Comparative Analysis of Some Modal Reconstruction Methods of the Shape of the Cornea from Corneal Elevation Data
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Purpose: A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity was performed, by using both standard radial polynomials and radial basis functions (RBFs). The hypothesis was that the correct approach in the case of highly irregular corneas should combine several bases. Methods: Standard approaches of reconstruction by Zernike and other types of radial polynomials were compared with the discrete least-squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the absence of measurement noise. For the reconstruction by polynomials, the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF was performed by using a regular grid of centers. Results: The quality of fit was assessed by computing for each surface the mean square errors (MSEs) of the reconstruction by LSF, measured at the sa...