Local fitted curves.

<div><p>Bleaching curves computed from fitted parameters averaged over several small spatial regions. The blue curve is the fitting for the intensity vector averaged over the annulus-like area between two blue ovals shown in (a). Green, black, and purple curves show similar bleaching kinetics. The yellow curve corresponds to the region close to the fovea where not much rhodopsin is expected and the fit becomes a steady line. Blood vessels do not exhibit the bleaching model although the fit (red) still shows some bleaching behavior. Nevertheless, the intensity values appear far off.</p> <p>(a) regions marked on the first image of the stack</p> <p>(b) respective fitted bleaching curves computed using the vectors of the averaged intensities.</p></div

Bleaching curve and its fit (II).

<div><p>The fit near the fovea does not show the typical bleaching behavior because there are almost no rods present. Instead, the minimization procedure leads to a linear fit. By averaging an 8 by 8 pixel region outside the fovea, we derive a typical bleaching curve with a good fit. All further computations are computed using this 64 pixel averaging to effectively suppress the noise in the cSLO measurements.</p> <p>(a) non-averaged image stack, curve chosen near the fovea, parameters</p> <p>(b) averaged over square neighborhoods (8 × 8 pixels).</p></div

Histogram of computed parameter <i>b</i>.

<p>We optimized all 3 parameters <i>p</i>, <i>b</i>, and <i>c</i> at the same time and plotted a representative histogram of parameter <i>b</i>. The counts cluster tightly around the mean, enabling us to assign the highest count to <i>b</i>₀, keep it fixed throughout the image and only optimize over the remaining two parameters <i>p</i> and <i>c</i>.</p

Rod rhodopsin measurement (I) and Blood vessel detection.

<div><p>We determined <i>b</i> ≈ 0.04 through the largest count in the histogram, which corresponds to the fit associated to an average of a large annulus area. The gradient descent minimization scheme led to the optimized parameters </p><p></p><p></p><p></p><p><mi>a</mi><mo>^</mo></p><p></p><p></p><p></p> and <p></p><p></p><p></p><p><mi>c</mi><mo>^</mo></p><p></p><p></p><p></p>, where the macular pigment distribution was used to refine the initial value <i>a</i>₀. Blood vessels show up as artifacts in the resulting rhodopsin maps and must still be removed.<p></p> <p>We detect blood vessels through a scheme that evolves from the computational minimization of <i>E</i> related to the rhodopsin model. Spatial regions where the numerical algorithm converges significantly slower than in other image parts shall be identified as blood vessels. The number of required iterations leads to an image which can simply be thresholded to identify retinal blood vessels.</p> <p>(a) spatial map of parameter </p><p></p><p></p><p></p><p><mi>c</mi><mo>^</mo></p><p></p><p></p><p></p> optimal within the model. Brighter means increase in rhodopsin density, but brightest spots occur as registration artifacts along blood vessels. Therefore, the grayscale colormap is suppressed.<p></p> <p>(b) extracted mask of blood vessels derived from thresholding the number of iterations needed for convergence in the optimization scheme. Simple pixel growth in the mask would lead to complete coverage of the vessels.</p></div

Biomedical and mathematical abbreviations and terms.

<p>Biomedical and mathematical abbreviations and terms.</p

Macular pigment measurement.

<div><p>Two bands of a multi-spectral autofluorescence image set are shown and a representative macular pigment map derived from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.e022" target="_blank">formula (5)</a>, where we optimized the map over several choices of weights to maximize self-consistency of the measurement. The macular pigment is concentrated in the macula and rapidly decays with distance to the center of the fovea. Although vessels and optic disc can still be recognized visually, the pixel magnitudes are so small that their contribution in the further steps is negligible.</p> <p>(a) blue excitation</p> <p>(b) yellow excitation</p> <p>(c) spatial map of MP density</p> <p>(d) horizontal and vertical MP profiles, averaged over small stripes.</p></div

Rod rhodopsin measurement (II).

<div><p>To derive the final rhodopsin map, we first detect the blood vessels. Instead of a binary vessel mask, we use a gradual interface at vessel borders resulting in a smooth vessel mask as proposed in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.e063" target="_blank">Eq (22)</a>. Inpainting based on <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.e060" target="_blank">Eq (21)</a> was used to remove the retinal blood vessels from the final rhodopsin map leading to a smooth rod rhodopsin map. We show the computed parameter <i>γ</i>, which is the sum of emission and excitation rhodopsin absorbance. Since the emission rhodopsin absorbance (590<i>nm</i>-600<i>nm</i>) is neglible, <i>γ</i> indeed is the rhodopsin absorbance at 488<i>nm</i>. The center of the fovea lacks rhodopsin whose density increases when moving apart from the center. Consistently with the rod distribution described in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.ref008" target="_blank">8</a>], rod rhodopsin increases most rapidly along the superior vertical meridian and increases least rapidly along the nasal horizontal meridian. Although we do not see a connected hot spot of highest rod rhodopsin density, we observe larger and more connected areas of highest rhodopsin density in the superior retina than in the inferior retina, again, consistent with the rod distribution in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.ref008" target="_blank">8</a>].</p> <p>(a) cropped rhodopsin map from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0131881#pone.0131881.g006" target="_blank">Fig 6a</a> to be inpainted</p> <p>(b) smooth mask <i>χ</i> used in the spatial consistency forcing term</p> <p>(c) the final output showing the distribution of the rhodopsin optical density <i>γ</i>, i.e., the rhodopsin absorbance at 488<i>nm</i>. Units are suppressed to indicate that we compute its distribution rather than absolute quantitative optical densities as we are not able to validate overall amplitudes due to background in our image sets.</p> <p>(d) horizontal and vertical rhodopsin profiles, averaged over small stripes.</p></div

A novel iris transillumination grading scale allowing flexible assessment with quantitative image analysis and visual matching

<p><b>Purpose:</b> To develop a sensitive scale of iris transillumination suitable for clinical and research use, with the capability of either quantitative analysis or visual matching of images.</p> <p><b>Methods:</b> Iris transillumination photographic images were used from 70 study subjects with ocular or oculocutaneous albinism. Subjects represented a broad range of ocular pigmentation. A subset of images was subjected to image analysis and ranking by both expert and nonexpert reviewers. Quantitative ordering of images was compared with ordering by visual inspection. Images were binned to establish an 8-point scale. Ranking consistency was evaluated using the Kendall rank correlation coefficient (Kendall’s tau). Visual ranking results were assessed using Kendall’s coefficient of concordance (Kendall’s <i>W</i>) analysis.</p> <p><b>Results:</b> There was a high degree of correlation among the image analysis, expert-based and non-expert-based image rankings. Pairwise comparisons of the quantitative ranking with each reviewer generated an average Kendall’s tau of 0.83 ± 0.04 (<i>SD</i>). Inter-rater correlation was also high with Kendall’s <i>W</i> of 0.96, 0.95, and 0.95 for nonexpert, expert, and all reviewers, respectively.</p> <p><b>Conclusions:</b> The current standard for assessing iris transillumination is expert assessment of clinical exam findings. We adapted an image-analysis technique to generate quantitative transillumination values. Quantitative ranking was shown to be highly similar to a ranking produced by both expert and nonexpert reviewers. This finding suggests that the image characteristics used to quantify iris transillumination do not require expert interpretation. Inter-rater rankings were also highly similar, suggesting that varied methods of transillumination ranking are robust in terms of producing reproducible results.</p