The geometrical basis of the eyelid contour

Purpose: To derive a two-dimensional, frontal-view model of eyelid contour. Methods: Observational study. Palpebral fissure images of 110 normal subjec ts were acquired with a charge-coupled device camera and processed with Nat ional Institutes of Health Image software on a Macintosh computer. Monocula r frontal-view images of the palpebral fissures were recorded and second-de gree polynomial functions were fitted to both upper and lower eyelid contou rs for two areas: the whole eye lid margin (ciliated and inner canthal port ions) and the ciliated portion alone. In addition, frontal and lateral palp ebral fissure images were obtained. From the frontal view, the upper and lo wer ciliated contours were fitted with quadratic functions. From the latera l view, the upper and lower lateral angles, formed by the upper and lower e yelid margins and the axial axis, were measured. Results: Exclusion of the inner canthal portion of the eyelid contour led t o a much better quadratic fit for the contours. The sine (sin) of the upper lateral angle was strongly correlated with the parameter A of the quadrati c function fitted to the upper eyelid (the parameter A determines the curva ture of the function around its extremum point). For the lower eyelid, this correlation was not significant. Conclusions: The parabolic shape of the upper ciliated contour seen in two- dimensional images can be justified geometrically in a simple way, allowing a precise quantification of its shape. The same was not true for the lower eyelid. The parabolic shape of the upper eyelid can be demonstrated, using the Taylor series, to be a close approximation of the are of a circle.