D.R. Iskander

Optimal modeling of corneal surfaces with Zernike polynomials

Zernike polynomials are often used as an expansion of corneal height data and for analysis of optical wavefronts. Accurate modeling of corneal surfaces with Zernike polynomials involves selecting the order of the polynomial expansion based on the measured data. The authors have compared the efficacy of various classical model order selection techniques that can be utilized for this purpose, and propose an approach based on the bootstrap. First, it is shown in simulations that the bootstrap method outperforms the classical model order selection techniques. Then, it is proved that the bootstrap technique is the most appropriate method in the context of fitting Zernike polynomials to corneal elevation data, allowing objective selection of the optimal number of Zernike terms. The process of optimal fitting of Zernike polynomials to corneal elevation data is discussed and examples are given for normal corneas and for abnormal corneas with significant distortion. The optimal model order varies as a function of the diameter of the cornea.

Analyzing the dynamic wavefront aberrations in the human eye

The optics of the human eye are not static in steady viewing conditions and exhibit microfluctuations. Previous methods used for analyzing dynamic changes in the eyes optics include simple Fourier-transform-based methods, which have been used in studies of the eyes accommodation response. However, dedicated tools for the analysis of dynamic wavefront aberrations have not been reported. We propose a set of signal processing tools, the combination of which uncovers aspects of the dynamics of eyes optical aberrations which were hidden from conventional analysis techniques. The methodology includes extraction of artifacts from potentially significant eye movements, filtering, optimal parametric signal modeling, and frequency and time-frequency representations. The exposition of the techniques and their advantages over traditional techniques is illustrated for real dynamic eye wavefront aberration measurements.

Evaluating tear film stability in the human eye with high-speed videokeratoscopy

High-speed videokeratoscopy (HSV) is an emerging technology that has the potential to acquire information on the dynamics of corneal topography and tear-film behavior. We show that the surface regularity and asymmetry indices, which are traditionally used for characterizing the stability of precorneal tear film, have limitations in the context of HSV because they are highly sensitive to natural ocular microfluctuations. To overcome this problem, we propose a new microfluctuation-independent surface indicator. It is based on the root-mean-square of the error of the parametric model fit to the surface. Further, we develop techniques for estimating the tear film build-up and break-up times. The tear film build-up time estimator is based on the proposed RMS fit surface indicator while the tear film break-up time estimator is derived directly from a set of consecutive HSV digital images, without the need for estimating the resulting corneal surface.

Automatic pupillometry from digital images

Determination of two-dimensional characteristics of the anterior surface of the eye is becoming increasingly important in modern optometry and ophthalmology practice. In particular, accurate estimation of the pupil size and centration is crucial in customized refractive surgery, corneal transplantation, and advanced contact lens fitting. The pupil parameters change under different lighting conditions so they often need to be related to some fixed reference such as the limbus outline. However, current commercial pupillometers do not estimate limbus position. We present a novel algorithm for automatic extraction of pupil parameters from digital images that takes the relative limbus information into account. The algorithm utilizes several customized image processing techniques that form a robust procedure which performs well for a wide range of clinical images. We apply the developed algorithm to images obtained by a standard digital camera, and specialized ophthalmic instruments such as a wavefront sensor and a high-speed imaging system.

Automatic estimation of the corneal limbus in videokeratoscopy

An algorithm for estimating the corneal limbus from videokeratoscopic images is proposed. After the image is transformed to a polar grid, a novel edge-detection procedure, suitable for the detection of the soft edge produced by the limbus, is used to locate the limbus. Outliers due to the eyelids, eyelashes, and videokeratoscopic rings are removed by taking advantage of the approximate circularity of the cornea. An ellipse which minimizes the sum of the squared algebraic errors is fitted to the remaining edge points. Comparisons between the proposed algorithm, a manual computer-based technique and an algorithm which uses conventional edge-detection techniques demonstrate the accuracy of the proposed algorithm.

Assessment of Tear Film Surface Quality Using Dynamic-Area High-Speed Videokeratoscopy

A new method for noninvasive assessment of tear film surface quality (TFSQ) is proposed. The method is based on high-speed videokeratoscopy in which the corneal area for the analysis is dynamically estimated in a manner that removes videokeratoscopy interference from the shadows of eyelashes but not that related to the poor quality of the precorneal tear film that is of interest. The separation between the two types of seemingly similar videokeratoscopy interference is achieved by region-based classification in which the overall noise is first separated from the useful signal (unaltered videokeratoscopy pattern), followed by a dedicated interference classification algorithm that distinguishes between the two considered interferences. The proposed technique provides a much wider corneal area for the analysis of TFSQ than the previously reported techniques. A preliminary study with the proposed technique, carried out for a range of anterior eye conditions, showed an effective behavior in terms of noise to signal separation, interference classification, as well as consistent TFSQ results. Subsequently, the method proved to be able to not only discriminate between the bare eye and the lens on eye conditions but also to have the potential to discriminate between the two types of contact lenses.

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

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.

Context-based modelling of interferometric signals for the assessment of tear-film surface quality

Modelling of interferometric signals related to tear film surface quality is considered. In the context of tear film surface quality estimation in normal healthy eyes, two clinical parameters are of interest: the build-up time, and the average interblink surface quality. The former is closely related to the signal derivative while the latter to the signal itself. Polynomial signal models, chosen for a particular set of noisy interferometric measurements, can be optimally selected, in some sense, with a range of information criteria such as AIC, MDL, Cp, and CME. Those criteria, however, do not always guarantee that the true derivative of the signal is accurately represented and they often overestimate it. Here, a practical method for judicious selection of model order in a polynomial fitting to a signal is proposed so that the derivative of the signal is adequately represented. The paper highlights the importance of context-based signal modelling in model order selection.

Computationally efficient interference detection in videokeratoscopy images

An optimal videokeratoscopic image presents a strong well-oriented pattern over the majority of the measured corneal surface. In the presence of interference, arising from reflections from eyelashes or tear film instability, the patternpsilas flow is disturbed and the local orientation of the area of interference is no longer coherent with the global flow. Detecting and analysing videokeratoscopic pattern interference is important when assessing tear film surface quality, break-up time and location as well as designing tools that provide a more accurate static measurement of corneal topography. In this paper a set of algorithms for detecting interference patterns in videokeratoscopic images is presented. First a frequency approach is used to subtract the background information from the oriented structure and then a gradient-based analysis is used to obtain the patternpsilas orientation and coherence. The proposed techniques are compared to a previously reported method based on statistical block normalisation and Gabor filtering. The results indicate that the proposed technique leads, in most cases: to a better videokeratoscopic interference detection system, that for a given probability of the useful signal detection (99.7%) has a significantly lower probability of false alarm, and at the same time is computationally much more efficient than the previously reported method.

Formulation and comparison of two detectors of independent timing jitter in a complex harmonic

Two detectors of symmetrically distributed independent timing jitter in a data record composed of a complex harmonic in additive white Gaussian noise are proposed. The proposed detectors are computationally efficient, and although they are formulated using asymptotic results, they may be effectively used with small sample lengths under a wide range of conditions. The conditions required for consistency of the detectors are derived and examined for important special cases. The performances of the detectors are analyzed using simulations.