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

Image Guided Respiratory Motion Analysis: Time Series and Image Registration.

The efficacy of Image guided radiation therapy (IGRT) systems relies on accurately extracting, modeling and predicting tumor movement with imaging techniques. This thesis investigates two key problems associated with such systems: motion modeling and image processing. For thoracic and upper abdominal tumors, respiratory motion is the dominant factor for tumor movement. We have studied several special structured time series analysis techniques to incorporate the semi-periodicity characteristics of respiratory motion. The proposed methods are robust towards large variations among fractions and populations; the algorithms perform stably in the presence of sparse radiographic observations with noise. We have proposed a subspace projection method to quantitatively evaluate the semi-periodicity of a given observation trace; a nonparametric local regression approach for real-time prediction of respiratory motion; a state augmentation scheme to model hysteresis; and an ellipse tracking algorithm to estimate the trend of respiratory motion in real time. For image processing, we have focused on designing regularizations to account for prior information in image registration problems. We investigated a penalty function design that accommodates tissue-type-dependent elasticity information. We studied a class of discontinuity preserving regularizers that yield smooth deformation estimates in most regions, yet allow discontinuities supported by data. We have further proposed a discriminate regularizer that preserves shear discontinuity, but discourages folding or vacuum generating flows. In addition, we have initiated a preliminary principled study on the fundamental performance limit of image registration problems. We proposed a statistical generative model to account for noise effect in both source and target images, and investigated the approximate performance of the maximum-likelihood estimator corresponding to the generative model and the commonly adopted M-estimator. A simple example suggests that the approximation is reasonably accurate. Our studies in both time series analysis and image registration constitute essential building-blocks for clinical applications such as adaptive treatment. Besides their theoretical interests, it is our sincere hope that with further justifications, the proposed techniques would realize its clinical value, and improve the quality of life for patients.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/60673/1/druan_1.pd

Anatomical Image Series Analysis in the Computational Anatomy Random Orbit Model

Serially acquired medical imagery plays an important role in the computational study of human anatomy. In this work, we describe the development of novel algorithms set in the large deformation diffeomorphic metric mapping framework for analyzing serially acquired imagery of two general types: spatial image series and temporal image series. In the former case, a critical step in the analysis of neural connectivity from serially-sectioned brain histology data is the reconstruction of spatially distorted image volumes and registration into a common coordinate space. In the latter case, computational methods are required for building low dimensional representations of the infinite dimensional shape space standard to computational anatomy. Here, we review the vast body of work related to volume reconstruction and atlas-mapping of serially-sectioned data as well as diffeomorphic methods for longitudinal data and we position our work relative to these in the context of the computational anatomy random orbit model. We show how these two problems are embedded as extensions to the classic random orbit model and use it to both enforce diffeomorphic conditions and analyze the distance metric associated to diffeomorphisms. We apply our new algorithms to histology and MRI datasets to study the structure, connectivity, and pathological degeneration of the brain

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceComputational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model the organ development across time (growth or aging), to establish their variability, and to correlate this variability information with other functional, genetic or structural information. The Mathematical Foundations of Computational Anatomy (MFCA) workshop aims at fostering the interactions between the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum for the exchange of the theoretical ideas and aims at being a source of inspiration for new methodological developments in computational anatomy. A special emphasis is put on theoretical developments, applications and results being welcomed as illustrations. Following the successful rst edition of this workshop in 20061 and second edition in New-York in 20082, the third edition was held in Toronto on September 22 20113. Contributions were solicited in Riemannian and group theoretical methods, geometric measurements of the anatomy, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, modeling of growth and longitudinal shape changes. 22 submissions were reviewed by three members of the program committee. To guaranty a high level program, 11 papers only were selected for oral presentation in 4 sessions. Two of these sessions regroups classical themes of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session of 5 papers addresses more application oriented works on computational anatomy

