Automatic segmentation of wall structures from cardiac images

One important topic in medical image analysis is segmenting wall structures from different cardiac medical imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI). This task is typically done by radiologists either manually or semi-automatically, which is a very time-consuming process. To reduce the laborious human efforts, automatic methods have become popular in this research. In this thesis, features insensitive to data variations are explored to segment the ventricles from CT images and extract the left atrium from MR images. As applications, the segmentation results are used to facilitate cardiac disease analysis. Specifically, 1. An automatic method is proposed to extract the ventricles from CT images by integrating surface decomposition with contour evolution techniques. In particular, the ventricles are first identified on a surface extracted from patient-specific image data. Then, the contour evolution is employed to refine the identified ventricles. The proposed method is robust to variations of ventricle shapes, volume coverages, and image quality. 2. A variational region-growing method is proposed to segment the left atrium from MR images. Because of the localized property of this formulation, the proposed method is insensitive to data variabilities that are hard to handle by globalized methods. 3. In applications, a geometrical computational framework is proposed to estimate the myocardial mass at risk caused by stenoses. In addition, the segmentation of the left atrium is used to identify scars for MR images of post-ablation.PhDCommittee Chair: Yezzi, Anthony; Committee Co-Chair: Tannenbaum, Allen; Committee Member: Egerstedt, Magnus ; Committee Member: Fedele, Francesco ; Committee Member: Stillman, Arthur; Committee Member: Vela,Patrici

Variational methods for texture segmentation

In the last decades, image production has grown significantly. From digital photographs to the medical scans, including satellite images and video films, more and more data need to be processed. Consequently the number of applications based on digital images has increased, either for medicine, research for country planning or for entertainment business such as animation or video games. All these areas, although very different one to another, need the same image processing techniques. Among all these techniques, segmentation is probably one of the most studied because of its important role. Segmentation is the process of extracting meaningful objects from an image. This task, although easily achieved by the human visual system, is actually complex and still a true challenge for the image processing community despite several decades of research. The thesis work presented in this manuscript proposes solutions to the image segmentation problem in a well established mathematical framework, i.e. variational models. The image is defined in a continuous space and the segmentation problem is expressed through a functional or energy optimization. Depending on the object to be segmented, this energy definition can be difficult; in particular for objects with ambiguous borders or objects with textures. For the latter, the difficulty lies already in the definition of the term texture. The human eye can easily recognize a texture, but it is quite difficult to find words to define it, even more in mathematical terms. There is a deliberate vagueness in the definition of texture which explains the difficulty to conceptualize a model able to describe it. Often these textures can neither be described by homogeneous regions nor by sharp contours. This is why we are first interested in the extraction of texture features, that is to say, finding one representation that can discriminate a textured region from another. The first contribution of this thesis is the construction of a texture descriptor from the representation of the image similar to a surface in a volume. This descriptor belongs to the framework of non-supervised segmentation, since it will not require any user interaction. The second contribution is a solution for the segmentation problem based on active contour models and information theory tools. Third contribution is a semi-supervised segmentation model, i.e. where constraints provided by the user will be integrated in the segmentation framework. This processus is actually derived from the graph of image patches. This graph gives the connectivity measure between the different points of the image. The segmentation will be expressed by a graph partition and a variational model. This manuscript proposes to tackle the segmentation problem for textured images

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Proceedings of the fifth international workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015)

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 first edition of this workshop in 20061, the second edition in New-York in 20082, the third edition in Toronto in 20113, the forth edition in Nagoya Japan on September 22 20134, the fifth edition was held in Munich on October 9 20155.Contributions were solicited in Riemannian, sub-Riemannian and group theoretical methods, advanced statistics on deformations and shapes, metrics for computational anatomy, statistics of surfaces, time-evolving geometric processes, stratified spaces, optimal transport, approximation methods in statistical learning and related subjects. Among the submitted papers, 14 were selected andorganized in 4 oral sessions

Foetal echocardiographic segmentation

Congenital heart disease affects just under one percentage of all live births [1]. Those defects that manifest themselves as changes to the cardiac chamber volumes are the motivation for the research presented in this thesis. Blood volume measurements in vivo require delineation of the cardiac chambers and manual tracing of foetal cardiac chambers is very time consuming and operator dependent. This thesis presents a multi region based level set snake deformable model applied in both 2D and 3D which can automatically adapt to some extent towards ultrasound noise such as attenuation, speckle and partial occlusion artefacts. The algorithm presented is named Mumford Shah Sarti Collision Detection (MSSCD). The level set methods presented in this thesis have an optional shape prior term for constraining the segmentation by a template registered to the image in the presence of shadowing and heavy noise. When applied to real data in the absence of the template the MSSCD algorithm is initialised from seed primitives placed at the centre of each cardiac chamber. The voxel statistics inside the chamber is determined before evolution. The MSSCD stops at open boundaries between two chambers as the two approaching level set fronts meet. This has significance when determining volumes for all cardiac compartments since cardiac indices assume that each chamber is treated in isolation. Comparison of the segmentation results from the implemented snakes including a previous level set method in the foetal cardiac literature show that in both 2D and 3D on both real and synthetic data, the MSSCD formulation is better suited to these types of data. All the algorithms tested in this thesis are within 2mm error to manually traced segmentation of the foetal cardiac datasets. This corresponds to less than 10% of the length of a foetal heart. In addition to comparison with manual tracings all the amorphous deformable model segmentations in this thesis are validated using a physical phantom. The volume estimation of the phantom by the MSSCD segmentation is to within 13% of the physically determined volume

