June 2015
Volume 56, Issue 7
ARVO Annual Meeting Abstract  |   June 2015
Comparison of interpolation algorithms for static visual field data
Author Affiliations & Notes
  • Travis Smith
    Ophthalmology, Oregon Health & Science University, Portland, OR
  • Ning Smith
    Center for Health Research, Kaiser Permanente, Portland, OR
  • Richard G Weleber
    Ophthalmology, Oregon Health & Science University, Portland, OR
  • Footnotes
    Commercial Relationships Travis Smith, Foundation Fighting Blindness (F), Hear See Hope (F); Ning Smith, None; Richard Weleber, AGTC SAB (S), Foundation Fighting Blindness ESAB (F), U.S. patent no. 8657446, Method and apparatus for visual field monitoring, also known as Visual Field Modeling and Analysis (P)
  • Footnotes
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Investigative Ophthalmology & Visual Science June 2015, Vol.56, 3907. doi:
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      Travis Smith, Ning Smith, Richard G Weleber; Comparison of interpolation algorithms for static visual field data. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):3907.

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      © ARVO (1962-2015); The Authors (2016-present)

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Static perimetry generates 3-D data (x-y test location and z sensitivity value) representing the visual field (VF), sometimes called the hill of vision (HOV), which is often sparsely sampled. Data interpolation produces a finer HOV representation to aid interpretation, visual display, and quantitative analysis. The goal of this study is to compare the accuracy of several scattered data interpolation algorithms and identify the optimal one for VF data.


Full-field VF data was analyzed from 129 exams of 10 normal subjects and 10 retinitis pigmentosa (RP) patients that passed quality assessment. Data was acquired with the Octopus 900 with 164 radially oriented, centrally condensed test points using GATEi, target size V, and a 10 cd/m2 background. Repeated exams for each subject were included if obtained within 90 days of the first. Interpolation accuracy was assessed by the root mean square error (RMSE) and mean absolute error (MAE) from leave-one-out cross-validation (LOOCV) after blind spot removal. In LOOCV, each location’s z-value is interpolated from the other 163 points and compared with a target value to produce an error residual; this is repeated for all locations in each exam. Two types of target values were considered: the median z-value at each location across all exams for that eye (Target 1), and the measured z-value itself (Target 2). LOOCV was performed with the 8 nonparametric interpolation methods in the top row of Table 1. Significance was assessed by one-sided paired t-tests with Bonferroni correction.


Table 1 summarizes the interpolator performances. Linear radial basis function (RBF) interpolation had the smallest mean RMSE and MAE compared to all other methods for both target types, significant (p<0.006) in each case except those identified by * in Table 1. Linear RBF performance was significantly better in RP patients than in normals in all scenarios.


Interpolation of static VF data was most accurate with a linear RBF kernel. Accuracy improved in subjects with visual field loss, likely due to higher spatial correlation in the data. Future work will assess parametric and regularized methods to mitigate overfitting, incorporate a larger number of exams, and analyze the influence of perimetric test grid density and target size on interpolation accuracy.  

Mean RMSE and mean MAE values (both in dB) across all exams for each interpolator analyzed, as assessed by LOOCV.
Mean RMSE and mean MAE values (both in dB) across all exams for each interpolator analyzed, as assessed by LOOCV.


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