Modeling corneal topography with a subdivision scheme in keratoconus

Abstract

Videokeratoscopy is often unable to obtain complete data sets in cases of irregular or asymmetric corneal topography. Subdivision schemes are very common in computer graphics for completion and smoothing of surfaces. Based on a network of triangular facets a smooth and complete surface in a standard coordinate system can be derived from topographic raw data. We examined 88 patients with keratoconus and 40 normal controls. Polygons and polyhedra were defined from videokeratoscopic height data, and a surface was modeled using a modified butterfly subdivision scheme for a nonuniform sampled grid. To assess the model quality topographic raw data were changed to missing values centrally (at the apex of the cone) and in four midperipheral quadrants. The target value was the root mean square error, comparing the remodeled value of the subdivision scheme to the raw data at the position of the missing values for each group. Due to the nonuniform mesh of our Placido-based topographer we used a dynamic adaptive model and the governing dynamic differential equation. With a single missing value, no difference was detected between normals and patients with keratoconus. For a missing area consisting of 13 raw data points, the remodeling error was significantly higher in patients with keratoconus than in normals. With the neighborhood of 13 missing data points, the apex of the cone was remodeled in both groups of patients with less precision than with the peripheral missing data. The locality of the equation systems to be solved and the easy calculation of explicit formulas for the normals may simplify ray-tracing techniques and make subdivision attractive for large datasets in corneal topography even with irregular patterns.