Automatic Spatiotemporal Analysis of Cardiac Image Series

RÉSUMÉ À ce jour, les maladies cardiovasculaires demeurent au premier rang des principales causes de décès en Amérique du Nord. Chez l’adulte et au sein de populations de plus en plus jeunes, la soi-disant épidémie d’obésité entraînée par certaines habitudes de vie tels que la mauvaise alimentation, le manque d’exercice et le tabagisme est lourde de conséquences pour les personnes affectées, mais aussi sur le système de santé. La principale cause de morbidité et de mortalité chez ces patients est l’athérosclérose, une accumulation de plaque à l’intérieur des vaisseaux sanguins à hautes pressions telles que les artères coronaires. Les lésions athérosclérotiques peuvent entraîner l’ischémie en bloquant la circulation sanguine et/ou en provoquant une thrombose. Cela mène souvent à de graves conséquences telles qu’un infarctus. Outre les problèmes liés à la sténose, les parois artérielles des régions criblées de plaque augmentent la rigidité des parois vasculaires, ce qui peut aggraver la condition du patient. Dans la population pédiatrique, la pathologie cardiovasculaire acquise la plus fréquente est la maladie de Kawasaki. Il s’agit d’une vasculite aigüe pouvant affecter l’intégrité structurale des parois des artères coronaires et mener à la formation d’anévrismes. Dans certains cas, ceux-ci entravent l’hémodynamie artérielle en engendrant une perfusion myocardique insuffisante et en activant la formation de thromboses. Le diagnostic de ces deux maladies coronariennes sont traditionnellement effectués à l’aide d’angiographies par fluoroscopie. Pendant ces examens paracliniques, plusieurs centaines de projections radiographiques sont acquises en séries suite à l’infusion artérielle d’un agent de contraste. Ces images révèlent la lumière des vaisseaux sanguins et la présence de lésions potentiellement pathologiques, s’il y a lieu. Parce que les séries acquises contiennent de l’information très dynamique en termes de mouvement du patient volontaire et involontaire (ex. battements cardiaques, respiration et déplacement d’organes), le clinicien base généralement son interprétation sur une seule image angiographique où des mesures géométriques sont effectuées manuellement ou semi-automatiquement par un technicien en radiologie. Bien que l’angiographie par fluoroscopie soit fréquemment utilisé partout dans le monde et souvent considéré comme l’outil de diagnostic “gold-standard” pour de nombreuses maladies vasculaires, la nature bidimensionnelle de cette modalité d’imagerie est malheureusement très limitante en termes de spécification géométrique des différentes régions pathologiques. En effet, la structure tridimensionnelle des sténoses et des anévrismes ne peut pas être pleinement appréciée en 2D car les caractéristiques observées varient selon la configuration angulaire de l’imageur. De plus, la présence de lésions affectant les artères coronaires peut ne pas refléter la véritable santé du myocarde, car des mécanismes compensatoires naturels (ex. vaisseaux----------ABSTRACT Cardiovascular disease continues to be the leading cause of death in North America. In adult and, alarmingly, ever younger populations, the so-called obesity epidemic largely driven by lifestyle factors that include poor diet, lack of exercise and smoking, incurs enormous stresses on the healthcare system. The primary cause of serious morbidity and mortality for these patients is atherosclerosis, the build up of plaque inside high pressure vessels like the coronary arteries. These lesions can lead to ischemic disease and may progress to precarious blood flow blockage or thrombosis, often with infarction or other severe consequences. Besides the stenosis-related outcomes, the arterial walls of plaque-ridden regions manifest increased stiffness, which may exacerbate negative patient prognosis. In pediatric populations, the most prevalent acquired cardiovascular pathology is Kawasaki disease. This acute vasculitis may affect the structural integrity of coronary artery walls and progress to aneurysmal lesions. These can hinder the blood flow’s hemodynamics, leading to inadequate downstream perfusion, and may activate thrombus formation which may lead to precarious prognosis. Diagnosing these two prominent coronary artery diseases is traditionally performed using fluoroscopic angiography. Several hundred serial x-ray projections are acquired during selective arterial infusion of a radiodense contrast agent, which reveals the vessels’ luminal area and possible pathological lesions. The acquired series contain highly dynamic information on voluntary and involuntary patient movement: respiration, organ displacement and heartbeat, for example. Current clinical analysis is largely limited to a single angiographic image where geometrical measures will be performed manually or semi-automatically by a radiological technician. Although widely used around the world and generally considered the gold-standard diagnosis tool for many vascular diseases, the two-dimensional nature of this imaging modality is limiting in terms of specifying the geometry of various pathological regions. Indeed, the 3D structures of stenotic or aneurysmal lesions may not be fully appreciated in 2D because their observable features are dependent on the angular configuration of the imaging gantry. Furthermore, the presence of lesions in the coronary arteries may not reflect the true health of the myocardium, as natural compensatory mechanisms may obviate the need for further intervention. In light of this, cardiac magnetic resonance perfusion imaging is increasingly gaining attention and clinical implementation, as it offers a direct assessment of myocardial tissue viability following infarction or suspected coronary artery disease. This type of modality is plagued, however, by motion similar to that present in fluoroscopic imaging. This issue predisposes clinicians to laborious manual intervention in order to align anatomical structures in sequential perfusion frames, thus hindering automation o

