Several probabilistic models have been applied for speckle modeling in OCT images. In the recent study, the generalized gamma distribution, among several other models considered, has been shown to optimally fit the human corneal OCT speckle.
17 In this study, the statistics of rabbit corneal speckle were investigated by fitting probability distribution functions to the pixel intensities of the transformed and normalized earlier B-scans in each of the three selected ROIs and each considered IOP level. Specifically Rayleigh, Gamma, Weibull, Nakagami, and Generalized Gamma distributions were considered as they were found to effectively model both ultrasound examination and OCT speckle.
17,22–27 In a preliminary step, the goodness-of-fit (GoF) of each model was estimated by calculating the mean squared error between the fitted probability density function and the kernel density estimator.
Figure 2 shows that GOF for the three considered ROIs and the seven levels of IOP for untreated and treated eyes, whereas in
Figure 3, illustrative histograms of corneal speckle for pROI of a crosslinked eyes are shown against the five estimated probability density functions for the lowest and highest considered levels of IOP (i.e., 15 mm Hg and 45 mm Hg). Because the generalized gamma distribution showed the best overall average GOF among the five considered distributions and it was also statistically significantly different from the other considered models (Wilcoxon test, all pairs
P < 0.001; see
Fig. 4), it was used as the statistical model of the corneal OCT speckle in further analyses. The probability density function of generalized gamma distribution is given by:
\begin{eqnarray*}f\left( {x;a,v,p} \right) = \frac{{\left| p \right|}}{{{\rm{\Gamma }}\left( v \right){a^{pv}}}}{x^{pv - 1}}\exp {\rm{\;}}\left\{ {{{\left( { - \frac{x}{a}} \right)}^p}} \right\},\end{eqnarray*}
where
a is the scale parameter (in units of normalized amplitude),
v and
p ≠ 0 (both in arbitrary units) are the shape parameters,
x ≥ 0 is the pixel intensity, and Γ is the conventional gamma function.
28 The scale parameter has been proposed to indicate the average backscattered power, whereas the ratio of the shape parameters (
v/
p) to indicate scatter density.
27