Deformable Groupwise Registration Using a Locally Low-Rank Dissimilarity Metric for Myocardial Strain Estimation from Cardiac Cine MRI Images

Objective: Cardiovascular magnetic resonance-feature tracking (CMR-FT) represents a group of methods for myocardial strain estimation from cardiac cine MRI images. Established CMR-FT methods are mainly based on optical flow or pairwise registration. However, these methods suffer from either inaccurate estimation of large motion or drift effect caused by accumulative tracking errors. In this work, we propose a deformable groupwise registration method using a locally low-rank (LLR) dissimilarity metric for CMR-FT. Methods: The proposed method (Groupwise-LLR) tracks the feature points by a groupwise registration-based two-step strategy. Unlike the globally low-rank (GLR) dissimilarity metric, the proposed LLR metric imposes low-rankness on local image patches rather than the whole image. We quantitatively compared Groupwise-LLR with the Farneback optical flow, a pairwise registration method, and a GLR-based groupwise registration method on simulated and in vivo datasets. Results: Results from the simulated dataset showed that Groupwise-LLR achieved more accurate tracking and strain estimation compared with the other methods. Results from the in vivo dataset showed that Groupwise-LLR achieved more accurate tracking and elimination of the drift effect in late-diastole. Inter-observer reproducibility of strain estimates was similar between all studied methods. Conclusion: The proposed method estimates myocardial strains more accurately due to the application of a groupwise registration-based tracking strategy and an LLR-based dissimilarity metric. Significance: The proposed CMR-FT method may facilitate more accurate estimation of myocardial strains, especially in diastole, for clinical assessments of cardiac dysfunction

Variational Methods in Shape Space

This dissertation deals with the application of variational methods in spaces of geometric shapes. In particular, the treated topics include shape averaging, principal component analysis in shape space, computation of geodesic paths in shape space, as well as shape optimisation. Chapter 1 provides a brief overview over the employed models of shape space. Geometric shapes are identified with two- or three-dimensional, deformable objects. Deformations will be described via physical models; in particular, the objects will be interpreted as consisting of either a hyperelastic solid or a viscous liquid material. Furthermore, the description of shapes via phase fields or level sets is briefly introduced. Chapter 2 reviews different and related approaches to shape space modelling. References to related topics in image segmentation and registration are also provided. Finally, the relevant shape optimisation literature is introduced. Chapter 3 recapitulates the employed concepts from continuum mechanics and phase field modelling and states basic theoretical results needed for the later analysis. Chapter 4 addresses the computation of shape averages, based on a hyperelastic notion of shape dissimilarity: The dissimilarity between two shapes is measured as the minimum deformation energy required to deform the first into the second shape. A corresponding phase-field model is introduced, analysed, and finally implemented numerically via finite elements. A principal component analysis of shapes, which is consistent with the previously introduced average, is considered in Chapter 5. Elastic boundary stresses on the average shape are used as representatives of the input shapes in a linear vector space. On these linear representatives, a standard principal component analysis can be performed, where the employed covariance metric should be properly chosen to depend on the input shapes. Chapter 6 interprets shapes as belonging to objects made of a viscous liquid and correspondingly defines geodesic paths between shapes. The energy of a path is given as the total physical dissipation during the deformation of an object along the path. A rigid body motion invariant time discretisation is achieved by approximating the dissipation along a path segment by the deformation energy of a small solid deformation. The numerical implementation is based on level sets. Chapter 7 is concerned with the optimisation of the geometry and topology of solid structures that are subject to a mechanical load. Given the load configuration, the structure rigidity, its volume, and its surface area shall be optimally balanced. A phase field model is devised and analysed for this purpose. In this context, the use of nonlinear elasticity allows to detect buckling phenomena which would be ignored in linearised elasticity

Advanced Medical Image Registration Methods for Quantitative Imaging and Multi-Channel Images

This thesis proposes advanced medical image registration methods for applications that can be grouped in two broad themes. The first theme focuses on registration techniques increasing the reliability of _quantitative measurements_ extracted from sets of medical images. The second theme that is considered in this thesis is the registration of _multi-channel_ images

Analysis of the developing brain using image registration

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