Automatic Spatiotemporal Analysis of Cardiac Image Series

RÉSUMÉ À ce jour, les maladies cardiovasculaires demeurent au premier rang des principales causes de décès en Amérique du Nord. Chez l’adulte et au sein de populations de plus en plus jeunes, la soi-disant épidémie d’obésité entraînée par certaines habitudes de vie tels que la mauvaise alimentation, le manque d’exercice et le tabagisme est lourde de conséquences pour les personnes affectées, mais aussi sur le système de santé. La principale cause de morbidité et de mortalité chez ces patients est l’athérosclérose, une accumulation de plaque à l’intérieur des vaisseaux sanguins à hautes pressions telles que les artères coronaires. Les lésions athérosclérotiques peuvent entraîner l’ischémie en bloquant la circulation sanguine et/ou en provoquant une thrombose. Cela mène souvent à de graves conséquences telles qu’un infarctus. Outre les problèmes liés à la sténose, les parois artérielles des régions criblées de plaque augmentent la rigidité des parois vasculaires, ce qui peut aggraver la condition du patient. Dans la population pédiatrique, la pathologie cardiovasculaire acquise la plus fréquente est la maladie de Kawasaki. Il s’agit d’une vasculite aigüe pouvant affecter l’intégrité structurale des parois des artères coronaires et mener à la formation d’anévrismes. Dans certains cas, ceux-ci entravent l’hémodynamie artérielle en engendrant une perfusion myocardique insuffisante et en activant la formation de thromboses. Le diagnostic de ces deux maladies coronariennes sont traditionnellement effectués à l’aide d’angiographies par fluoroscopie. Pendant ces examens paracliniques, plusieurs centaines de projections radiographiques sont acquises en séries suite à l’infusion artérielle d’un agent de contraste. Ces images révèlent la lumière des vaisseaux sanguins et la présence de lésions potentiellement pathologiques, s’il y a lieu. Parce que les séries acquises contiennent de l’information très dynamique en termes de mouvement du patient volontaire et involontaire (ex. battements cardiaques, respiration et déplacement d’organes), le clinicien base généralement son interprétation sur une seule image angiographique où des mesures géométriques sont effectuées manuellement ou semi-automatiquement par un technicien en radiologie. Bien que l’angiographie par fluoroscopie soit fréquemment utilisé partout dans le monde et souvent considéré comme l’outil de diagnostic “gold-standard” pour de nombreuses maladies vasculaires, la nature bidimensionnelle de cette modalité d’imagerie est malheureusement très limitante en termes de spécification géométrique des différentes régions pathologiques. En effet, la structure tridimensionnelle des sténoses et des anévrismes ne peut pas être pleinement appréciée en 2D car les caractéristiques observées varient selon la configuration angulaire de l’imageur. De plus, la présence de lésions affectant les artères coronaires peut ne pas refléter la véritable santé du myocarde, car des mécanismes compensatoires naturels (ex. vaisseaux----------ABSTRACT Cardiovascular disease continues to be the leading cause of death in North America. In adult and, alarmingly, ever younger populations, the so-called obesity epidemic largely driven by lifestyle factors that include poor diet, lack of exercise and smoking, incurs enormous stresses on the healthcare system. The primary cause of serious morbidity and mortality for these patients is atherosclerosis, the build up of plaque inside high pressure vessels like the coronary arteries. These lesions can lead to ischemic disease and may progress to precarious blood flow blockage or thrombosis, often with infarction or other severe consequences. Besides the stenosis-related outcomes, the arterial walls of plaque-ridden regions manifest increased stiffness, which may exacerbate negative patient prognosis. In pediatric populations, the most prevalent acquired cardiovascular pathology is Kawasaki disease. This acute vasculitis may affect the structural integrity of coronary artery walls and progress to aneurysmal lesions. These can hinder the blood flow’s hemodynamics, leading to inadequate downstream perfusion, and may activate thrombus formation which may lead to precarious prognosis. Diagnosing these two prominent coronary artery diseases is traditionally performed using fluoroscopic angiography. Several hundred serial x-ray projections are acquired during selective arterial infusion of a radiodense contrast agent, which reveals the vessels’ luminal area and possible pathological lesions. The acquired series contain highly dynamic information on voluntary and involuntary patient movement: respiration, organ displacement and heartbeat, for example. Current clinical analysis is largely limited to a single angiographic image where geometrical measures will be performed manually or semi-automatically by a radiological technician. Although widely used around the world and generally considered the gold-standard diagnosis tool for many vascular diseases, the two-dimensional nature of this imaging modality is limiting in terms of specifying the geometry of various pathological regions. Indeed, the 3D structures of stenotic or aneurysmal lesions may not be fully appreciated in 2D because their observable features are dependent on the angular configuration of the imaging gantry. Furthermore, the presence of lesions in the coronary arteries may not reflect the true health of the myocardium, as natural compensatory mechanisms may obviate the need for further intervention. In light of this, cardiac magnetic resonance perfusion imaging is increasingly gaining attention and clinical implementation, as it offers a direct assessment of myocardial tissue viability following infarction or suspected coronary artery disease. This type of modality is plagued, however, by motion similar to that present in fluoroscopic imaging. This issue predisposes clinicians to laborious manual intervention in order to align anatomical structures in sequential perfusion frames, thus hindering automation o

