Groupwise Multimodal Image Registration using Joint Total Variation

In medical imaging it is common practice to acquire a wide range of modalities (MRI, CT, PET, etc.), to highlight different structures or pathologies. As patient movement between scans or scanning session is unavoidable, registration is often an essential step before any subsequent image analysis. In this paper, we introduce a cost function based on joint total variation for such multimodal image registration. This cost function has the advantage of enabling principled, groupwise alignment of multiple images, whilst being insensitive to strong intensity non-uniformities. We evaluate our algorithm on rigidly aligning both simulated and real 3D brain scans. This validation shows robustness to strong intensity non-uniformities and low registration errors for CT/PET to MRI alignment. Our implementation is publicly available at https://github.com/brudfors/coregistration-njtv

A Combinatorial Solution to Non-Rigid 3D Shape-to-Image Matching

We propose a combinatorial solution for the problem of non-rigidly matching a 3D shape to 3D image data. To this end, we model the shape as a triangular mesh and allow each triangle of this mesh to be rigidly transformed to achieve a suitable matching to the image. By penalising the distance and the relative rotation between neighbouring triangles our matching compromises between image and shape information. In this paper, we resolve two major challenges: Firstly, we address the resulting large and NP-hard combinatorial problem with a suitable graph-theoretic approach. Secondly, we propose an efficient discretisation of the unbounded 6-dimensional Lie group SE(3). To our knowledge this is the first combinatorial formulation for non-rigid 3D shape-to-image matching. In contrast to existing local (gradient descent) optimisation methods, we obtain solutions that do not require a good initialisation and that are within a bound of the optimal solution. We evaluate the proposed method on the two problems of non-rigid 3D shape-to-shape and non-rigid 3D shape-to-image registration and demonstrate that it provides promising results.Comment: 10 pages, 7 figure

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Gaussian Process Morphable Models

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models, and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, an SSM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics, but is flexible enough to explain shapes that cannot be represented by the SSM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach, whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes,including methods for multi-scale, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images

Diffeomorphic image registration with applications to deformation modelling between multiple data sets

Over last years, the diffeomorphic image registration algorithms have been successfully introduced into the field of the medical image analysis. At the same time, the particular usability of these techniques, in majority derived from the solid mathematical background, has been only quantitatively explored for the limited applications such as longitudinal studies on treatment quality, or diseases progression. The thesis considers the deformable image registration algorithms, seeking out those that maintain the medical correctness of the estimated dense deformation fields in terms of the preservation of the object and its neighbourhood topology, offer the reasonable computational complexity to satisfy time restrictions coming from the potential applications, and are able to cope with low quality data typically encountered in Adaptive Radiotherapy (ART). The research has led to the main emphasis being laid on the diffeomorphic image registration to achieve one-to-one mapping between images. This involves introduction of the log-domain parameterisation of the deformation field by its approximation via a stationary velocity field. A quantitative and qualitative examination of existing and newly proposed algorithms for pairwise deformable image registration presented in this thesis, shows that the log-Euclidean parameterisation can be successfully utilised in the biomedical applications. Although algorithms utilising the log-domain parameterisation have theoretical justification for maintaining diffeomorphism, in general, the deformation fields produced by them have similar properties as these estimated by classical methods. Having this in mind, the best compromise in terms of the quality of the deformation fields has been found for the consistent image registration framework. The experimental results suggest also that the image registration with the symmetrical warping of the input images outperforms the classical approaches, and simultaneously can be easily introduced to most known algorithms. Furthermore, the log-domain implicit group-wise image registration is proposed. By linking the various sets of images related to the different subjects, the proposed image registration approach establishes a common subject space and between-subject correspondences therein. Although the correspondences between groups of images can be found by performing the classic image registration, the reference image selection (not required in the proposed implementation), may lead to a biased mean image being estimated and the corresponding common subject space not adequate to represent the general properties of the data sets. The approaches to diffeomorphic image registration have been also utilised as the principal elements for estimating the movements of the organs in the pelvic area based on the dense deformation field prediction system driven by the partial information coming from the specific type of the measurements parameterised using the implicit surface representation, and recognising facial expressions where the stationary velocity fields are used as the facial expression descriptors. Both applications have been extensively evaluated based on the real representative data sets of three-dimensional volumes and two-dimensional images, and the obtained results indicate the practical usability of the proposed techniques

Dual Quaternions as Constraints in 4D-DPM Models for Pose Estimation

This work was partially financed by Plan Nacional de Investigacion y Desarrollo (I+D), Comision Interministerial de Ciencia y Tecnologia (FEDER-CICYT) under the project DPI2013-44227-R.Martínez Bertí, E.; Sánchez Salmerón, AJ.; Ricolfe Viala, C. (2017). Dual Quaternions as Constraints in 4D-DPM Models for Pose Estimation. Sensors. 17 (8)(1913):1-16. https://doi.org/10.3390/s17081913S11617 (8)191