Novel approaches to statistical shape modelling of bone

The femur is the longest bone in the human body and serves the important purposes of load-bearing and allowing bipedal locomotion. Accurate modelling of the variation in shape within the healthy adult population can be useful for a variety of applications: from the mere anatomical description of its features, in order to better understand its function, to more complex tasks such as pathology detection or surgical planning. Statistical Shape Modelling (SSM) is a well-established technique that enables to capture the variability within a set of training shapes and describes it with a reduced set of variables. The aim of this thesis is to evaluate the performance of a SSM based on a point cloud representation of shape, and introduce and test subsequent improvements to the modelling process that can increase its clinical relevance and scope of application. The standard approach to SSM employs a dimension-reducing technique, generally by means of Principal Component Analysis (PCA). However, this approach favours the compactness of the model, thus not focusing on other aspects that may be more relevant to clinical practice. Although rotation of the principal components is commonly performed as a post-processing step in statistical analysis involving PCA, it is not routinely applied in SSM. By applying this class of rotation, the components' effects are more localised, allowing a better interpretation, understanding and classification of pathological deformities. Among other possible representations, the Medial Axis Transform (MAT) could offer a further insight into shape modelling, since it allows the information about thickness to be decoupled from the rest of the shape. SSMs based on this representation can lead to a di erent perspective on the understanding of femoral anatomy and function,and can also enable the reconstruction of the complete anatomy starting from a reduced set of features, with diverse applications in the elds of surgical planning, forensic science and paleontology