Vestnik КRAUNC. Fiz.-Mat. nauki. 2022. vol. 38. no. 1. P. 84-105. ISSN 2079-6641

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MSC 65K10, 65C35, 68U10

Research Article

RAPID — A model of fast eye pupil registration and tracking by a modified metaheuristic differential evolution method based on the Verhulst-Pearl equation

Y. V. Grushko

Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatskiy, Pogranichnaya str., 4, Russia


This paper proposes a model of fast registration and pupil tracking — «RAPID», for devices with limited computing resource (weak personal computers, smartphones, embedded systems based on ARM architecture) in order to reduce the cost of technology for individual use by people with disabilities and medical institutions. The model is based on the idea of representing the process of video oculography as a multidimensional global optimization problem and its solution by the metaheuristic method of differential evolution. The optimization problem (objective function) is formalized as a search for the region that approximates the pupil in the three-dimensional parameter space most completely — the position and approximate size of the pupil. For the considered optimization problem we propose a modification of differential evolution method based on the process of formation of genetic isolations of population of solutions in the neighborhood of all local and global extremums of the target function followed by growth of the most adapted isolation (near the global extremum) and degeneration of others according to the differential Verhulst-Pearl equation. This behavior makes the search algorithm less «greedy» and makes it possible to correctly extract the pupil from the full frame. The developed tracking model can be used in the development of software packages in the task of augmentative communication for patients with lateral amyotrophic sclerosis or diplegia syndromes, on non-specialized devices, as well as in ophthalmological complexes and infrared-pupillometers.

Key words: videooculography, differential evolution, multivariate global optimization, region of interest, Hough transform, Verhulst-Pearl model.

DOI: 10.26117/2079-6641-2022-38-1-84-105

Original article submitted: 15.02.2022

Revision submitted: 01.03.2022

For citation. Grushko Y. V. RAPID — A model of fast eye pupil registration and tracking by a modified metaheuristic differential evolution method based on the Verhulst-Pearl equation. Vestnik KRAUNC. Fiz.-mat. nauki. 2022, 38: 1, 84-105. DOI: 10.26117/2079-6641-2022-38-1-84-105

The content is published under the terms of the Creative Commons Attribution 4.0 International License (

© Grushko Y. V., 2022

Funding. Scientific research work of Vitus Bering Kamchatka State University, № AAAA-A19-119072290002-9.

Competing interests. The author declares that there are no conflicts of interest with respect to authorship and publication.

Contribution and responsibility. The author contributed to the writing of the article and is solely responsible for submitting the final version of the article to the press. The final version of the manuscript was approved by the author.

Acknowledgments. I express my gratitude to the supervisor, Doctor of Physical and Mathematical Sciences R.I. Parovik for a number of comments that contributed to the improvement of the presented work.


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Grushko Yuriy Vasilyevich – PhD student of the Fac. of Phys. & Math., Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatskiy, Russia, ORCID 0000-0002-3663-0018.

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