Corneal topography is a medical imaging technique to get the 3D shape of the cornea as a set of 3D points of its anterior
and posterior surfaces. From these data, topographic maps can be derived to assist the ophthalmologist in the diagnosis of
disorders. In this paper, we compare three different mathematical parametric representations of the corneal surfaces leastsquares fitted to the data provided by corneal topography. The parameters obtained from these models reduce the
dimensionality of the data from several thousand 3D points to only a few parameters and could eventually be useful for
diagnosis, biometry, implant design etc. The first representation is based on Zernike polynomials that are commonly used
in optics. A variant of these polynomials, named Bhatia-Wolf will also be investigated. These two sets of polynomials are
defined over a circular domain which is convenient to model the elevation (height) of the corneal surface. The third
representation uses Spherical Harmonics that are particularly well suited for nearly-spherical object modeling, which is
the case for cornea. We compared the three methods using the following three criteria: the root-mean-square error (RMSE),
the number of parameters and the visual accuracy of the reconstructed topographic maps. A large dataset of more than
2000 corneal topographies was used. Our results showed that Spherical Harmonics were superior with a RMSE mean
lower than 2.5 microns with 36 coefficients (order 5) for normal corneas and lower than 5 microns for two diseases
affecting the corneal shapes: keratoconus and Fuchs’ dystrophy
