Objective Estimation for Uncertainty of Restoring Corneal Topography Surface

Abstract

 

Purpose

 

Corneal topography (CT) field can be restored from measurements data by decomposing available data into Zernike polynomials and mapping the CT field in the desired area. The accuracy of such restoration depends on the measurement noise and number of available data. Here we present an algorithm for CT data assimilation, which yields both CT map and an objective estimation of the restoration accuracy.

 

Methods

 

The Kalman-Bucy technique is used to combine measured CT heights with a priori mean and covariance of Zernike coefficients, estimated for the general population (CT data for 308 virgin eyes). This algorithm yields a statistically optimal estimate of Zernike coefficients for the measured field and also their covariance matrix, which provides a measure of the measurement uncertainty. The efficiency of the proposed method is demonstrated using archived corneal topography data from previous clinical studies.

 

Results

 

For any CT measurement the proposed technique yields an estimate of Zernike amplitudes and their covariance matrix, which result in a reconstructed map of CT heights with no gaps within the area (Fig.1A). The covariance matrix gives the uncertainty (std) of CT height restoration (Fig.1B). The uncertainty is higher at the area edges, because the restoration is based mainly on the data from internal area. Restored field in the measurement gaps has the highest uncertainty, close to the a priori variance of the general population.

 

Conclusions

 

The proposed algorithm assimilates measurement data together with a priori information, derived from statistics of general population, which protects the results from measurement outliers. It restores the CT field in the entire area and provides an objective estimate of measurement uncertainty, based on the measurement noise level and the number of available data. The uncertainty map displays the areas where the map is less reliable and to what extent.

 

 

A B Fig. 1. A - CT height measured with Atlas topographer and restored within 6mm diameter circle. B - Estimated uncertainty of measured and restored CT height (Hyperopia Sph=2.25D, Cyl=0.25D)

 

Keywords: 552 imaging methods (CT, FA, ICG, MRI, OCT, RTA, SLO, ultrasound) • 551 imaging/image analysis: non-clinical • 681 refractive surgery: corneal topography