# Perspective Morphometric Criteria for Facial Beauty and Proportion Assessment
## 4 Discussion  
Results provided by literature analysis have led to the first outcome of this research, namely the expanded set of measures, each of which is characterized by a mean value and standard deviation. In the literature, a measure is considered relevant for women's facial attractiveness if a statistically significant number of _attractive_ women possess similar values of the same measure and, conversely, that measure assumes different values in subjects belonging to the _normal_ woman set. The critical point is to define a ground truth, i.e., a set of measures distinctive for _attractive_ women. All the studies carried out in this field agree upon considering _attractive_ those women's faces that are commonly positively evaluated in terms of facial beauty and proportion, and thus famous actresses or beauty contest participants, especially those that move on to the final stage of national competitions. The present work has focused on gathering measures validated in past studies, building the expanded set of measures defined on facial landmarks and analyzing a public database of _normal_ women, the Bosphorus. Unfortunately, some of the landmarks used in the literature were not present in the set of data of the Bosphorus database. For this reason, an expert has manually added those missing landmarks lying on soft tissue, but some of the hard tissue landmarks have not been considered due to  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Measures** & \begin{tabular}{c} **Cluster 4 +** \\ **5 (\#17)** \\ \end{tabular}  & \begin{tabular}{c} **Cluster 5** \\ **(\#7)** \\ \end{tabular}  & \begin{tabular}{c} **Cluster 4** \\ **(\#10)** \\ \end{tabular}  & \begin{tabular}{c} **Cluster 3** \\ **(\#10)** \\ \end{tabular}  & \ \begin{tabular}{c} **Cluster 2** \\ **(\#11)** \\ \end{tabular}  & \begin{tabular}{c} **Cluster 1** \\ **(\#6)** \\ \end{tabular}  \\ \hline ls-sto & 2 (12\%) & 0 (0\%) & 2 (20\%) & 4 (40\%) & 11 (100\%) & 5 (83\%) \\ (sn-pg)/(n-sn) & 2 (12\%) & 1 (14\%) & 1 (10\%) & 6 (60\%) & 1 (9\%) & 5 (83\%) \\ n-sn & 3 (18\%) & 2 (29\%) & 1 (10\%) & 6 (60\%) & 3 (27\%) & 5 (83\%) \\ sn-gn & 3 (18\%) & 0 (0\%) & 3 (30\%) & 4 (40\%) & 11 (100\%) & 5 (83\%) \\ (t\_r-n)/(t\_r-sn) & 3 (18\%) & 0 (0\%) & 3 (30\%) & 4 (40\%) & 4 (36\%) & 3 (50\%) \\ ex\_r-ex\_l & 4 (23\%) & 1 (14\%) & 3 (30\%) & 5 (50\%) & 6 (54\%) & 5 (83\%) \\ sl-n-sn & 4 (23\%) & 2 (29\%) & 2 (20\%) & 5 (50\%) & 6 (54\%) & 2 (33\%) \\ (t\_r\_l)/(n-pg) & 4 (23\%) & 0 (0\%) & 4 (40\%) & 4 (40\%) & 6 (54\%) & 3 (50\%) \\ n-gn & 5 (29\%) & 0 (0\%) & 5 (50\%) & 6 (60\%) & 6 (54\%) & 5 (83\%) \\ li-sto & 5 (29\%) & 2 (29\%) & 3 (30\%) & 3 (30\%) & 7 (64\%) & 5 (83\%) \\ n-pm-pg & 5 (29\%) & 1 (14\%) & 4 (40\%) & 5 (50\%) & 3 (27\%) & 2 (33\%) \\ (sn-gn)/(n-gn) & 5 (29\%) & 1 (14\%) & 4 (40\%) & 7 (70\%) & 3 (27\%) & 2 (33\%) \\ en\_l-n-en\_r & 6 (35\%) & 3 (43\%) & 3 (30\%) & 6 (60\%) & 6 (54\%) & 4 (67\%) \\ (sn-pg)/(n-pg) & 6 (35\%) & 2 (29\%) & 4 (40\%) & 3 (30\%) & 4 (36\%) & 2 (33\%) \\ n-pg & 7 (41\%) & 3 (43\%) & 4 (40\%) & 7 (70\%) & 6 (54\%) & 5 (83\%) \\ pg-n-ls & 7 (41\%) & 0 (0\%) & 7 (70\%) & 3 (30\%) & 6 (54\%) & 4 (67\%) \\ (n-sn)/(n-pg) & 7 (41\%) & 3 (43\%) & 4 (40\%) & 4 (40\%) & 7 (64\%) & 3 (50\%) \\ ls-li & 8 (47\%) & 2 (29\%) & 6 (60\%) & 6 (60\%) & 5 (45\%) & 4 (67\%) \\ en\_r-en\_l & 8 (47\%) & 4 (57\%) & 4 (40\%) & 7 (70\%) & 4 (36\%)the impossibility of identifying them without live palpation. Consequently, a limited set of measures that could have been included in the expanded set has been discarded. In order to analyze the Bosphorus, a methodology able to integrate information provided by different sources was required. Thus, the algorithm based on the penalty mechanism has been developed, and the results have been clustered to provide the possibility of classifying faces into 5 different levels. The cluster numbering is from 5-1, that means it ranges from the most compliance with the well-proportioned standard face to the least.