Modeling the corneal topography with a subdivision scheme in cases of keratoconus

Background. Videokeratoscopy is often unable to obtain complete data sets i n cases of irregular or asymmetric corneal topography. Subdivision schemes are very common in computer graphics for completion and smoothing of surfac es. Based on a network of triangular facets a smooth and complete surface i n a standard coordinate system can be derived from topographic raw data. Patients and methods. We examined 88 patients with keratoconus and 40 norma l controls. Polygons and polyhedra were defined from videokeratoscopic heig ht data, and a surface was modeled using a modified butterfly subdivision s cheme for a nonuniform sampled grid. To assess the model quality topographi c raw data were changed to missing values centrally (at the apex of the con e) acid in four midperipheral quadrants. The target value was the root mean square error, comparing the remodeled value of the subdivision scheme to t he raw data at the position of the missing values for each group. Results. Due to the nonuniform mesh of our Placido-based topographer we use d a dynamic adaptive model and the governing dynamic differential equation. With a single missing value, no difference was detected between normals an d patients with keratoconus. For a missing area consisting of 13 raw data p oints, the remodeling error was significantly higher in patients with kerat oconus 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 precis ion than with the peripheral missing data. Conclusion. The locality of the equation systems to be solved and the easy calculation of explicit formulas for the normals may simplify ray-tracing t echniques and make subdivision attractive for large datasets in corneal top ography even with irregular patterns.