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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.

In model-based medical image analysis, three features of interest are the shape of structures of interest, their relative pose, and image intensity profiles representative of some physical property. Often, these are modelled separately through statistical models by decomposing the object's features into a set of basis functions through principal geodesic analysis or principal component analysis. However, analysing multiple objects in an image using multiple single object models may lead to large errors and uncertainties, especially around organ boundaries. A question that comes to mind is what kind of advantages can be gained from combining the three features of interest in the same statistical space for analysing images. This study presents a statistical modelling method for automatic learning of shape, pose and intensity features in medical images which we call the Dynamic multi feature-class Gaussian process models (DMFC-GPM). A DMFC-GPM is a Gaussian process (GP)-based model with a shared latent space that encodes linear and non-linear variation. Our method is defined in a continuous domain with a principled way to represent shape, pose and intensity feature classes in a linear space, based on deformation fields. A deformation field-based metric is adapted in the method for modelling shape and intensity feature variation as well as for comparing rigid transformations (pose). Moreover, DMFC-GPMs inherit properties intrinsic to GPs including marginalisation and regression. Furthermore, they allow for adding additional pose feature variability on top of those obtained from the image acquisition process; what we term as permutation modelling. For image analysis tasks using DMFC-GPMs, we adapt Metropolis-Hastings algorithms making the prediction of features fully probabilistic. We validate the method using controlled synthetic data and we perform experiments on bone structures from CT images of the shoulder to illustrate the efficacy of the model for pose and shape feature prediction. The model performance results suggest that this new modelling paradigm is robust, accurate, accessible, and has potential applications in a multitude of scenarios including the management of musculoskeletal disorders, clinical decision making and image processing.

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