Objective estimation for uncertainty of restoring corneal topography surface

Mapping corneal topography (CT) measurement data into a desired area can be based on data interpolation or fitting available data onto orthogonal functions. The restored CT map covers the entire area of interest, although its accuracy remains unknown. Here, a mathematical algorithm is presented for CT data assimilation, which yields both an entire CT map and an objective estimation of the map restoration accuracy.

All available CT elevation data are fitted on Zernike polynomials. Then, a Kalman filter is used to combine CT measurement data together with a priori statistics of Zernike coefficients estimated for the general population. The proposed technique yields the statistically optimal estimation for CT Zernike amplitudes and their covariance matrix. The entire CT elevation map is restored from Zernike amplitudes, and the amplitude covariance matrix is converted into a CT uncertainty map, which provides an objective estimate of the CT map quality.

The performance of the proposed method is demonstrated using CT data from a retrospective clinical study. The restored CT map has the highest uncertainty in measurement gaps, where no CT data are available. This uncertainty is close to the a priori variance of the general population.

Corneal topography mapping, based on the Kalman filter, constitutes a statistically optimal method of measurement data assimilation. It combines measurement data weighted by their quality and a priori knowledge of corneal shape, which protects the results from measurement outliers. The uncertainty magnitude depends on the number of pixels and the measurement noise level.