Statistical Signal and Image Processing Techniques in Corneal Modeling

In this thesis, we consider two interrelated problems, which are the enhancement of videokeratoscopic images for more accurate corneal topography estimation and model-order selection of corneal surfaces when expanded using orthogonal Zernike polynomials. Corneal topography estimation that is based on the Placido disk principle relies on good quality of pre-corneal tear film and sufficiently wide eyelid (palpebral) aperture to avoid reflections from eyelashes. However, in practice, these conditions are not always fulfilled resulting in missing regions, smaller corneal coverage, and subsequently poorer estimates of corneal topography. Our aim is to enhance the standard operating range of a Placido disk videokeratoscope to obtain reliable corneal topography estimates in patients with poor tear film quality, such as encountered in those diagnosed with dry eye, and with narrower palpebral apertures as in the case of Asian subjects. This is achieved by incorporating in the instrument's own topography estimation algorithm an image processing technique that comprises of linear adaptive filter (based on Wiener filtering theory) and non-linear filter (based on morphological operations). The experimental results from measurements of test surfaces and real corneas show that the incorporation of the proposed technique results in better estimates of corneal topography and, in many cases, to a significant increase in the estimated coverage area making such an enhanced videokeratoscope a better tool for clinicians. On the other hand, corneal height-data are typically modeled using a set of orthogonal Zernike polynomials. We address the estimation of the number of Zernike polynomials, which is formalized as a model-order selection problem in linear regression. Classical information theoretic criteria tend to overestimate the corneal surface due to the weakness of their penalty functions, while bootstrap-based techniques tend to underestimate the surface or require extensive processing. We propose to use the Efficient Detection Criterion (EDC), which has the same general form of information theoretic-based criteria, as an alternative to estimating the optimal number of Zernike polynomials. We first show, via simulations, that the EDC outperforms a large number of information theoretic criteria and resampling-based techniques. We then illustrate that using the EDC for real corneas results in models that are in closer agreement with clinical expectations and provides means for distinguishing normal corneal surfaces from astigmatic and keratoconic surfaces. The two problems are interrelated in the sense that appropriate modeling for corneal surfaces, regardless of the used functions, requires accurate corneal topography that can be efficiently estimated provided that the videokeratoscopic image is not degraded