Fully automatic evaluation of the corneal endothelium from in vivo confocal microscopy

Abstract

Background: Manual and semi-automatic analyses of images, acquired in vivo by confocal microscopy, are often used to determine the quality of corneal endothelium in the human eye. These procedures are highly time consuming. Here, we present two fully automatic methods to analyze and quantify corneal endothelium imaged by in vivo white light slit-scanning confocal microscopy.

Methods: In the first approach, endothelial cell density is estimated with the help of spatial frequency analysis. We evaluate published methods, and propose a new, parameter-free method. In the second approach, based on the stochastic watershed, cells are automatically segmented and the result is used to estimate cell density, polymegathism (cell size variability) and pleomorphism (cell shape variation). We show how to determine optimal values for the three parameters of this algorithm, and compare its results to a semi-automatic delineation by a trained observer.

Results: The frequency analysis method proposed here is more precise than any published method. The segmentation method outperforms the fully automatic method in the NAVIS software (Nidek Technologies Srl, Padova, Italy), which significantly overestimates the number of cells for cell densities below approximately 1200 mm(-2), as well as previously published methods.

Conclusions: The methods presented here provide a significant improvement over the state of the art, and make in vivo, automated assessment of corneal endothelium more accessible. The segmentation method proposed paves the way to many possible new morphometric parameters, which can quickly and precisely be determined from the segmented image.

Figure 1

Different endothelial cell count methods performed with NAVIS software on the same confocal image of corneal endothelium after keratoplasty.(a) Region of interest. Scale bar = 100 μm. (b) Automatic cell count. Endothelial cell density: 2213 mm ⁻²; Polymegathism: 79.0%; Pleomorphism: 33.3%. User interaction time: ≤1 min. (c) Polygonal area selection with manual cell count. Endothelial cell density: 687 mm ⁻²; Polymegathism: could not be determined; Pleomorphism: could not be determined. User interaction time: 4 min. (d) Manual selection of individual cell borders with manual cell count. Endothelial cell density: 669 mm ⁻²; Polymegathism: 21.5%; Pleomorphism: 52.4%. User interaction time: 20 min.

Figure 2

Enhancement of the central ring.(a) Magnitude of the frequency spectrum $\left|\mathcal{F}\right|$ for a typical image; only the central part is shown. (b) The image ${\mathcal{F}}^{\prime }$; the central peak has been removed, which enhances the ring. (c) Radial mean projections for $\left|\mathcal{F}\right|$ (top) and ${\mathcal{F}}^{\prime }$ (bottom); note that the peak corresponding to the characteristic frequency is much more salient in the bottom graph. The vertical scaling in the two graphs is not the same.

Figure 3

Relation between cell shape, characteristic frequency, and cell density. Synthetic, band-limited images (350×350 pixels) of (a) square and (c) hexagonal cell pattern with 25 pixel side-to-side length for each cell. (b, d) Magnitude of the central region of the respective frequency spectra. Characteristic frequencies are $\frac{14}{350}=\frac{1}{25}{\mathit{\text{px}}}^{-1}$ and $\frac{16}{350}\approx \frac{2}{\sqrt{3}}\frac{1}{25}{\mathit{\text{px}}}^{-1}$, respectively.

Figure 4

Schematic representation of the segmentation procedure, as detailed in the “Methods” section.

Figure 5

Relative error in estimated cell density for the various frequency analysis methods, as standard box plots. The box indicates the interquartile range, the line inside the box indicates the median, the whiskers indicate the extrema, and the dots indicate outliers.

Figure 6

Mean F-measure for all images in the data set, with u=30 and different values of k _σ and k _h. Black indicates F≤0.8, white is for F=0.9142, and occurs at k _σ=0.17 and k _h=0.002 (marked by the red circle); this is the global maximum. This same combination of parameters were found to be optimal in each of the cases during leave-one-out cross validation.

Figure 7

Example results of the fully automatic segmentation algorithm.(a) The image used in Figure 1, and (b) the segmentation result. This is an endothelium with a low cell density, for which the NAVIS automatic method failed (compare with Figure 1b and d). The result of the proposed method produced a reasonable result, with only two cells too many (white arrows) and a few misplaced cell boundaries (black arrows). (c) One of the images for which the segmentation (d) had a perfect score. (e) A typical high-density endothelium, for which the segmentation (f) only had two oversegmented cells. Scale bars = 50 μm.

Figure 8

Cell density. Estimated cell density (left) and error in estimated cell density (right), compared with the manual ground truth, for the segmentation method proposed here (×) and the NAVIS software in fully automatic mode (·). Note that the NAVIS software has an error that depends on the cell density. To the right, standard box plots summarize the results. The error of the modeRMrec method is included for comparison.

Figure 9

Polymegathism. Estimated polymegathism (left) and error in estimated polymegathism (right), compared with the manual ground truth, for the segmentation method proposed here (×) and the NAVIS software in fully automatic mode (·). To the right, standard box plots summarize the results.

Figure 10

Pleomorphism. Estimated pleomorphism (left) and error in estimated pleomorphism (right), compared with the manual ground truth, for the segmentation method proposed here (×) and the NAVIS software in fully automatic mode (·). To the right, standard box plots summarize the results.

Figure 11

Example image where the cell pattern has a strong directional preference (panel a). The ring in the frequency spectrum (panel b) is elliptic. Scale bar = 50 μm.

Figure 12

The only image in data set where the reconstruction by dilation step in modeRMrec fails (panel a). In (panel b), magnitude of the corresponding frequency spectrum. Scale bar = 50 μm.