Eigencorneas: application of principal component analysis to corneal topography. (14th September 2014)

• Record Type: Journal Article
• Authors: Rodríguez, Pablo; Navarro, Rafael; Rozema, Jos J.
• Is Part Of: Ophthalmic and physiological optics. Volume 34:Number 6(2014:Nov.)
• Page Start: 667
• Page End: 677
• Publication Date: 2014-09-14
• Subjects: Ophthalmology -- Periodicals; Physiological optics -- Periodicals; Optometry -- Periodicals; Optics -- Periodicals; Vision -- Periodicals; 617.75
• DOI: 10.1111/opo.12155
• Languages: English
• ISSNs: 0275-5408

Abstract

<abstract abstract-type="main" id="opo12155-abs-0001"> <title>Abstract</title> <sec id="opo12155-sec-0001" sec-type="section"> <title>Purpose</title> <p>To determine the minimum number of orthonormal basis functions needed to accurately represent the great majority of corneal topographies from a normal population.</p> </sec> <sec id="opo12155-sec-0002" sec-type="section"> <title>Methods</title> <p>Principal Component Analysis was applied to the elevation topographies of the anterior and posterior corneal surfaces and central thickness of 368 eyes of 184 healthy subjects. PCA was applied directly to the input elevation data points and after fitting them to Zernike polynomials (up to 8th order, 8 mm diameter). The anterior and posterior surfaces, as well as right eye and left eye data, were analysed both separately and jointly. A threshold based on the amount of explained variance (99%) was applied to determine the minimum number of basis functions (eigencorneas) or degrees of freedom (DoF) in the population.</p> </sec> <sec id="opo12155-sec-0003" sec-type="section"> <title>Results</title> <p>The eigenvectors directly obtained from elevation data resemble Zernike polynomials. The separate principal component analysis on the Zernike coefficients of anterior and posterior surfaces yielded 5 and 9 DoF, respectively. An additional reduction to 11 DoF (instead of 15 DoF) was achieved when performing a joint PCA that included both surfaces as well as central thickness. Finally, a further reduction was obtained by pooling right and left eye data together, to only 18 DoF.</p> </sec> <sec id="opo12155-sec-0004" sec-type="section"> <title>Conclusions</title> <p>The combination of Zernike fit and Principal Component Analysis yields a strong reduction of dimensionality of elevation topography data, to only 19 independent parameters (18 DoF plus population average), which indicates a high degree of correlation existing between anterior and posterior surfaces, and between eyes. The resulting eigencorneas are especially well suited for practical applications, as they are uncorrelated and orthonormal linear combinations of Zernike polynomials.</p> </sec> </abstract>