Efficient probabilistic and geometric anatomical mapping using particle mesh approximation on GPUs

pre-printDeformable image registration in the presence of considerable contrast differences and large size and shape changes presents significant research challenges. First, it requires a robust registration framework that does not depend on intensity measurements and can handle large nonlinear shape variations. Second, it involves the expensive computation of nonlinear deformations with high degrees of freedom. Often it takes a significant amount of computation time and thus becomes infeasible for practical purposes. In this paper, we present a solution based on two key ideas: a new registration method that generates a mapping between anatomies represented as a multicompartment model of class posterior images and geometries and an implementation of the algorithm using particle mesh approximation on Graphical Processing Units (GPUs) to fulfill the computational requirements. We show results on the registrations of neonatal to 2-year old infant MRIs. Quantitative validation demonstrates that our proposed method generates registrations that better maintain the consistency of anatomical structures over time and provides transformations that better preserve structures undergoing large deformations than transformations obtained by standard intensity-only registration. We also achieve the speedup of three orders of magnitudes compared to a CPU reference implementation, making it possible to use the technique in time-critical applications

ANALYSIS OF GEOMETRIC SHAPES WITH VARIFOLD REPRESENTATION

This thesis is concerned with the theory and applications of varifolds to the representation, approximation, and diffeomorphic registration of shapes. Originating from geometric measure theory, the theory of varifolds provides a convenient way to represent geometric shapes like curves, surfaces or, submanifolds both in continuous and discrete settings. Previous works in shape analysis have made use of this representation as a surrogate to design numerically tractable fidelity terms for curve and surface registration problems. So far, these approaches have primarily focused on processing submanifold data and were not designed to handle more general structures. The varifold representation however provides a very flexible framework that is not restricted to submanifolds but its generality has not yet been exploited to its full extent in shape analysis. In this work, we take a step in this direction by considering deformations acting on general varifolds, and propose a mathematical model for diffeomorphic registration of varifolds under a natural group action which we formulate as an optimal control problem. This new framework allows us to tackle diffeomorphic registration problems for a much wider class of geometric objects and lead to a more versatile algorithmic pipeline. Varifold matching frameworks heavily rely on the kernel metrics defined on the varifolds spaces. However, the properties of this type of metrics and their relationships with the classical metrics/topologies on measure spaces have not been investigated thoroughly yet. In this work, we study in detail the construction of kernel metrics on the space of varifold and the resulting topological properties of those metrics. Based on these results, we address the problem of optimal finite approximations (quantization) for kernel metrics, propose a projection-based approach for varifold representation, and show a $\Gamma$-convergence property for the discrete registration functionals. In the last part of this thesis, we tackle the imbalanced shape matching problems, namely the situation in which the source and target shapes involve considerable variations of mass or density which cannot be entirely described by diffeomorphic transformations. We extend our varifold matching model by augmenting the diffeomorphic component with a global or local density changes. Based on the optimality conditions provided by the Pontryagin maximum principle, we derive a shooting algorithm to numerically estimate solutions and illustrate the practical interest of this model for several types of geometric data such as fiber bundles with inconsistent fiber densities or partially observed and incomplete surfaces

Uncertainty Quantification, Image Synthesis and Deformation Prediction for Image Registration

Image registration is essential for medical image analysis to provide spatial correspondences. It is a difficult problem due to the modeling complexity of image appearance and the computational complexity of the deformable registration models. Thus, several techniques are needed: Uncertainty measurements of the high-dimensional parameter space of the registration methods for the evaluation of the registration result; Registration methods for registering healthy medical images to pathological images with large appearance changes; Fast registration prediction techniques for uni-modal and multi-modal images. This dissertation addresses these problems and makes the following contributions: 1) A frame- work for uncertainty quantification of image registration results is proposed. The proposed method for uncertainty quantification utilizes a low-rank Hessian approximation to evaluate the variance/co- variance of the variational Gaussian distribution of the registration parameters. The method requires significantly less storage and computation time than computing the Hessian via finite difference while achieving excellent approximation accuracy, facilitating the computation of the variational approximation; 2) An image synthesis deep network for pathological image registration is developed. The network transforms a pathological image into a ‘quasi-normal’ image, making registrations more accurate; 3) A patch-based deep learning framework for registration parameter prediction using image appearances only is created. The network is capable of accurately predicting the initial momentum for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model for both uni-modal and multi-modal registration problems, while increasing the registration speed by at least an order of magnitude compared with optimization-based approaches and maintaining the theoretical properties of LDDMM. Applications of the methods include 1) Uncertainty quantification of LDDMM for 2D and 3D medical image registrations, which could be used for uncertainty-based image smoothing and subsequent analysis; 2) Quasi-normal image synthesis for the registration of brain images with tumors with potential extensions to other image registration problems with pathologies and 3) deformation prediction for various brain datasets and T1w/T2w magnetic resonance images (MRI), which could be incorporated into other medical image analysis tasks such as fast multi-atlas image segmentation, fast geodesic image regression, fast atlas construction and fast user-interactive registration refinement.Doctor of Philosoph

