Rodríguez Pablo, Navarro Rafael, Rozema Jos J
ICMA, Consejo Superior de Investigaciones Científicas-Universidad de Zaragoza, Facultad de Ciencias, Zaragoza, Spain.
Ophthalmic Physiol Opt. 2014 Nov;34(6):667-77. doi: 10.1111/opo.12155. Epub 2014 Sep 14.
To determine the minimum number of orthonormal basis functions needed to accurately represent the great majority of corneal topographies from a normal population.
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.
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.
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.
确定准确表示正常人群中绝大多数角膜地形图所需的正交基函数的最小数量。
对184名健康受试者的368只眼睛的角膜前、后表面高度地形图和中央厚度进行主成分分析。主成分分析直接应用于输入的高度数据点，并在将它们拟合到泽尼克多项式（最高8阶，直径8毫米）之后进行。分别对前、后表面以及右眼和左眼数据进行单独和联合分析。应用基于解释方差量（99%）的阈值来确定人群中基函数（特征角膜）或自由度（DoF）的最小数量。
直接从高度数据获得的特征向量类似于泽尼克多项式。对前、后表面的泽尼克系数进行单独主成分分析分别得到5个和9个自由度。在进行包括两个表面以及中央厚度的联合主成分分析时，自由度进一步减少到11个（而不是15个）。最后，通过将右眼和左眼数据合并在一起，自由度进一步减少到仅18个。
泽尼克拟合和主成分分析的结合使高度地形图数据的维度大幅降低，仅为19个独立参数（18个自由度加总体平均值），这表明前、后表面之间以及两眼之间存在高度相关性。所得的特征角膜特别适合实际应用，因为它们是泽尼克多项式的不相关且正交的线性组合。