Atlas Construction for Measuring the Variability of Complex Anatomical Structures

RÉSUMÉ La recherche sur l'anatomie humaine, en particulier sur le cœur et le cerveau, est d'un intérêt particulier car leurs anomalies entraînent des pathologies qui sont parmi les principales causes de décès dans le monde et engendrent des coûts substantiels. Heureusement, les progrès en imagerie médicale permettent des diagnostics et des traitements autrefois impossibles. En contrepartie, la quantité phénoménale de données produites par ces technologies nécessite le développement d'outils efficaces pour leur traitement. L'objectif de cette thèse est de proposer un ensemble d'outils permettant de normaliser des mesures prélevées sur différents individus, essentiels à l'étude des caractéristiques de structures anatomiques complexes. La normalisation de mesures consiste à rassembler une collection d'images dans une référence commune, aussi appelée construction d'atlas numériques, afin de combiner des mesures provenant de différents patients. Le processus de construction inclut deux étapes principales; la segmentation d'images pour trouver des régions d'intérêts et le recalage d'images afin de déterminer les correspondances entres régions d'intérêts. Les méthodes actuelles de constructions d'atlas peuvent nécessiter des interventions manuelles, souvent fastidieuses, variables, et sont en outre limitées par leurs mécanismes internes. Principalement, le recalage d'images dépend d'une déformation incrémentales d'images sujettes a des minimums locaux. Le recalage n'est ainsi pas optimal lors de grandes déformations et ces limitations requièrent la nécessite de proposer de nouvelles approches pour la construction d'atlas. Les questions de recherche de cette thèse se concentrent donc sur l'automatisation des méthodes actuelles ainsi que sur la capture de déformations complexes de structures anatomiques, en particulier sur le cœur et le cerveau. La méthodologie adoptée a conduit à trois objectifs de recherche spécifiques. Le premier prévoit un nouveau cadre de construction automatise d'atlas afin de créer le premier atlas humain de l'architecture de fibres cardiaques. Le deuxième vise à explorer une nouvelle approche basée sur la correspondance spectrale, nommée FOCUSR, afin de capturer une grande variabilité de formes sur des maillages. Le troisième aboutit finalement à développer une approche fondamentalement différente pour le recalage d'images à fortes déformations, nommée les démons spectraux. Le premier objectif vise plus particulièrement à construire un atlas statistique de l'architecture des fibres cardiaques a partir de 10 cœurs ex vivo humains. Le système développé a mené à deux contributions techniques et une médicale, soit l'amélioration de la segmentation de structures cardiaques et l'automatisation du calcul de forme moyenne, ainsi que notamment la première étude chez l'homme de la variabilité de l'architecture des fibres cardiaques. Pour résumer les principales conclusions, les fibres du cœur humain moyen varient de +- 12 degrés, l'angle d'helix s'étend entre -41 degrés (+- 26 degrés) sur l'épicarde à +66 degrés (+- 15 degrés) sur l'endocarde, tandis que l'angle transverse varie entre +9 degrés (+- 12 degrés) et +34 degrés (+- 29 degrés) à travers le myocarde. Ces résultats sont importants car ces fibres jouent un rôle clef dans diverses fonctions mécaniques et électrophysiologiques du cœur. Le deuxième objectif cherche à capturer une grande variabilité de formes entre structures anatomiques complexes, plus particulièrement entre cortex cérébraux à cause de l'extrême variabilité de ces surfaces et de leur intérêt pour l'étude de fonctions cognitives. La nouvelle méthode de correspondance surfacique, nommée FOCUSR, exploite des représentations spectrales car l'appariement devient plus facile et rapide dans le domaine spectral plutôt que dans l'espace Euclidien classique. Dans sa forme la plus simple, FOCUSR améliore les méthodes spectrales actuelles par un recalage non rigide des représentations spectrales, toutefois, son plein potentiel est atteint en exploitant des données supplémentaires lors de la mise en correspondance. Par exemple, les résultats ont montré que la profondeur des sillons et de la courbure du cortex cérébral améliore significativement la correspondance de surfaces de cerveaux. Enfin, le troisième objectif vise à améliorer le recalage d'images d'organes ayant des fortes variabilités entre individus ou subis de fortes déformations, telles que celles créées par le mouvement cardiaque. La méthodologie amenée par la correspondance spectrale permet d'améliorer les approches conventionnelles de recalage d'images. En effet, les représentations spectrales, capturant des similitudes géométriques globales entre différentes formes, permettent de surmonter les limitations actuelles des méthodes de recalage qui restent guidées par des forces locales. Le nouvel algorithme, nommé démons spectraux, peut ainsi supporter de très grandes déformations locales et complexes entre images, et peut être tout autant adapté a d'autres approches, telle que dans un cadre de recalage conjoint d'images. Il en résulte un cadre complet de construction d'atlas, nommé démons spectraux multijoints, où la forme moyenne est calculée directement lors du processus de recalage plutôt qu'avec une approche séquentielle de recalage et de moyennage. La réalisation de ces trois objectifs spécifiques a permis des avancées dans l'état de l'art au niveau des méthodes de correspondance spectrales et de construction d'atlas, en permettant l'utilisation d'organes présentant une forte variabilité de formes. Dans l'ensemble, les différentes stratégies fournissent de nouvelles contributions sur la façon de trouver et d'exploiter des descripteurs globaux d'images et de surfaces. D'un point de vue global, le développement des objectifs spécifiques établit un lien entre : a) la première série d'outils, mettant en évidence les défis à recaler des images à fortes déformations, b) la deuxième série d'outils, servant à capturer de fortes déformations entre surfaces mais qui ne reste pas directement applicable a des images, et c) la troisième série d'outils, faisant un retour sur le traitement d'images en permettant la construction d'atlas a partir d'images ayant subies de fortes déformations. Il y a cependant plusieurs limitations générales qui méritent d'être investiguées, par exemple, les données partielles (tronquées ou occluses) ne sont pas actuellement prises en charge les nouveaux outils, ou encore, les stratégies algorithmiques utilisées laissent toujours place à l'amélioration. Cette thèse donne de nouvelles perspectives dans les domaines de l'imagerie cardiaque et de la neuroimagerie, toutefois, les nouveaux outils développés sont assez génériques pour être appliqués a tout recalage d'images ou de surfaces. Les recommandations portent sur des recherches supplémentaires qui établissent des liens avec la segmentation à base de graphes, pouvant conduire à un cadre complet de construction d'atlas où la segmentation, le recalage, et le moyennage de formes seraient tous interdépendants. Il est également recommandé de poursuivre la recherche sur la construction de meilleurs modèles électromécaniques cardiaques à partir des résultats de cette thèse. En somme, les nouveaux outils offrent de nouvelles bases de recherche et développement pour la normalisation de formes, ce qui peut potentiellement avoir un impact sur le diagnostic, ainsi que la planification et la pratique d'interventions médicales.