## 4 Discussion  
The here presented work was mainly aimed at illustrating the procedure to adopt in order to build an SSM. Two databases referring to two different bone sites were used to illustrate the procedure. The proximal femur database was definitely larger and could therefore be considered more exhaustive compared to the available mandible database, which was more limited. In both cases, PCA proved its efficiency in summarizing the main anatomical features: 40 mandibles were considered, and as a result of PCA, 15 components sufficed to generate a theoretically infinite set of different mandible shapes, able to cover 90% of the variability identified in the original database. As far as the 98 proximal femurs database is concerned, 90% of the shape variance could be covered by nine PCs. The geometry of the proximal femur is certainly simpler compared to a full mandible, and it is not therefore surprising that a smaller number of PCs was required to cover almost the whole variability present in the more numerous database; this aspect is also confirmed from the work of [PERSON] et al. (2020). From this perspective, the number of PCs is actually a measure of the geometric shape complexity ([PERSON] et al., 2020). The generation of new geometries must follow the empirically estimated frequency distributions of weight components, in order that the actual variability found in nature is reproduced. The hypothesis of a normal distribution is questionable according to the  
Figure 7: New set of 20 femurs, generated through inverse transform sampling, applied on empirical cumulative weight distribution of weights for each component. results that were obtained: therefore, the authors preferred to avoid fitting the cumulative frequency with a known statistical distribution. If statistical tests were performed to check weight distributions normality, this statistical hypothesis would not be rejected in most cases. However, it is well known that failure to reject statistical hypothesis does not mean, as assumed by some authors, that the normality of the distribution has been demonstrated [22]: the approach followed herein by the authors was therefore certainly considered more precautionary. The possibility to create a statistically sound set of bones is a mandatory issue when, for instance, a prosthesis needs to be designed to cover the need of a whole population [23]. In addition, it can provide key information for the design of parametric [24] and modular [25] models. Three-dimensional models can also be used to create patient-specific finite element models [6; 26] or multibody models in order to study the structural behaviour of a prosthesis or of a synthesis device [27; 28]: in this whole context, working on iso-topological meshes allows straightforward applications in the setup of numerical procedures, without additional need for technical skills. Statistical shape models might also be used for diagnostic purposes, in order to assess if a certain morphology could be considered as \"normal\", checking if it falls inside a given probability range [29] as well as more deeply investigating relations between anatomy and a number of pathologies [30; 31; 32]. The application of the SSM method was presented here to also consider the possibility of predicting of new bone shapes. It must be said that CT scan data allows not only the three-dimensional reconstruction of external and internal anatomical structures, but also the extrapolation of information on material mechanical properties [30; 33; 34]. In this context, when dealing with bones, the possibility to generate new instances enables us to gather not only the shape but also the local density that may indeed be preferable, in order to have a full bone model for further investigations (i.e., static and dynamic analyses).