A Two-zone Mathematical Model of Normal Foveal Reflectance in Fundus Photographs

Abstract

Abstract: : Purpose: To develop a mathematical model describing the reflectance pattern of the normal fovea in fundus photographs. Methods: Digitized unfiltered data from the green channel of 5 normal fundus photographs, scanned at 1350 pixels per inch, were represented by their (x, y) pixel coordinates in the horizontal plane and their gray scale intensity values z(x, y). A general elliptic quadratic polynomial q(x, y) = ax² + bxy +cy² +dx + ey + constant in two variables was fit by custom software using least squares methods to the data set z(x, y) of the intensity values. Two concentric foveal zones (central 500 micron disc and paracentral 1500 micron annulus) were identified on the original image, and quadratics q1 and q2 were fit to each region separately. The results were compared to one and three-zone models. To determine the accuracy of each fit, the mean and standard deviation of the absolute errors at each pixel were calculated and scaled to the net intensity range as a percentage. To further validate the mathematical model, its ability to reconstruct the entire foveal background from sparse clusters of pixel values (3% of the entire data set on average) was tested. Results: For the two-zone elliptic model, the mean absolute errors and standard deviations per image ranged from 5.4 +/- 4.2% to 7.2 +/- 6.2%; the mean of these mean errors was 6.1%. The mean of the mean absolute errors for the five single zone models was 7.8% and for the three-zone models 5.1%. The mean absolute errors of the five images reconstructed from sparse pixel values using the 2-zone model ranged from 6.2 +/- 4.6% to 8.7 +/- 5.7% (mean of mean errors 7.2%). Conclusions: The two-zone elliptic quadratic polynomial model can accurately represent foveal reflectance intensities, which are an indirect measure for the density of pigmentation and its geometric distribution. Use of three zones provides further incremental accuracy. The ability of the model to reconstruct the foveal background from a small subset of data points may serve as the basis for improved macular image analysis.

Keywords: macula/fovea • imaging/image analysis: non-clinical • optical properties