# A Fully Automated Pipeline for a Robust Conjunctival Hyperenia Estimation
## 3 Results
### Efron Scale Prediction  
We processed the dataset of 280 samples using our automated pipeline extracting the full set of features. In this dataset, we have two images for each eye (nasal and temporal); thus, we use the average of each feature extracted on the two samples. The full set of 10 features were used for the ridge regression model estimating the correlation between the ground truth Efron values and the predicted ones. We trained the regression model using a 10-fold cross validation: in this way, we can ensure that the model predicts the outcome on a completely novel set of samples. We tuned the pipeline parameters using a grid search algorithm to better fit the available data. The best model found is able to predict the correct Efron scale values with a [PERSON]'s rank correlation coefficient of 0.701 and a corresponding \(p\)-value of \(10^{-22}\) (ref. Figure 4a). An example of the prediction obtained on the test set is showed in Figure 5  
We apply the same pipeline for 100 different cross validations to test the robustness of our model. In each iteration, a different 10-fold cross validation is provided to the ridge regression: in this way, we test the sensitivity of the model to different training sets. The resulting distribution of [PERSON]'s rank correlation coefficient (ref. Figure 4b) shows the robustness of the developed model: the estimated coefficients are centered around a value of 0.69 with a spread of 0.008. Figure 2: Results obtained by the trained Mobile U-Net model on the 18 test images. (**a**) evolution of the average accuracy and average IoU along the training epochs (100). The IoU score is more informative given that it is robust to unbalances in the sample, differently from the accuracy score; (**b**) example of the results obtained on a test image. On the top-left, the ground truth. On the top-right, the predicted segmentation. On the bottom-left, the raw (input) image. On the bottom-right, the resulting ROI of the conjunctival area. The developed model uses a combination of the extracted features to find the best parameters for the regression model. Despite the resulting performances, we evaluate the informative power of each feature independently. We apply the same cross validation procedure using each feature singularly one by one: in this way, we can assign to each of them its informative power given by the associated Spearman's correlation coefficient. As expected, not all the features are equally informative, but only three of them are associated with a Spearman's correlation coefficient greater than 0.55 (in absolute values). We found as the most informative feature the _score\({}_{1}\)_ (ref. Table 2) with a correlation coefficient of 0.64, immediately followed by the _average saturation_ and _average blue channel_ with 0.61 and \(-0.56\), respectively. Thus, the results obtained by our predicted model are related to the informative power of these three features. Figure 3: Comparison between the raw image and the result of our standardization algorithm. (**a**,**c**) the original image and corresponding enlarged area. In this case, the image acquisition was performed with an incorrect light exposition, which leads to an unbalanced redness component along the entire conjunctiva area. It is evident in the enlarged section how the vessel color tends to be very close to the background, making it their evaluation difficult and creating a false positive redness component in the conjunctiva. (**b**,**d**) the standardized image and corresponding enlarged area. The standardization algorithm allows for better discriminating the vessels network component from the red-like background. In the enlarged portion, we can see how the algorithm is able to split the vessels with the uniform background, despite the latter having a non-negligible redness component; (**e**) the vessels network segmentation estimated on the raw image; (**f**) the vessels network segmentation estimated on the standardized image.