A Multi-Resolution t-Mixture Model Approach to Robust Group-wise Alignment of Shapes

A novel probabilistic, group-wise rigid registration framework is proposed in this study, to robustly align and establish correspondence across anatomical shapes represented as unstructured point sets. Student’s t-mixture model (TMM) is employed to exploit their inherent robustness to outliers. The primary application for such a framework is the automatic construction of statistical shape models (SSMs) of anatomical structures, from medical images. Tools used for automatic segmentation and landmarking of medical images often result in segmentations with varying proportions of outliers. The proposed approach is able to robustly align shapes and establish valid correspondences in the presence of considerable outliers and large variations in shape. A multi-resolution registration (mrTMM) framework is also formulated, to further improve the performance of the proposed TMM-based registration method. Comparisons with a state-of-the art approach using clinical data show that the mrTMM method in particular, achieves higher alignment accuracy and yields SSMs that generalise better to unseen shapes

Generalised coherent point drift for group-wise registration of multi-dimensional point sets

In this paper we propose a probabilistic approach to group-wise registration of unstructured high-dimensional point sets. We focus on registration of generalised point sets which encapsulate both the positions of points on surface boundaries and corresponding normal vectors describing local surface geometry. Richer descriptions of shape can be especially valuable in applications involving complex and intricate variations in geometry, where spatial position alone is an unreliable descriptor for shape registration. A hybrid mixture model combining Student’s t and Von-Mises-Fisher distributions is proposed to model position and orientation components of the point sets, respectively. A group-wise rigid and non-rigid registration framework is then formulated on this basis. Two clinical data sets, comprising 27 brain ventricle and 15 heart shapes, were used to assess registration accuracy. Significant improvement in accuracy and anatomical validity of the estimated correspondences was achieved using the proposed approach, relative to state-of-the-art point set registration approaches, which consider spatial positions alone

A Probabilistic Framework for Statistical Shape Models and Atlas Construction: Application to Neuroimaging

Accurate and reliable registration of shapes and multi-dimensional point sets describing the morphology/physiology of anatomical structures is a pre-requisite for constructing statistical shape models (SSMs) and atlases. Such statistical descriptions of variability across populations (regarding shape or other morphological/physiological quantities) are based on homologous correspondences across the multiple samples that comprise the training data. The notion of exact correspondence can be ambiguous when these data contain noise and outliers, missing data, or significant and abnormal variations due to pathology. But, these phenomena are common in medical image-derived data, due, for example, to inconsistencies in image quality and acquisition protocols, presence of motion artefacts, differences in pre-processing steps, and inherent variability across patient populations and demographics. This thesis therefore focuses on formulating a unified probabilistic framework for the registration of shapes and so-called \textit{generalised point sets}, which is robust to the anomalies and variations described. Statistical analysis of shapes across large cohorts demands automatic generation of training sets (image segmentations delineating the structure of interest), as manual and semi-supervised approaches can be prohibitively time consuming. However, automated segmentation and landmarking of images often result in shapes with high levels of outliers and missing data. Consequently, a robust method for registration and correspondence estimation is required. A probabilistic group-wise registration framework for point-based representations of shapes, based on Student’s t-mixture model (TMM) and a multi-resolution extension to the same (mrTMM), are formulated to this end. The frameworks exploit the inherent robustness of Student’s t-distributions to outliers, which is lacking in existing Gaussian mixture model (GMM)-based approaches. The registration accuracy of the proposed approaches was quantitatively evaluated and shown to outperform the state-of-the-art, using synthetic and clinical data. A corresponding improvement in the quality of SSMs generated subsequently was also shown, particularly for data sets containing high levels of noise. In general, the proposed approach requires fewer user specified parameters than existing methods, whilst affording much improved robustness to outliers. Registration of generalised point sets, which combine disparate features such as spatial positions, directional/axial data, and scalar-valued quantities, was studied next. A hybrid mixture model (HMM), combining different types of probability distributions, was formulated to facilitate the joint registration and clustering of multi-dimensional point sets of this nature. Two variants of the HMM were developed for modelling: (1) axial data; and (2) directional data. The former, based on a combination of Student’s t, Watson and Gaussian distributions, was used to register hybrid point sets comprising magnetic resonance diffusion tensor image (DTI)-derived quantities, such as voxel spatial positions (defining a region/structure of interest), associated fibre orientations, and scalar measures reflecting tissue anisotropy. The latter meanwhile, formulated using a combination of Student’s t and Von-Mises-Fisher distributions, is used for the registration of shapes represented as hybrid point sets comprising spatial positions and associated surface normal vectors. The Watson-variant of the HMM facilitates statistical analysis and group-wise comparisons of DTI data across patient populations, presented as an exemplar application of the proposed approach. The Fisher-variant of the HMM on the other hand, was used to register hybrid representations of shapes, providing substantial improvements over point-based registration approaches in terms of anatomical validity in the estimated correspondences

Exploration of the Human Purkinje Network in Virtual Populations

This thesis investigates the Purkinje network (PN) and its dependency on the heart shape (HS) through cardiac simulation on virtual populations (VPs). The heart is a complex organ and essential to the wellbeing of humans; its dysfunction is responsible for more than 27% of all deaths in the UK. The PN delivers the activation impulse to the ventricles of the heart and ensures their synchronous activation. Thus, the morphology of the PN is important, but it varies between species and in vivo imaging is not feasible. However, computer simulation could provide an alternative experimental tool. In simulation of the cardiac electrophysiology, the PN is often replaced by stimulus points on the HS that are fitted to physiological measurements (heart activation times, ECG). Thus, not allowing the study of the PN morphology, nor studies of arrhythmia involving re-entry into the PN. In this thesis, three studies involving explicit models of PNs have been conducted. First, an efficient algorithm for solving electrophysiology models for the PN is introduced. These allow performing simulations of physiological activations. To minimise the time for simulations, parallelisation with CPU and GPU architectures are investigated, which is of interest for VP studies. In the second study, false tendons (FTs) are studied, which provide an additional connection from the left bundle branch (LBB) and are potentially beneficial in case of LBB block. Therefore, the reduction in activation times by FT is studied as a function of the HS. In the third study, an automatically generated VP is used to explore uncertainty in the PN morphology. The conjecture is that the PN structure adapts to the HS. The coverage of the septum and the minimum distance of the PN to the base are varied. The features of the resulting ECG are used to find the PN that gives maximally synchronised contraction