Large Deformation Diffeomorphic Metric Mapping Provides New Insights into the Link Between Human Ear Morphology and the Head-Related Transfer Functions

The research findings presented in this thesis is composed of four sections. In the first section of this thesis, it is shown how LDDMM can be applied to deforming head and ear shapes in the context of morphoacoustic study. Further, tools are developed to measure differences in 3D shapes using the framework of currents and also to compare and measure the differences between the acoustic responses obtained from BEM simulations for two ear shapes. Finally this section introduces the multi-scale approach for mapping ear shapes using LDDMM. The second section of the thesis estimates a template ear, head and torso shape from the shapes available in the SYMARE database. This part of the thesis explains a new procedure for developing the template ear shape. The template ear and head shapes were are verified by comparing the features in the template shapes to corresponding features in the CIPIC and SYMARE database population. The third section of the thesis examines the quality of the deformations from the template ear shape to target ears in SYMARE from both an acoustic and morphological standpoint. As a result of this investigation, it was identified that ear shapes can be studied more accurately by the use of two physical scales and that scales at which the ear shapes were studied were dependent on the parameters chosen when mapping ears in the LDDMM framework. Finally, this section concludes by noting how shape distances vary with the acoustic distances using the developed tools. In the final part of this thesis, the variations in the morphology of ears are examined using the Kernel Principle Component Analysis (KPCA) and the changes in the corresponding acoustics are studied using the standard principle component analysis (PCA). These examinations involved identifying the number of kernel principle components that are required in order to model ear shapes with an acceptable level of accuracy, both morphologically and acoustically

Doctor of Philosophy

dissertationStochastic methods, dense free-form mapping, atlas construction, and total variation are examples of advanced image processing techniques which are robust but computationally demanding. These algorithms often require a large amount of computational power as well as massive memory bandwidth. These requirements used to be ful lled only by supercomputers. The development of heterogeneous parallel subsystems and computation-specialized devices such as Graphic Processing Units (GPUs) has brought the requisite power to commodity hardware, opening up opportunities for scientists to experiment and evaluate the in uence of these techniques on their research and practical applications. However, harnessing the processing power from modern hardware is challenging. The di fferences between multicore parallel processing systems and conventional models are signi ficant, often requiring algorithms and data structures to be redesigned signi ficantly for efficiency. It also demands in-depth knowledge about modern hardware architectures to optimize these implementations, sometimes on a per-architecture basis. The goal of this dissertation is to introduce a solution for this problem based on a 3D image processing framework, using high performance APIs at the core level to utilize parallel processing power of the GPUs. The design of the framework facilitates an efficient application development process, which does not require scientists to have extensive knowledge about GPU systems, and encourages them to harness this power to solve their computationally challenging problems. To present the development of this framework, four main problems are described, and the solutions are discussed and evaluated: (1) essential components of a general 3D image processing library: data structures and algorithms, as well as how to implement these building blocks on the GPU architecture for optimal performance; (2) an implementation of unbiased atlas construction algorithms|an illustration of how to solve a highly complex and computationally expensive algorithm using this framework; (3) an extension of the framework to account for geometry descriptors to solve registration challenges with large scale shape changes and high intensity-contrast di fferences; and (4) an out-of-core streaming model, which enables developers to implement multi-image processing techniques on commodity hardware

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

Shape-correlated statistical modeling and analysis for respiratory motion estimation

Respiratory motion challenges image-guided radiation therapy (IGRT) with location uncertainties of important anatomical structures in the thorax. Effective and accurate respiration estimation is crucial to account for the motion effects on the radiation dose to tumors and organs at risk. Moreover, serious image artifacts present in treatment-guidance images such 4D cone-beam CT cause difficulties in identifying spatial variations. Commonly used non-linear dense image matching methods easily fail in regions where artifacts interfere. Learning-based linear motion modeling techniques have the advantage of incorporating prior knowledge for robust motion estimation. In this research shape-correlation deformation statistics (SCDS) capture strong correlations between the shape of the lung and the dense deformation field under breathing. Dimension reduction and linear regression techniques are used to extract the correlation statistics. Based on the assumption that the deformation correlations are consistent between planning and treatment time, patient-specific SCDS trained from a 4D planning image sequence is used to predict the respiratory motion in the patient's artifact-laden 4D treatment image sequence. Furthermore, a prediction-driven atlas formation method is developed to weaken the consistency assumption, by integrating intensity information from the target images and the SCDS predictions into a common optimization framework. The strategy of balancing between the prediction constraints and the intensity-matching forces makes the method less sensitive to variation in the correlation and utilizes intensity information besides the lung boundaries. This strategy thus provides improved motion estimation accuracy and robustness. The SCDS-based methods are shown to be effective in modeling and estimating respiratory motion in lung, with evaluations and comparisons carried out on both simulated images and patient images