Results with the validation set

Although the validation set (40 images) was generated randomly from images from the development set, we ensured that it included 20 normal LASER IVCM images and 20 abnormal LASER IVCM images. The proposed cell segmentation network achieved an AUC of 0.9436, sensitivity of 0.6483 and specificity of 0.9504. The average relative errors of the number of cells, ECD, CV and HEX between the automated values and manual values were 16.46%, 13.14%, 17.99% and 29.68%, respectively. When analyzing the normal and abnormal LASER IVCM images separately, we found that based on manual calculation, the average number of cells for the 20 normal images and 20 abnormal images in the validation set was 139 cells and 37 cells, respectively, and the average ECDs were 2602 cells/mm2 and 821 cells/mm2, respectively. The average relative errors of the number of cells, ECD, CV and HEX for the 20 normal images were 16.44%, 6.92%, 13.93% and 13.48%, respectively, while the corresponding values for the 20 abnormal images were 16.48%, 19.36%, 22.04% and 45.88%, respectively. The above results show that (1) the abnormal images had a much lower number of cells and lower cell density than the normal images, indicating that the abnormal corneal endothelial condition in our study was very severe; (2) it was more challenging to accurately estimate the morphometric parameters for the abnormal images; and (3) when the segmentation results were inconsistent with the manual labels, the estimations were more easily affected for images with a lower number of cells, especially the estimations of HEX.

Results with the two testing sets

For all images in the normal and abnormal CEC testing sets, only the manually calculated ECDs were available for comparison. The Pearson’s correlation coefficient between the automatically and manually calculated ECD was 0.8470 for the normal CEC testing set ( = 225.837 + 0.892, P = 0.055 > 0.05) and 0.9447 for the abnormal CEC testing set ( = 104.991 + 1.014, P = 0.000 < 0.05). The 95% limits of agreement between the manually and automatically calculated ECD were between 329.0 and − 579.5 (concordance correlation coefficient = 0.93, Fig. 4) for the abnormal CEC testing set using the proposed system. Examples of abnormal CEC images from patients with different severities are presented in Fig. 5.

Fig. 4

Bland-Altman plot comparing the manually and automatically calculated ECDs for the abnormal CEC testing set using the proposed system. CEC, corneal endothelial cell; ECD, endothelial cell density

Fig. 5

Seven examples of abnormal CEC images from patients with different severities were recognized by the proposed system. The cells in red indicate abnormally segmented cells that were excluded from the calculations. a ECD under 500 cells/mm2; b to e ECD under 1000 cells/mm2; f ECD under 1500 cells/mm2; g ECD under 2000 cells/mm2. The automated estimations are shown below. CEC, corneal endothelial cell; ECD, endothelial cell density; CV, coefficient of variation in cell area; HEX, percentage of hexagonal cells

The inclusion of abnormal LASER IVCM images in the development set will be very helpful for expanding the application scope of our system in clinical trials, where such abnormal cases more urgently require an accurate diagnosis. To demonstrate this point, we also evaluated system_normal on the two testing sets for comparison. The Pearson’s correlation coefficient between the ECD calculated by system_normal and the manually calculated ECD was 0.8491 for the normal CEC testing set ( = 212.203 + 0.898, P = 0.07 > 0.05) and 0.9220 for the abnormal CEC testing set ( = 4.636 + 1.047, P = 0.925 > 0.05). The 95% limits of agreement between the manually and automatically calculated ECDs were between 614.6 and − 463.1 (concordance correlation coefficient = 0.91) for the abnormal CEC testing set. Comparing the above results of system_normal with those of the proposed system in this study, we can see that the proposed system (1) yields a substantial 0.0227 improvement in the correlation between the ECDs for abnormal images but a slight 0.0021 reduction in the correlation between the ECDs for normal images; (2) yields a 0.02 improvement in the concordance correlation coefficient between the ECDs for abnormal images; and (3) is more effective in estimating cell density for both normal and abnormal images.

Using the proposed system, the average relative error between the automatically and manually calculated ECDs was 0.0957 for the normal CEC testing set and 0.1245 for the abnormal CEC testing set; in comparison, the average relative error between the ECD calculated from system_normal and the manually calculated ECD was 0.0966 for the normal CEC testing set and 0.1522 for the abnormal CEC testing set. This also shows the effectiveness of the proposed system in estimating cell density in LASER IVCM images with widely varying ECDs. In each image, the relative error tended to decrease as the ECD increased (Fig. 6).

