Structural feature amplification in malaria cell images via Hankel determinants and sine-associated Sakaguchi functions

R Kamali; S. Prema; R Kamali; S. Prema

doi:10.3934/math.20261039

AIMS Mathematics

2026, Volume 11, Issue 8: 25924-25957. doi: 10.3934/math.20261039

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Research article

Structural feature amplification in malaria cell images via Hankel determinants and sine-associated Sakaguchi functions

R Kamali ,
S. Prema ^,

Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai, Tamil Nadu, India

Received: 27 June 2026 Revised: 04 August 2026 Accepted: 07 August 2026 Published: 20 August 2026
MSC : 30C45, 30C50

Logarithmic coefficients occupy an essential place in geometric function theory and are linked to univalent and close-to-convex functions. In this paper, the authors considered the third Hankel determinant connected with logarithmic coefficients of certain subfamilies of Sakaguchi functions, which also include sine-associated Sakaguchi functions. Sharp coefficient estimates and upper bounds were obtained for subclasses of functions, which led to obtaining new coefficient results in complex analysis and establishing connections between logarithmic coefficients and geometric function subclasses. Moreover, the proposed theoretical approach was used for enhancing the images of malaria cells with the help of the suggested Hankel-determinant-based image enhancement pipeline. Pixel intensity local distributions were considered via analytic functions, and logarithmic coefficients were used for computing the clarity factor required for adaptive sharpening of the image. Thus, a mathematically motivated Hankel-determinant-based image enhancement framework was developed, where a clipped clarity factor ensures stable enhancement. Experimental results demonstrated competitive image quality (PSNR = 23.92 dB, SSIM = 0.92, SNR = 18.66 dB, and CNR = 2.67) with improved preservation of chromatin structures and vacuoles, making the method suitable for malaria image preprocessing.
- holomorphic functions,
- Hankel determinant,
- subordination,
- logarithmic coefficients,
- Sakaguchi functions,
- malaria parasite detection,
- image enhancement
Citation: R Kamali, S. Prema. Structural feature amplification in malaria cell images via Hankel determinants and sine-associated Sakaguchi functions[J]. AIMS Mathematics, 2026, 11(8): 25924-25957. doi: 10.3934/math.20261039

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Abstract

Logarithmic coefficients occupy an essential place in geometric function theory and are linked to univalent and close-to-convex functions. In this paper, the authors considered the third Hankel determinant connected with logarithmic coefficients of certain subfamilies of Sakaguchi functions, which also include sine-associated Sakaguchi functions. Sharp coefficient estimates and upper bounds were obtained for subclasses of functions, which led to obtaining new coefficient results in complex analysis and establishing connections between logarithmic coefficients and geometric function subclasses. Moreover, the proposed theoretical approach was used for enhancing the images of malaria cells with the help of the suggested Hankel-determinant-based image enhancement pipeline. Pixel intensity local distributions were considered via analytic functions, and logarithmic coefficients were used for computing the clarity factor required for adaptive sharpening of the image. Thus, a mathematically motivated Hankel-determinant-based image enhancement framework was developed, where a clipped clarity factor ensures stable enhancement. Experimental results demonstrated competitive image quality (PSNR = 23.92 dB, SSIM = 0.92, SNR = 18.66 dB, and CNR = 2.67) with improved preservation of chromatin structures and vacuoles, making the method suitable for malaria image preprocessing.

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