Research articles
ScienceAsia 51S (2025):ID 2025021 1-8 |doi:
10.2306/scienceasia1513-1874.2025.s021
Geometrical approach for identifying the corners of convex
bodies composed by circular arcs
Asama Jampeepana,*, Supanut Chaideeb, Papangkorn Inkeawc
ABSTRACT: Thispaperpresentsamathematical approachfor accurately identifying the iris boundaries in photographic
pictures, specifically focusing on eye position detection. This issue is of significance for several applications, especially
in the field of eye tracking. Suppose that the detected data of the iris combined with eyelids is given. We assumed
that the shape of the detected data is represented by the boundary of a convex body composed of circular arcs that
represent the boundaries of the iris, upper eyelid, and lower eyelid. The objective is to identify the iris boundary
from generated points on the boundary of the convex body corresponding to the position of gaze. We investigate the
geometric properties of convex bodies, specifically focusing on their corners, which are non-differentiable points. An
algorithm is then established to classify points to the iris boundary or the eyelids. This is done by utilizing convex
hull and exterior angle analysis. The set of finite points around the boundary of the iris can be used to approximate
the center of the iris. The experiments were conducted using both ideally generated data and real data obtained from
photographic images of eyes.
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| a |
Program in Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University,
Chiang Mai 50200 Thailand |
| b |
Advanced Research Center for Computational Simulation (ARCCoS), Department of Mathematics, Faculty of
Science, Chiang Mai University, Chiang Mai 50200 Thailand |
| c |
Data Science Research Center, Department of Computer Science, Faculty of Science, Chiang Mai University,
Chiang Mai 50200 Thailand |
* Corresponding author, E-mail: AsamaCMU@gmail.com
Received 1 Dec 2024, Accepted 0 0000
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