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 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. RESULTS: 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. 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 arc of a circle.

Digital image processing measurement of the upper eyelid contour in Graves disease and congenital blepharoptosis.

OBJECTIVE: This study used image processing techniques to quantify the upper eyelid contour of patients with Graves upper eyelid retraction and congenital blepharoptosis. DESIGN: The study design was a cross-sectional study. PARTICIPANTS: A total of 29 patients with Graves disease, 22 patients with congenital blepharoptosis, and 50 patients with no history of eye disease participated. INTERVENTION: The images of the palpebral fissure of all participants were transferred to a personal computer and processed with NIH Image 1.55 software. MAIN OUTCOME MEASURES: The following parameters were analyzed: the curvature of the upper eyelid contour, the position of the contour peak relative to the midline, and the ratio between the temporal and nasal upper quadrant areas of the palpebral fissure. RESULTS: All upper eyelid contours could be fitted with second-degree polynomial functions. The mean temporal/nasal area ratio was 1.33 mm in patients with Graves disease, 0.92 mm in patients with blepharoptosis, and 1.04 mm in control subjects. The peak of the upper eyelid contour was found to be lateral to the midline in control subjects (1.05 mm) and in patients with Graves disease (2.09 mm). In patients with blepharoptosis, the peak was 0.69 mm medial to the midline. Overall, the distance between the midpupil and the upper eyelid margin was correlated with several factors: the degree of curvature, the position of the peak of the eyelid contour, and the temporal/nasal area ratio. CONCLUSIONS: In Graves eyelid retraction, the curvature of the upper eyelid is enhanced, the peak of the contour is displaced laterally, and the temporal upper quadrant area is increased. Conversely, in congenital blepharoptosis, the eyelid is almost flat, the peak of the contour is displaced medially, and the upper quadrant area is diminished. The lateral segment of the upper eyelid is more involved than the nasal segment in both Graves upper eyelid retraction and congenital blepharoptosis.