Eigencorneas: application of principal component analysis to corneal topography

Area of Science:

• Ophthalmology and Vision Science
• Biomedical Engineering
• Computational Biology

Background:

• Corneal topography provides detailed surface maps crucial for diagnosing and managing eye conditions.
• High-dimensional corneal data presents challenges for analysis and clinical application.
• Dimensionality reduction techniques are needed to simplify complex topographical datasets.

Purpose of the Study:

• To ascertain the minimal number of orthonormal basis functions required for accurate representation of typical corneal topographies.
• To establish a reduced, yet comprehensive, set of parameters for describing normal corneal shape.

Main Methods:

• Principal Component Analysis (PCA) was applied to corneal elevation data (anterior, posterior surfaces, and central thickness) from 184 healthy subjects.
• PCA was performed on both raw elevation data and Zernike polynomial-fitted data (up to 8th order).
• Analysis included separate and joint examination of corneal surfaces and individual eyes, aiming for 99% variance explanation.

Main Results:

• Eigenvectors from direct elevation data analysis resembled Zernike polynomials.
• Separate PCA of anterior and posterior surfaces yielded 5 and 9 degrees of freedom (DoF), respectively.
• Joint analysis of surfaces and central thickness reduced DoF to 11; pooling right and left eyes further reduced it to 18 DoF.

Conclusions:

• Combining Zernike fitting with PCA effectively reduces corneal topography data dimensionality to 19 independent parameters (18 DoF + average).
• This reduction highlights significant correlations between corneal surfaces and between eyes.
• The derived 'eigencorneas' are uncorrelated, orthonormal combinations of Zernike polynomials, suitable for practical applications.