The geometrical basis of the eyelid contour

To derive a two-dimensional, frontal-view model of eyelid contour.

Observational study. Palpebral fissure images of 110 normal subjects were acquired with a charge-coupled device camera and processed with National Institutes of Health Image software on a Macintosh computer. Monocular frontal-view images of the palpebral fissures were recorded and second-degree polynomial functions were fitted to both upper and lower eyelid contours for two areas: the whole eyelid margin (ciliated and inner canthal portions) and the ciliated portion alone. In addition, frontal and lateral palpebral fissure images were obtained. From the frontal view, the upper and lower ciliated contours were fitted with quadratic functions. From the lateral view, the upper and lower lateral angles, formed by the upper and lower eyelid margins and the axial axis, were measured.

Exclusion of the inner canthal portion of the eyelid contour led to 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 quadratic function fitted to the upper eyelid (the parameter A determines the curvature of the function around its extremum point). For the lower eyelid, this correlation was not significant.

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 arc of a circle.