In recent years, the rapid development of deep learning approaches has paved the way to explore the underlying factors that explain the data. In particular, several methods have been proposed to learn to identify and disentangle these underlying explanatory factors in order to improve the learning process and model generalization. However, extracting this representation with little or no supervision remains a key challenge in machine learning. In this paper, we provide a theoretical outlook on recent advances in the field of unsupervised representation learning with a focus on auto-encoding-based approaches and on the most well-known supervised disentanglement metrics. We cover the current state-of-the-art methods for learning disentangled representation in an unsupervised manner while pointing out the connection between each method and its added value on disentanglement. Further, we discuss how to quantify disentanglement and present an in-depth analysis of associated metrics. We conclude by carrying out a comparative evaluation of these metrics according to three criteria, (i) modularity, (ii) compactness and (iii) informativeness. Finally, we show that only the Mutual Information Gap score (MIG) meets all three criteria.

Patient-specific biomechanical simulations of joints require accurate reconstruction of bony anatomy from medical image data. The articular geometries of the joints may influence their biomechanics. Statistical shape models (SSMs) have become ubiquitous in the literature and aim to capture the natural variation of biological objects. They work by learning the variation from training examples to define the space of valid biological shapes. However, the kinematic information descriptive of the anato-physiological relationship of two interacting objects is not generally encoded in the SSM. Here, we propose a framework for developing combined statistical shape and kinematics models (SSKMs) as Gaussian process morphable models to analyse the shape and kinematics relationship. We demonstrate the framework on a three-dimensional (3D) image data set consisting of ten right-handed cadaveric shoulder joints acquired using computed tomography. Additionally, we simulate specific bone motions to encode kinematics in the combined model. Our SSKM built from shoulder data (matching scapulae and humeri) correctly depicts a correlation between the shape and kinematics as hypothesized. We furthermore demonstrate the ability to marginalize from the SSKM to obtain shape-only variation and kinematics-only variation. Future work aims to use the SSKM framework to understand the relationships between kinematics and shape for various joints as well as to develop patient-specific computational models to evaluate joint biomechanics.

In this study we have described the use of statistical shape modeling (SSM) technique in evaluating the morphological variation of shoulder bones from a South African population. The anatomical landmark selections were carried out, followed by the registration of the meshes which were validated before establishing the dense correspondence. The SSMs were built and average shape comparison from each side for each bone were made in order to evaluate handedness. In general, there was no error found around the gleno-humeral region which may suggest that the usage of contralateral healthy shoulder could serve as an informed decision making tool for surgery and prosthesis design.