement. J. King Saud Univ. Comput. Inf. Sci. (2019). https://doi.org/10.1016/j.jksuci.2019.05.010

    Article  Google Scholar 

  28. Xiaojie Guo, Yu., Li, Haibin Ling: LIME: Low-light image enhancement via illumination map estimation. IEEE Trans. Image Process. 26, 982–93 (2017)

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  29. Hasikin, K., Isa, N.A.M.: Adaptive fuzzy contrast factor enhancement technique for low contrast and nonuniform illumination images. SIViP 8, 1591–603 (2014)

    Article  Google Scholar 

  30. Roy, S., Shivakumara, P., Jalab, H.A., Ibrahim, R.W., Pal, U., Lu, T.: Fractional poisson enhancement model for text detection and recognition in video frames. Pattern Recogn. 52, 433–47 (2016)

    Article  ADS  Google Scholar 

  31. Fu, X., Zeng, D., Huang, Y., Liao, Y., Ding, X., Paisley, J.: A fusion-based enhancing method for weakly illuminated images. Signal Process. 129, 82–96 (2016)

    Article  Google Scholar 

  32. Zhang, X., Yan, H.: Image enhancement algorithm using adaptive fractional differential mask technique. Math. Found. Comput. 2, 347 (2019)

    Article  Google Scholar 

  33. Khmag, A.: Digital image noise removal based on collaborative filtering approach and singular value decomposition. Multimed. Tools Appl. 81, 16645–16660 (2022). https://doi.org/10.1007/s11042-022-12774-7

    Article  Google Scholar 

  34. Khmag, A.: Additive Gaussian noise removal based on generative adversarial network model and semi-soft thresholding approach. Multimed. Tools Appl. 82, 7757–7777 (2023). https://doi.org/10.1007/s11042-022-13569-6

    Article  Google Scholar 

  35. Khmag, A., Ramli, A.R., Al-haddad, S.A.R., et al.: Natural image noise level estimation based on local statistics for blind noise reduction. Vis. Comput. 34, 575–587 (2018). https://doi.org/10.1007/s00371-017-1362-0

    Article  Google Scholar 

  36. Zhou, M., Jin, K., Wang, S., Ye, J., Qian, D.: Color retinal image enhancement based on luminosity and contrast adjustment. IEEE Trans. Biomed. Eng. 65(3), 521–527 (2018). https://doi.org/10.1109/TBME.2017.2700627

    Article  ADS  PubMed  Google Scholar 

  37. Gupta, B., Tiwari, M.: Color retinal image enhancement using luminosity and quantile based contrast enhancement. Multidimension. Syst. Signal Process. 30(4), 1829–1837 (2019). https://doi.org/10.1007/s11045-019-00630-1

    Article  Google Scholar 

  38. Priyadharsini, C., Jagadeesh, K.R.: Retinal image enhancement based on color dominance of image. Sci. Rep. 13, 7172 (2023). https://doi.org/10.1038/s41598-023-34212-w

    Article  CAS  Google Scholar 

  39. Wang, Y.P., Wu, Q., Castleman, K., Xiong, Z.: Chromosome image enhancement using multiscale differential operators. IEEE Trans. Med. Imag. 22, 685–693 (2003). https://doi.org/10.1109/TMI.2003.812255

  40. Román, J.C.M., Noguera, J.L.V., Legal-Ayala, H., Pinto-Roa, D., Gomez-Guerrero, S., García-Torres, M.: Entropy and contrast enhancement of infrared thermal images using the multiscale top-hat transform. Entropy 21, 244 (2019). https://doi.org/10.3390/e21030244

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgements

Authors thank for providing free access of Messidor database.

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Authors and Affiliations

  1. Division of Mathematics, School of Advanced Sciences, Vellore Institute of Technology Chennai Campus, Chennai, 600 127, India

    E. K. Nithiyanandham & B. Srutha Keerthi

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  1. E. K. Nithiyanandham
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  2. B. Srutha Keerthi
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Correspondence to B. Srutha Keerthi.

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Nithiyanandham, E.K., Keerthi, B.S. A new proposed model for image enhancement using the coefficients obtained by a subclass of the Sakaguchi-type function. SIViP 18, 1455–1462 (2024). https://doi.org/10.1007/s11760-023-02861-z

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