Partial reconstruction of sparse and incomplete point clouds applied to the generation of corneal topographic maps of healthy and diseased patients

• Improvement of digital corneal models using extrapolation techniques. • Missing data extrapolated using polynomial, biharmonic splines and RBF functions. • Mean Average Percentage Error index is used for method comparison. • Fitting valid up to 5.2/4.2 mm radius on anterior/posterior surfaces respectively. • Extrapolation method must be chosen wisely. The presence of unmeasured areas or areas with missing data in corneal topographies greatly affect the quality of digital corneal models. These are more frequent in posterior than in anterior corneal surface. This work seeks to complete and improve digital corneal models generated from incomplete point clouds obtained with commercial tomographic equipment, applying three interpolation/extrapolation techniques based on population data (Polynomial, Biharmonic Splines and Cubic Radial Base Functions). 43 personalized corneal models of patients with different grades of keratoconus were used to test each interpolation method. All interpolation results were compared using the Mean Average Percentage Error (MAPE) index, observing that it is possible to interpolate/extrapolate up to the radius 5.2 mm on the anterior face and up to 4.2 mm on the posterior face in general, but none of the methods stand out above the others for all the situations considered. Consequently, extrapolation method must be chosen carefully.