Modeling Corneal Surfaces With Rational Functions for High-Speed Videokeratoscopy Data Compression

Abstract

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Evaluation of the Shape Symmetry of Bilateral Normal Corneas in a Chinese Population

“…While it is recognized that more sophisticated geometric models exist such as Zernike [26] and rational functions [27], which have the potential to more accurately represent corneal surface, these models have several limitations. Models based on Zernike polynomials may oscillate between values to be fitted, have poor asymptotic properties [28] and it is hard to assess a priori how many terms are necessary to achieve an acceptable fitting accuracy [29].…”

Zernike vs. Bessel circular functions in visual optics

“…Many alternative functional representations have been proposed to describe ophthalmic surfaces, ranging from generalised conic functions to more complicated representations such as the fractional Zernike polynomials and spherical harmonics . Other techniques include combinations of modal and zonal approaches .…”

Eigencorneas: application of principal component analysis to corneal topography

“…On the one hand, their low dimensionality facilitates a simple, fast and robust implementation, which consists of subtracting the mean and fitting the eigenvectors to the residual. The possibility of a complete characterization of the corneal shape with just a few parameters may be useful as well, such as in data compression . Furthermore, each eigenvector coefficient means a progressively finer correction to the initial rough approximation given by the mean.…”