Fig 1.
FAZ identification and choriocapillaris binarization.
Fig 1.A shows an example of normal superficial vascular layer of the retina. The FAZ is highlighted in blue. Fig 1.B shows the original choriocapillaris of the same subject (on the left) with the central 100 x 100 pixel area considered for the estimation of the parameters of the Ising model highlighted by a red square; the same area highlighted on the thresholded version of the same image to create a binary image for density calculation. Notice the projection artifacts from superficial vessels on the right side of the image and how they are excluded by considering the central part of the image.
Fig 2.
Choriocapillaris density estimation at increasing ROI radius.
Fig 2.A-C shows density estimates of three exemplar choriocapillaris images. Scattered points indicate the random density measures taken on the binarized image of the choriocapillaris with circular ROIs with different radii randomly extracted from a uniform distribution interval [10, 1000] μm with 10 μm spacing and random displacement from the FAZ center (independently sampled from a bivariate isotropic normal distribution with zero mean and σ = 10 pixel (100 μm) to simulate small errors in the manual placement of the measuring circular area). Mean and Mean ± STD were calculated at each radius length an overlaid on the scattered points (blue lines and red lines respectively). Notice how the variability of the measure decreases between 400 and 600 μm radius length.
Table 1.
Descriptive statistics of important variables.
Table 2.
Correlation of different quantities tested.
Fig 3.
Effect of threshold selection on Standard Density estimates.
The figure shows how density estimates in a circular area with a radius of 450 μm (Standard Density) change when using different threshold values to obtain binary images from decorrelation agiograms of the choriocapillaris. The threshold has been increased at 0.1 steps and applied to all images each time to calculate the density. The blue line represents the mean density value at each threshold value, the red dots represent the value calculated for each image and the pink arrow point highlights the threshold value used in this study. Note how the selected value is centered on the sigmoid shaped curve of mean densities, allowing a wide range of possible values.
Fig 4.
Block diagram of the image processing steps for the Ising model.
The block diagram shows the preprocessing steps used to obtain the final binary image used to calculate the parameters of the Ising model. In the first step we identified the FAZ on the superficial layer; then we thresholded the choriocapillaris image as described in the Method section (fixed threshold after adaptive histogram equalization); finally, we selected the central 100 x 100 pixel area centered on the FAZ from the thresholded and used that to estimate the β and γ parameters.
Fig 5.
Correlation of the Ising model parameters.
Fig 5-A shows a plot of the negative correlation of the two parameters of the Ising model (p<0.01). Fig 5-B shows a plot of the choriocapillaris density of the γ parameter of the Ising model (p<0.01).
Fig 6.
Effect of threshold selection on Ising model parameters and square density.
The figure shows how parameter estimates from the Ising model change when using different threshold values to obtain binary images from decorrelation agiograms of the choriocapillaris. The threshold has been increased at 0.1 steps and applied to all images each time to calculate the density. In each plot, the blue line represents the mean of the parameter estimates at each threshold value, the red dots represent the value calculated for each image and the pink arrow point highlights the threshold value used in this study. The plot on the far left shows how the density estimate on the square area used for the Ising model calculations changes with different threshold values. As for the plot in Fig 3 the selected threshold is centered on the sigmoid shaped curve of the mean density values. The middle and rightmost plots show how parameter estimates from the Ising model change when using different threshold values. The selected threshold is in the center of the interval where stable measures are obtained. Note how the parameter estimates become unstable with extreme threshold values.
Fig 7.
Simulation from the Ising model of different choriocapillaris textures.
Fig 7.A-D shows simulation from the Ising model using a Metropolis–Hastings sampler. On the left, the original image from a healthy subject, on the center the simulation from the Ising model trained on the original texture. On the far right, a graph showing how the Hamiltonian of the system decreases as the simulation goes on (sampled every 1000 iterations). Estimated coefficients for the Ising model are reported on the top of each original image, the white pixel density (denoted as D) is reported below each respective choriocapillaris image, both original and simulated.