Comparison of nonparametric methods for static visual field interpolation

Visual field testing with standard automated perimetry produces a sparse representation of a sensitivity map, sometimes called the hill of vision (HOV), for the retina. Interpolation or resampling of these data is important for visual display, clinical interpretation, and quantitative analysis. Our objective was to compare several popular interpolation methods in terms of their utility to visual field testing. We evaluated nine nonparametric scattered data interpolation algorithms and compared their performances in normal subjects and patients with retinal degeneration. Interpolator performance was assessed by leave-one-out cross-validation accuracy and high-density interpolated HOV surface smoothness. Radial basis function (RBF) interpolation with a linear kernel yielded the best accuracy, with an overall mean absolute error (MAE) of 2.01 dB and root-mean-square error (RMSE) of 3.20 dB that were significantly better than all other methods (p ≤ 0.003). Thin-plate spline RBF interpolation yielded the best smoothness results (p < 0.001) and scored well for accuracy with overall MAE and RMSE values of 2.08 and 3.28 dB, respectively. Natural neighbor interpolation, which may be a more readily accessible method to some practitioners, also performed well. While no interpolator will be universally optimal, these interpolators are good choices among nonparametric methods.