Geometric morphometrics for 3D dense surface correspondence: population comparisons of shoulder bone morphology

Background: Comparisons in morphological shape/form across population groups could provide population differences that might assist in making decisions on diagnosis and prognosis by the clinician. Geometric morphometrics (GM) is one of the fields that help to provide such population comparisons. In medical imaging and related disciplines, GM is commonly done using annotated landmarks or distances measured from 3D surfaces (consisting of triangular meshes). However, these landmarks may not be sufficient to describe the complete shape. This project aimed to develop GM for analysis that consider all vertices in the triangular mesh as landmarks. The developed methods were applied to South African and Swiss shoulder bones (scapula and humerus) to analyse morphological differences. Methods: The developed pipeline required first establishing correspondence across the datasets through a registration process. Gaussian process fitting was chosen to perform the registration since it is considered state-of-the-art. Secondly, a novel method for automatic identification of vertices or areas encoding the most shape/form variation was developed. Thirdly, a principal component analysis (PCA) that addressed the high dimensionality and lower sample size (HDLSS) phenomenon was adopted and applied to the dense correspondence data. This approach allowed for the stabilisation of the distribution of the data in low-dimensional form/shape space. Lastly, appropriate statistical tests were developed for population comparisons of the shoulder bones when dealing with HDLSS data in both form and shape space. Results: When the mesh-based GM analysis approach was applied to the training datasets (South African and Swiss shoulder bones), it was found that the anterior glenoid which is often the site of the shoulder dislocation is the most varied area of the glenoid. This has implications for diagnosis and provides knowledge for prosthesis design. The distribution of the data in the modified PCA space was shown to converge to a stable distribution when more vertices/landmarks are used for the analysis. South African and Swiss datasets were shown to be more distinguishable in a low-dimensional space when considering form rather than shape. It was found that left and right South African scapula bones are significantly different in terms of shape. Discussion: In general, it was observed that the two populations means can be significantly different in shape but not in form. An improved understanding of these observed shape and form differences has utility for shoulder arthroplasty prosthesis design and may also be useful for orthopaedic surgeons during surgical preoperative planning

Towards a framework for multi class statistical modelling of shape, intensity, and kinematics in medical images

Statistical modelling has become a ubiquitous tool for analysing of morphological variation of bone structures in medical images. For radiological images, the shape, relative pose between the bone structures and the intensity distribution are key features often modelled separately. A wide range of research has reported methods that incorporate these features as priors for machine learning purposes. Statistical shape, appearance (intensity profile in images) and pose models are popular priors to explain variability across a sample population of rigid structures. However, a principled and robust way to combine shape, pose and intensity features has been elusive for four main reasons: 1) heterogeneity of the data (data with linear and non-linear natural variation across features); 2) sub-optimal representation of three-dimensional Euclidean motion; 3) artificial discretization of the models; and 4) lack of an efficient transfer learning process to project observations into the latent space. This work proposes a novel statistical modelling framework for multiple bone structures. The framework provides a latent space embedding shape, pose and intensity in a continuous domain allowing for new approaches to skeletal joint analysis from medical images. First, a robust registration method for multi-volumetric shapes is described. Both sampling and parametric based registration algorithms are proposed, which allow the establishment of dense correspondence across volumetric shapes (such as tetrahedral meshes) while preserving the spatial relationship between them. Next, the framework for developing statistical shape-kinematics models from in-correspondence multi-volumetric shapes embedding image intensity distribution, is presented. The framework incorporates principal geodesic analysis and a non-linear metric for modelling the spatial orientation of the structures. More importantly, as all the features are in a joint statistical space and in a continuous domain; this permits on-demand marginalisation to a region or feature of interest without training separate models. Thereafter, an automated prediction of the structures in images is facilitated by a model-fitting method leveraging the models as priors in a Markov chain Monte Carlo approach. The framework is validated using controlled experimental data and the results demonstrate superior performance in comparison with state-of-the-art methods. Finally, the application of the framework for analysing computed tomography images is presented. The analyses include estimation of shape, kinematic and intensity profiles of bone structures in the shoulder and hip joints. For both these datasets, the framework is demonstrated for segmentation, registration and reconstruction, including the recovery of patient-specific intensity profile. The presented framework realises a new paradigm in modelling multi-object shape structures, allowing for probabilistic modelling of not only shape, but also relative pose and intensity as well as the correlations that exist between them. Future work will aim to optimise the framework for clinical use in medical image analysis

Vers un framework pour la modélisation statistique multi-classes de la forme, de l'intensité et de la cinématique dans les images médicales

This thesis focuses on the development of statistical learning-based models for human joints from medical images. The main contribution is a new mathematical formulation to model musculoskeletal systems by developing a unified computational latent space that embeds shape, kinematics and intensity features from given observations. This new space provides a continuous model capable of generating instances leveraging learnt feature correlations. A fitting method to apply models developed using this framework to unseen data is also proposed. The complete modeling and prediction framework is validated using bespoke synthetic data, showing that the framework faithfully encapsulates any prescribed morpho-functional relationships between objects, as well as their internal structural information. Finally, the framework is applied to the analysis of shoulder and hip joints from CT. The clinical interest is that the feature correlations learned by the model improve premorbid shape prediction and joint motion estimation accuracy, from two- and three-dimensional medical.Cette thèse porte sur le développement de modèles basés sur l’apprentissage statistique pour les complexes articulaires humains à partir d’images médicales. La principale contribution est une nouvelle formulation mathématique permettant de modéliser les systèmes musculo-squelettiques à l’aide d’un espace latent unifié qui intègre des caractéristiques de forme, de cinématique et d'intensité à partir d'observations données. Ce nouvel espace fournit un modèle continu capable de générer des instances en tirant parti des corrélations apprises entre caractéristiques. Une méthode d'ajustement est également proposée pour appliquer ce modèle sur de nouvelles données. La méthode complète de modélisation et de prédiction est validée à l'aide de données synthétiques entièrement contrôlées, et les résultats montrent que le modèle encapsule fidèlement les relations morpho-fonctionnelles imposées entre les objets, ainsi que leurs informations structurelles internes. Enfin, le modèle est utilisé pour analyser les articulations de l'épaule et de la hanche à partir d'images CT. L'intérêt clinique est que les corrélations de caractéristiques apprises par le modèle améliorent la prédiction de la forme pré-morbide et la précision de l'estimation du mouvement des articulations, à partir d'images médicales en deux ou trois dimensions

Unsupervised Learning of Disentangled Representation via Auto-Encoding: A Survey

International audienceIn 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