Robust model order selection for corneal height data based on τ estimation

Corneal height data, typically measured with a videokeratoscope, is modeled as a set of Zernike polynomials. Accurate corneal modeling is important, e.g. prior to surgery. The measurements require a good quality of the pre-corneal tear film and sufficiently wide eyelid aperture, which is not always fulfilled in practice. This results in missing values or outliers in the corneal topography map. We suggest to treat this problem by a new two step model selection procedure and introduce a criterion based on r-estimation, which is simultaneously statistically robust and efficient. For this, we exploit the asymptotic equivalence of τ-estimation to M-estimation. The performance is evaluated using simulations, as well as real data.