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Facial Plast Surg 2022; 38(03): 307-310
DOI: 10.1055/s-0041-1742200
Original Research

Mathematical Modeling of Eyebrow Curvature

Ann Q. Tran 
1   Department of Ophthalmology, University of Illinois Eye and Ear Infirmary, Chicago, Illinois
2   Department of Ophthalmology, Columbia University Irving Medical Center, Edward S. Harkness Eye Institute, New York, New York
,
Cameron Yang
3   Department of Ophthalmology, Ohio State University, Columbus, Ohio
,
Andrea A. Tooley
4   Department of Ophthalmology, Mayo Clinic, Rochester, Minnesota
,
Michael Kazim
2   Department of Ophthalmology, Columbia University Irving Medical Center, Edward S. Harkness Eye Institute, New York, New York
,
Lora R. Dagi Glass
2   Department of Ophthalmology, Columbia University Irving Medical Center, Edward S. Harkness Eye Institute, New York, New York
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Abstract

The aim of the study is to describe a mathematical model for analyzing eyebrow curvature that can be applied broadly to curvilinear facial features. A total of 100 digital images (50 men, 50 women) were obtained from standardized headshots of medical professionals. Images were analyzed in ImageJ by plotting either 8 or 15 points along the inferior-most row of contiguous brow cilia. A best-fit curve was automatically fit to these points in Microsoft Excel. The second derivative of the second-degree polynomial and a fourth-degree polynomial were used to evaluate brow curvature. Both techniques were subsequently compared with each other. A second-degree polynomial and fourth-degree polynomial were fit to all eyebrows. Plotting 15 points yielded greater goodness-of-fit than plotting 8 points along the inferior brow and allowed for more sensitive measurement of curvature across all images. A fourth-degree polynomial function provided a closer fit to the eyebrow than a second-degree polynomial function. This method provides a simple and reliable tool for quantitative analysis of eyebrow curvature from images. Fifteen-point plots and a fourth-degree polynomial curve provide a greater goodness-of-fit. The authors believe the described technique can be applied to other curvilinear facial features and will facilitate the analysis of standardized images.

Keywords

mathematical modeling - eyebrow curvature - facial features - curvilinear features


Publication History

Article published online:
03 February 2022

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