----------ABSTRACT Research on human anatomy, in particular on the heart and the brain, is a primary concern for society since their related diseases are among top killers across the globe and have exploding associated costs. Fortunately, recent advances in medical imaging offer new possibilities for diagnostics and treatments. On the other hand, the growth in data produced by these relatively new technologies necessitates the development of efficient tools for processing data. The focus of this thesis is to provide a set of tools for normalizing measurements across individuals in order to study complex anatomical characteristics. The normalization of measurements consists of bringing a collection of images into a common reference, also known as atlas construction, in order to combine measurements made on different individuals. The process of constructing an atlas involves the topics of segmentation, which finds regions of interest in the data (e.g., an organ, a structure), and registration, which finds correspondences between regions of interest. Current frameworks may require tedious and hardly reproducible user interactions, and are additionally limited by their computational schemes, which rely on slow iterative deformations of images, prone to local minima. Image registration is, therefore, not optimal with large deformations. Such limitations indicate the need to research new approaches for atlas construction. The research questions are consequently addressing the problems of automating current frameworks and capturing global and complex deformations between anatomical structures, in particular between human hearts and brains. More precisely, the methodology adopted in the thesis led to three specific research objectives. Briefly, the first step aims at developing a new automated framework for atlas construction in order to build the first human atlas of the cardiac fiber architecture. The second step intends to explore a new approach based on spectral correspondence, named FOCUSR, in order to precisely capture large shape variability. The third step leads, finally, to a fundamentally new approach for image registration with large deformations, named the Spectral Demons algorithm. The first objective aims more specifically at constructing a statistical atlas of the cardiac fiber architecture from a unique human dataset of 10 ex vivo hearts. The developed framework made two technical, and one medical, contributions, that are the improvement of the segmentation of cardiac structures, the automation of the shape averaging process, and more importantly, the first human study on the variability of the cardiac fiber architecture. To summarize the main finding, the fiber orientations in human hearts has been found to vary with about +- 12 degrees, the range of the helix angle spans from -41 degrees (+- 26 degrees) on the epicardium to +66 degrees (+- 15 degrees) on the endocardium, while, the range of the transverse angle spans from +9 degrees (+- 12 degrees) to +34 degrees (+- 29 degrees) across the myocardial wall. These findings are significant in cardiology since the fiber architecture plays a key role in cardiac mechanical functions and in electrophysiology. The second objective intends to capture large shape variability between complex anatomical structures, in particular between cerebral cortices due to their highly convoluted surfaces and their high anatomical and functional variability across individuals. The new method for surface correspondence, named FOCUSR, exploits spectral representations since matching is easier in the spectral domain rather than in the conventional Euclidean space. In its simplest form, FOCUSR improves current spectral approaches by refining spectral representations with a nonrigid alignment; however, its full power is demonstrated when using additional features during matching. For instance, the results showed that sulcal depth and cortical curvature improve significantly the accuracy of cortical surface matching. Finally, the third objective is to improve image registration for organs with a high inter-subject variability or undergoing very large deformations, such as the heart. The new approach brought by the spectral matching technique allows the improvement of conventional image registration methods. Indeed, spectral representations, which capture global geometric similarities and large deformations between different shapes, may be used to overcome a major limitation of current registration methods, which are in fact guided by local forces and restrained to small deformations. The new algorithm, named Spectral Demons, can capture very large and complex deformations between images, and can additionally be adapted to other approaches, such as in a groupwise configuration. This results in a complete framework for atlas construction, named Groupwise Spectral Demons, where the average shape is computed during the registration process rather than in sequential steps. The achievements of these three specific objectives permitted advances in the state-of-the-art of spectral matching methods and of atlas construction, enabling the registration of organs with significant shape variability. Overall, the investigation of these different strategies provides new contributions on how to find and exploit global descriptions of images and surfaces. From a global perspective, these objectives establish a link between: a) the first set of tools, that highlights the challenges in registering images with very large deformations, b) the second set of tools, that captures very large deformations between surfaces but are not applicable to images, and c) the third set of tools, that comes back on processing images and allows a natural construction of atlases from images with very large deformations. There are, however, several general remaining limitations, for instance, partial data (truncated or occluded) is currently not supported by the new tools, or also, the strategy for computing and using spectral representations still leaves room for improvement. This thesis gives new perspectives in cardiac and neuroimaging, yet at the same time, the new tools remain general enough for virtually any application that uses surface or image registration. It is recommended to research additional links with graph-based segmentation methods, which may lead to a complete framework for atlas construction where segmentation, registration and shape averaging are all interlinked. It is also recommended to pursue research on building better cardiac electromechanical models from the findings of this thesis. Nevertheless, the new tools provide new grounds for research and application of shape normalization, which may potentially impact diagnostic, as well as planning and performance of medical interventions

