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

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.

Dynamic multi feature-class Gaussian process models.

In model-based medical image analysis, three relevant features are the shape of structures of interest, their relative pose, and image intensity profiles representative of some physical properties. Often, these features 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 articulated objects in an image using independent single object models may lead to large uncertainties and impingement, especially around organ boundaries. Questions that come to mind are the feasibility of building a unique model that combines all three features of interest in the same statistical space, and what advantages can be gained for image analysis. This study presents a statistical modelling method for automatic analysis of shape, pose and intensity features in medical images which we call the Dynamic multi feature-class Gaussian process models (DMFC-GPM). The DMFC-GPM is a Gaussian process (GP)-based model with a shared latent space that encodes linear and non-linear variations. 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 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 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 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.

Cross-Modality Image Adaptation Based on Volumetric Intensity Gaussian Process Models (VIGPM).

Image-based diagnosis routinely depends on more that one image modality for exploiting the complementary information they provide. However, it is not always possible to obtain images from a secondary modality for several reasons such as cost, degree of invasiveness and non-availability of scanners. Three-dimensional (3D) morphable models have made a significant contribution to the field of medical imaging for feature-based analysis. Here we extend their use to encode 3D volumetric imaging modalities. Specifically, we build a Gaussian Process (GP) over transformations establishing anatomical correspondence between training images within a modality. Given, two different modalities, the GP's eigenspace (latent space) can then be used to provide a parametric representation of each image modality, and we provide an operator for cross-domain translation between the two. We show that the latent space yields samples that are representative of the encoded modality. We also demonstrate that a 3D volumetric image can be efficiently encoded in latent space and transferred to synthesize the corresponding image in another modality. The framework called VIGPM can be extended by designing a fitting process to learn an observation in a given modality and performing cross-modality synthesis. Clinical Relevance- The proposed method provides a way to access a multi modality image from one modality. Both the source and synthetic modalities are in anatomical correspondence giving access to registered complementary information.

Statistical shape-kinematics models of the skeletal joints: Application to the shoulder complex.

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.

Assessment of 3D morphological characteristics of the shoulder bones using statistical shape modeling: Prospective application to handedness.

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.