Explainable Anatomical Shape Analysis Through Deep Hierarchical Generative Models.

Quantification of anatomical shape changes currently relies on scalar global indexes which are largely insensitive to regional or asymmetric modifications. Accurate assessment of pathology-driven anatomical remodeling is a crucial step for the diagnosis and treatment of many conditions. Deep learning approaches have recently achieved wide success in the analysis of medical images, but they lack interpretability in the feature extraction and decision processes. In this work, we propose a new interpretable deep learning model for shape analysis. In particular, we exploit deep generative networks to model a population of anatomical segmentations through a hierarchy of conditional latent variables. At the highest level of this hierarchy, a two-dimensional latent space is simultaneously optimised to discriminate distinct clinical conditions, enabling the direct visualisation of the classification space. Moreover, the anatomical variability encoded by this discriminative latent space can be visualised in the segmentation space thanks to the generative properties of the model, making the classification task transparent. This approach yielded high accuracy in the categorisation of healthy and remodelled left ventricles when tested on unseen segmentations from our own multi-centre dataset as well as in an external validation set, and on hippocampi from healthy controls and patients with Alzheimer's disease when tested on ADNI data. More importantly, it enabled the visualisation in three-dimensions of both global and regional anatomical features which better discriminate between the conditions under exam. The proposed approach scales effectively to large populations, facilitating high-throughput analysis of normal anatomy and pathology in large-scale studies of volumetric imaging.

Quantifying Registration Uncertainty With Sparse Bayesian Modelling.

We investigate uncertainty quantification under a sparse Bayesian model of medical image registration. Bayesian modelling has proven powerful to automate the tuning of registration hyperparameters, such as the trade-off between the data and regularization functionals. Sparsity-inducing priors have recently been used to render the parametrization itself adaptive and data-driven. The sparse prior on transformation parameters effectively favors the use of coarse basis functions to capture the global trends in the visible motion while finer, highly localized bases are introduced only in the presence of coherent image information and motion. In earlier work, approximate inference under the sparse Bayesian model was tackled in an efficient Variational Bayes (VB) framework. In this paper we are interested in the theoretical and empirical quality of uncertainty estimates derived under this approximate scheme vs. under the exact model. We implement an (asymptotically) exact inference scheme based on reversible jump Markov Chain Monte Carlo (MCMC) sampling to characterize the posterior distribution of the transformation and compare the predictions of the VB and MCMC based methods. The true posterior distribution under the sparse Bayesian model is found to be meaningful: orders of magnitude for the estimated uncertainty are quantitatively reasonable, the uncertainty is higher in textureless regions and lower in the direction of strong intensity gradients.

Sparse Bayesian registration of medical images for self-tuning of parameters and spatially adaptive parametrization of displacements.

We extend Bayesian models of non-rigid image registration to allow not only for the automatic determination of registration parameters (such as the trade-off between image similarity and regularization functionals), but also for a data-driven, multiscale, spatially adaptive parametrization of deformations. Adaptive parametrizations have been used with success to promote both the regularity and accuracy of registration schemes, but so far on non-probabilistic grounds - either as part of multiscale heuristics, or on the basis of sparse optimization. Under the proposed model, a sparsity-inducing prior on transformation parameters complements the classical smoothness-inducing prior, and favors parametrizations that use few degrees of freedom. As a result, finer bases get introduced only in the presence of coherent image information and motion, while coarser bases ensure better extrapolation of the motion to textureless, uninformative regions. The space of possible parametrizations consists of arbitrary combinations of basis functions chosen among any preset, widely overcomplete (and typically multiscale) dictionary. Inference is tackled in an efficient Variational Bayes framework. In addition we propose a flexible mixture-of-Gaussian model of data that proves to be more faithful for a variety of image modalities than the sum-of-squared differences. The performance of the proposed approach is demonstrated on time series of (cine and tagged) magnetic resonance and echocardiographic cardiac images. The proposed algorithm matches the state-of-the-art on benchmark datasets evaluating accuracy of motion and strain, and is highly automated.

Sparse Bayesian registration.

We propose a Sparse Bayesian framework for non-rigid registration. Our principled approach is flexible, in that it efficiently finds an optimal, sparse model to represent deformations among any preset, widely overcomplete range of basis functions. It addresses open challenges in state-of-the-art registration, such as the automatic joint estimate of model parameters (e.g. noise and regularization levels). We demonstrate the feasibility and performance of our approach on cine MR, tagged MR and 3D US cardiac images, and show state-of-the-art results on benchmark datasets evaluating accuracy of motion and strain.