# A Fully Automated Pipeline for a Robust Conjunctival Hyperenia Estimation
## 4 Discussion  
The results obtained on the Efron scale predictions highlight a statistical agreement between only a small set of extracted features and the grading scores. In particular, we show the efficiency of some RGB measurements which have statistical significant correlations with the Efron grading scale values. Their efficiency is justified by their robustness to the most common issues in the image acquisition given by the light exposition and aperture of the slit lamp diaphragm. The best correlation performances are achieved by the measure proposed by [PERSON] et al. (_score\({}_{1}\)_): this measure is already known in literature as a feature related to the redness as much as the blue channel (the blue channel conserves the most informative component for the discrimination between the white-like conjunctiva area and the red-like vessels network). It is, however, interesting to notice how the saturation of the segmented vessels network area shows a not negligible correlation with the redness measure of the Efron scale. Moreover, the correlation between the image saturation and Efron values is a positive correlation, implying that the higher is the image exposition to the light with brighter red color and the higher tends to be the evaluation of the clinicians. The quality of the image certainly affects the evaluation of the clinicians, and it is quite obvious that, in a low contrast image, the evaluation of the vessels is harder for human eyes. The analysis of the single features correlation also explains the apparently low efficiency of the _score\({}_{2}\)_: despite the HSV color space being theoretically more robust than the RGB one and the high correlation between saturation and Efron values, the hue channel (\(\mu_{H}\)) tends to anti-correlate with the Efron scale. The combination of the HSV channels proposed by [PERSON] et al. does not take care about them and thus their score is penalized in relation to the others. The lowest predictive powers are achieved by the fractal features: the fractal analysis of the vessels network seems to be unrelated to the Efron values despite their theoretically information power in the description of the neo-genesis and ramification of the vessels. The fractal measures that are independent from the extension of the vessels network by definition can be seen as informative of the dynamic of the process of neo-genesis. Therefore, this lack of correlation seems to imply that the vessels growth is not different from the physiological condition. The methods to estimate conjunctival redness are usually assessed by evaluating the agreement of the estimates of a panel of experts. The same set of samples is shown to a pool (at least two) of experts, and they perform the grading evaluation under the same experimental conditions. In this way, one can double check the obtained results, comparing the efficiency of the model against the expert evaluation using the agreement between the experts as the _maximal obtainable correlation_: the rationale is that any automated method can not agree with the opinion of any single expert more than how much two experts can agree between themselves. In our work, each image was independently evaluated by three experts. It is important to notice that, despite our automated method not reaching a perfect prediction, we observed an internal agreement between the experts' evaluations of at most 0.84 (evaluated as Spearman's correlation coefficient). In this case, any automated pipeline trained on this dataset could not achieve a predictive power greater than this value. Any result higher than this should be regarded as over fitting. Our results also highlight a non-negligible correlation between the saturation of the image and the Efron scale values.