## 2 Materials and Methods
### PLR Features Extraction  
The acquisition protocol could be split into two conditions: the scotopic vision, related to the starting and ending points of the acquisition, in which the eye is in a low-light condition, and the photopic one, in which the eye is exposed to a light source. From both these conditions we can extract quantitative features able to describe the response of the pupil in terms of time and velocity. Analogous analyses could be performed considering the transition ranges from these two conditions. Many authors have already proposed several features for the quantitative description of the PLR signals [9; 11; 12; 15; 28; 29]. In this work we aimed to provide a global overview of the features obtainable by a PLR signal, considering the ones already used in the literature (some of which are in a limited number of works) together with a new set of features, given by the application of signal processing algorithms. All of these new proposed features rely on the quantification of biological interpretable aspects of the PLR signals. A global overview of the features already considered in the literature is shown in Table 1. \begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline
**Study (\(n\) = Sample Size)** & **Case Study** & **Proposed Feature(s)** \\ \hline [PERSON] et al. (review) & Alzheimer’s disease & • • Latency time of pupil constriction \\ \hline [PERSON] et al. (\(n\) = 222) & Diabetes & • Latency time of pupil constriction \\ \hline [PERSON] (\(n\) = 1406) & Aging, Sex, Smoking & • Minimum pumpil diameter  • Maximum constriction velocity  • Latency time scotopic phase \\ \hline [PERSON] et al. (\(n\) = 50) & Alzheimer’s disease & • Signal enclosing area \\ \hline [PERSON] et al. (\(n\) = 176) & Multiple sclerosis & • Average pupil diameter  • Latency time of pupil constriction  • Minimum pupil diameter  • Maximum constriction velocity  • Latency time scotopic phase \\ \hline [PERSON] et al. (\(n\) = 25) & Multiple sclerosis & • Maximum constriction velocity  • Latency time scotopic phase \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the PLR signal features already proposed in the literature. For each study, we reported the number of patients involved, the analyzed disease, and the set of features proposed for the quantitative analysis. All the features cited in this table were considered in the current work, providing a mathematical equation for their evaluation. The most direct features obtainable from the PLR signal (s(t)) are given by the diameter of the pupil at the initial scotopic phase of the acquisition. This measure represents the baseline of the entire signal and could be used to standardize the inter- and intrapatient acquisitions. For its quantification, we used the average value of the PLR signal D\({}_{0}\) obtained in the first scotopic phase, i.e., from the beginning of the acquisition to the point in which the derivative of the signal changes its sign [29] (ref. Figure 1b)  
\[D_{0}=\frac{1}{N}\sum_{1}^{N}s(t)\quad\quad\text{where }N\in 1^{st}\,\,scotopic \,\,region \tag{1}\]  
Starting from the initial scotopic phase, a second feature is given by the latency time of constriction (\(T_{p}\)), at the transition between the scotopic region and the photopic region. It consists of the time difference between the starting time of the photopic region (fixed to 3 \(s\) in our acquisitions) and the first response of the pupil (\(t_{photopic}\)), detected as the time at which the largest second derivative of the signal occurs [9; 11; 29] (ref. Figure 1c). Identifying the starting point of the photopic phase as described above, the latency time to constriction is given  
\[T_{p}=t_{photopic}-3s \tag{2}\]  
Moving to the photopic region, the s(t) signal will drastically drop-down, achieving its minimum value in terms of pupil diameter [12; 29; 30] (ref. Figure 1d). The minimum value achieved in this window (\(min[D]\)) was measured as a percentage of the signal centered on the baseline (ref.