Automatic whole heart segmentation based on image registration

Whole heart segmentation can provide important morphological information of the heart, potentially enabling the development of new clinical applications and the planning and guidance of cardiac interventional procedures. This information can be extracted from medical images, such as these of magnetic resonance imaging (MRI), which is becoming a routine modality for the determination of cardiac morphology. Since manual delineation is labour intensive and subject to observer variation, it is highly desirable to develop an automatic method. However, automating the process is complicated by the large shape variation of the heart and limited quality of the data. The aim of this work is to develop an automatic and robust segmentation framework from cardiac MRI while overcoming these difficulties. The main challenge of this segmentation is initialisation of the substructures and inclusion of shape constraints. We propose the locally affine registration method (LARM) and the freeform deformations with adaptive control point status to tackle the challenge. They are applied to the atlas propagation based segmentation framework, where the multi-stage scheme is used to hierarchically increase the degree of freedom. In this segmentation framework, it is also needed to compute the inverse transformation for the LARM registration. Therefore, we propose a generic method, using Dynamic Resampling And distance Weighted interpolation (DRAW), for inverting dense displacements. The segmentation framework is validated on a clinical dataset which includes nine pathologies. To further improve the nonrigid registration against local intensity distortions in the images, we propose a generalised spatial information encoding scheme and the spatial information encoded mutual information (SIEMI) registration. SIEMI registration is applied to the segmentation framework to improve the accuracy. Furthermore, to demonstrate the general applicability of SIEMI registration, we apply it to the registration of cardiac MRI, brain MRI, and the contrast enhanced MRI of the liver. SIEMI registration is shown to perform well and achieve significantly better accuracy compared to the registration using normalised mutual information

Automated analysis and visualization of preclinical whole-body microCT data

In this thesis, several strategies are presented that aim to facilitate the analysis and visualization of whole-body in vivo data of small animals. Based on the particular challenges for image processing, when dealing with whole-body follow-up data, we addressed several aspects in this thesis. The developed methods are tailored to handle data of subjects with significantly varying posture and address the large tissue heterogeneity of entire animals. In addition, we aim to compensate for lacking tissue contrast by relying on approximation of organs based on an animal atlas. Beyond that, we provide a solution to automate the combination of multimodality, multidimensional data.* Advanced School for Computing and Imaging (ASCI), Delft, NL * Bontius Stichting inz Doelfonds Beeldverwerking, Leiden, NL * Caliper Life Sciences, Hopkinton, USA * Foundation Imago, Oegstgeest, NLUBL - phd migration 201