Open Access

ARTICLE

A Novel Math-Inspired Metaheuristic Algorithm for Retinal Vessel Segmentation: Quadratic Interpolation Optimization (QIO) Algorithm

Mehmet Bahadır Çetinkaya^1,*, Sevim Adige^2,3

1 Department of Mechatronics Engineering, Faculty of Engineering, Erciyes University, Kayseri, Türkiye
2 Department of Electronics and Automation, Vocational School of Hendek, Sakarya University of Applied Sciences, Sakarya, Türkiye
3 Mechatronics Engineering, Graduate School of Natural and Applied Sciences, Erciyes University, Kayseri, Türkiye

* Corresponding Author: Mehmet Bahadır Çetinkaya. Email:

Journal on Artificial Intelligence 2026, 8, 89-106. https://doi.org/10.32604/jai.2026.074459

Received 11 October 2025; Accepted 06 January 2026; Issue published 13 February 2026

Abstract

Math-inspired metaheuristic algorithms stand out with their simple algorithm structures and the inclusion of fewer control parameters. In this study, the recently proposed math-inspired Quadratic Interpolation Optimization (QIO) algorithm was improved as a clustering-based algorithm and then applied to retinal vessel segmentation. Afterwards, its performance was compared with the math-inspired Sine Cosine Algorithm (SCA) and Arithmetic Optimization Algorithm (AOA), which have been frequently applied to engineering problems. First, the performance of the QIO algorithm was analyzed in terms of sensitivity (Se), specificity (Sp), accuracy (Acc), and precision (Prec). An average success rate of approximately 70% or higher indicates that the QIO algorithm is able to provide sufficient performance in clustering. Subsequently, detailed convergence analyses were performed in terms of mean squared error (MSE), CPU time, and convergence speed. The results demonstrate that the QIO algorithm reaches low MSE values at early cycles and shorter CPU times. Finally, to compare the statistical performance of the algorithms, analyses were also conducted based on standard deviation and the Wilcoxon Rank-Sum test. The results demonstrated the stability and robustness of the QIO algorithm. Consequently, it can be concluded that the QIO algorithm can be successfully applied to image processing.

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Keywords

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