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

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)

Variational models and numerical algorithms for effective image registration

The goal of image registration is to align two or more images of the same scene obtained at different times, from different perspectives, or sensors such as MRI, X-ray and CT. This step is required to facilitate automatic segmentation for tumour detection or to inform further decisions in treatment planning. It is an important and challenging subject which usually involves high storage, computational cost and dealing with distorted and occluded data. The paradigm behind image registration is to find a reasonable transformation so that the template image becomes similar to the so-called given reference image. Through such transformation, information from these images can be compared or combined. This thesis deals with the mathematical modelling of image registration by way of energy minimisation of a functional. We propose a new decomposition model for image registration which combines parametric transformation and non-parametric deformation. The first category of methods is based on a small number of parameters and for the second category the transformation is based on a functional map (or discretely a large number of parameters) with a regularisation term. We choose one cubic B-spline based model and the linear curvature model for the parametric and non-parametric parts respectively where the overall deformation consists of both global and local displacement for effective image registration. Some results for synthetic and real images will be presented to illustrate the effectiveness of the new model in contrast with the individual models. We then propose a novel variational model for image registration which employs Gaussian curvature as a regulariser. The model is motivated by the surface restoration work in geometric processing [21]. An effective numerical solver is provided for the model using an augmented Lagrangian method. Numerical experiments show that the new model outperforms three competing models based on, respectively, the linear curvature [24], the mean curvature [19] and the diffeomorphic demon models [93] in terms of robustness and accuracy. Finally, we present an improved model for joint segmentation and registration based on active contour without edges. The proposed model is motivated by an earlier model [58] and the linear curvature model [24]. Numerical results show that the new model outperforms the existing model for registration and segmentation of one or multiple objects in the image. The proposed model also leads to improved registration results when features exist inside the object

Compression of 4D medical image and spatial segmentation using deformable models

Ph.DDOCTOR OF PHILOSOPH