Fig. 6

Relative error of the estimates of ECD using the proposed system (colored circle) and system_normal (gray triangle) for the normal and abnormal CEC testing sets. a Relative error of the ECD using the two systems for the normal CEC testing set (the average relative errors were almost the same); b relative error of the ECD using the two systems for the abnormal CEC testing set. The dotted lines indicate the average relative errors. CEC, corneal endothelial cell; ECD, endothelial cell density

To further contrast the two systems, the ECDs estimated by the proposed system and system_normal for the abnormal testing set were compared using the paired-samples t test, which revealed a significant difference between the two systems (t = − 4.709, P = 0.000 < 0.001, Fig. 7a). When the manually calculated ECD was under 999 and 1000–1499 cells/mm2, there was a significant difference between the two systems (t = − 4.407, P = 0.000 < 0.001, Fig. 7b; t = − 3.266, P = 0.002 < 0.01, Fig. 7c). When the manually calculated ECD was higher than 1500 cells/mm2, there was no significant difference between the two systems (t = − 0.462, P = 0.646 > 0.05, Fig. 7d; t = − 1.140, P = 0.261 > 0.05, Fig. 7e; t = 1.890, P = 0.091 > 0.05, Fig. 7f). In Fig. 8, six examples of abnormal images were recognized by the proposed system and system_normal. As we can see, the proposed system obviously recognized more cells and had more accurate segmentation results than system_normal, further indicating the superiority of the proposed system.

Fig. 7

Results of the paired-samples t test using the two systems with the abnormal testing set (****P < 0.001, **P < 0.01, ns = not significant). a Manually calculated ECD from 0–4000 cells/mm2. b Manually calculated ECD from 0–999 cells/mm2. c Manually calculated ECD from 1000–1499 cells/mm2. d The manually calculated ECD from 1500–1999 cells/mm2. e Manually calculated ECD from 2000–2999 cells/mm2. f Manually calculated ECD from 3000–4000 cells/mm2. ECD, endothelial cell density

Fig. 8

Six examples of abnormal images (first row) recognized by the proposed system (second row) and system_normal (third row). a to f were abnormal images; a to d ECD under 1000 cells/mm2; e, f ECD under 2000 cells/mm2. The cells in red indicate abnormally segmented cells that were excluded from the calculations. The automated estimations are indicated below the corresponding images (estimations by system_normal are given in parenthesis). CEC, corneal endothelial cell; ECD, endothelial cell density; HEX, percentage of hexagonal cells

The average ECD variability using the proposed system for 1974 images [12] for 169 eyes in the normal CEC testing set was 0.0387; for the abnormal CEC testing set, we also sampled several LASER IVCM images taken from different locations for each eye to collect a total of 750 images for the 119 eyes (including the original 211 images). The average ECD variability was 0.0962.

Using the proposed system, the automatedly estimated morphometric parameters were 257 cells, 2648 ± 511 cells/mm2, 32.18 ± 6.70% and 56.23 ± 8.69% for the average number of cells, ECD, CV, and HEX, respectively, for the normal CEC testing set and 83 cells, 1450 ± 656 cells/mm2, 34.87 ± 10.53% and 42.55 ± 20.64% for the average number of cells, ECD, CV, and HEX, respectively, for the abnormal CEC testing set. As the number of detected cells in the images increased, the ECD from the proposed system increased linearly (Fig. 9a), the proposed CV decreased then approached values between 20% and 40% (Fig. 9b), while the proposed HEX varied considerably at the beginning and approached approximately 50% (Fig. 9c).

Fig. 9

Estimations of ECD, CV and HEX using the proposed system for abnormal (colored circle) and normal (gray square) CEC testing sets, displayed as a function of the number of detected cells in each image. CEC, corneal endothelial cell; ECD, endothelial cell density; CV, coefficient of variation in cell area; HEX, percentage of hexagonal cells

Furthermore, the proposed system was very efficient and processed (segmented and quantified) a single image in less than 1 s when run on a 12 GB NVIDIA Tesla K80 GPU and in less than 3 s on a 3.20 GHz Core i7-8700 CPU with 16 GB of RAM.