Cortical Surface Registration and Shape Analysis

A population analysis of human cortical morphometry is critical for insights into brain development or degeneration. Such an analysis allows for investigating sulcal and gyral folding patterns. In general, such a population analysis requires both a well-established cortical correspondence and a well-defined quantification of the cortical morphometry. The highly folded and convoluted structures render a reliable and consistent population analysis challenging. Three key challenges have been identified for such an analysis: 1) consistent sulcal landmark extraction from the cortical surface to guide better cortical correspondence, 2) a correspondence establishment for a reliable and stable population analysis, and 3) quantification of the cortical folding in a more reliable and biologically meaningful fashion. The main focus of this dissertation is to develop a fully automatic pipeline that supports a population analysis of local cortical folding changes. My proposed pipeline consists of three novel components I developed to overcome the challenges in the population analysis: 1) automatic sulcal curve extraction for stable/reliable anatomical landmark selection, 2) group-wise registration for establishing cortical shape correspondence across a population with no template selection bias, and 3) quantification of local cortical folding using a novel cortical-shape-adaptive kernel. To evaluate my methodological contributions, I applied all of them in an application to early postnatal brain development. I studied the human cortical morphological development using the proposed quantification of local cortical folding from neonate age to 1 year and 2 years of age, with quantitative developmental assessments. This study revealed a novel pattern of associations between the cortical gyrification and cognitive development.Doctor of Philosoph

Entropy-based particle correspondence for shape populations

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies

Doctor of Philosophy in Computing

dissertationStatistical shape analysis has emerged as an important tool for the quantitative analysis of anatomy in many medical imaging applications. The correspondence based approach to evaluate shape variability is a popular method, based on comparing configurations of carefully placed landmarks on each shape. In recent years, methods for automatic placement of landmarks have enhanced the ability of this approach to capture statistical properties of shape populations. However, biomedical shapes continue to present considerable difficulties in automatic correspondence optimization due to inherent geometric complexity and the need to correlate shape change with underlying biological parameters. This dissertation addresses these technical difficulties and presents improved shape correspondence models. In particular, this dissertation builds on the particle-based modeling (PBM) framework described by Joshua Cates' 2010 Ph.D. dissertation. In the PBM framework, correspondences are modeled as a set of dynamic points or a particle system, positioned automatically on shape surfaces by optimizing entropy contained in the model, with the idea of balancing model simplicity against accuracy of the particle system representation of shapes. This dissertation is a collection of four papers that extend the PBM framework to include shape regression and longitudinal analysis and also adds new methods to improve modeling of complex shapes. It also includes a summary of two applications from the field of orthopaedics. Technical details of the PBM framework are provided in Chapter 2, after which the first topic related to the study of shape change over time is addressed (Chapters 3 and 4). In analyses of normative growth or disease progression, shape regression models allow characterization of the underlying biological process while also facilitating comparison of a sample against a normative model. The first paper introduces a shape regression model into the PBM framework to characterize shape variability due to an underlying biological parameter. It further confirms the statistical significance of this relationship via systematic permutation testing. Simple regression models are, however, not sufficient to leverage information provided by longitudinal studies. Longitudinal studies collect data at multiple time points for each participant and have the potential to provide a rich picture of the anatomical changes occurring during development, disease progression, or recovery. The second paper presents a linear-mixed-effects (LME) shape model in order to fully leverage the high-dimensional, complex features provided by longitudinal data. The parameters of the LME shape model are estimated in a hierarchical manner within the PBM framework. The topic of geometric complexity present in certain biological shapes is addressed next (Chapters 5 and 6). Certain biological shapes are inherently complex and highly variable, inhibiting correspondence based methods from producing a faithful representation of the average shape. In the PBM framework, use of Euclidean distances leads to incorrect particle system interactions while a position-only representation leads to incorrect correspondences around sharp features across shapes. The third paper extends the PBM framework to use efficiently computed geodesic distances and also adds an entropy term based on the surface normal. The fourth paper further replaces the position-only representation with a more robust distance-from-landmark feature in the PBM framework to obtain isometry invariant correspondences. Finally, the above methods are applied to two applications from the field of orthopaedics. The first application uses correspondences across an ensemble of human femurs to characterize morphological shape differences due to femoroacetabular impingement. The second application involves an investigation of the short bone phenotype apparent in mouse models of multiple osteochondromas. Metaphyseal volume deviations are correlated with deviations in length to quantify the effect of cancer toward the apparent shortening of long bones (femur, tibia-fibula) in mouse models

SVA: Shape variation analyzer

Temporo-mandibular osteo arthritis (TMJ OA) is characterized by progressive cartilage degradation and subchondral bone remodeling. The causes of this pathology remain unclear. Current research efforts are concentrated in finding new biomarkers that will help us understand disease progression and ultimately improve the treatment of the disease. In this work, we present Shape Variation Analyzer (SVA), the goal is to develop a noninvasive technique to provide information about shape changes in TMJ OA. SVA uses neural networks to classify morphological variations of 3D models of the mandibular condyle. The shape features used for training include normal vectors, curvature and distances to average models of the condyles. The selected features are purely geometric and are shown to favor the classification task into 6 groups generated by consensus between two clinician experts. With this new approach, we were able to accurately classify 3D models of condyles. In this paper, we present the methods used and the results obtained with this new tool

Labeling lateral prefrontal sulci using spherical data augmentation and context-aware training

The inference of cortical sulcal labels often focuses on deep (primary and secondary) sulcal regions, whereas shallow (tertiary) sulcal regions are largely overlooked in the literature due to the scarcity of manual/well-defined annotations and their large neuroanatomical variability. In this paper, we present an automated framework for regional labeling of both primary/secondary and tertiary sulci of the dorsal portion of lateral prefrontal cortex (LPFC) using spherical convolutional neural networks. We propose two core components that enhance the inference of sulcal labels to overcome such large neuroanatomical variability: (1) surface data augmentation and (2) context-aware training. (1) To take into account neuroanatomical variability, we synthesize training data from the proposed feature space that embeds intermediate deformation trajectories of spherical data in a rigid to non-rigid fashion, which bridges an augmentation gap in conventional rotation data augmentation. (2) Moreover, we design a two-stage training process to improve labeling accuracy of tertiary sulci by informing the biological associations in neuroanatomy: inference of primary/secondary sulci and then their spatial likelihood to guide the definition of tertiary sulci. In the experiments, we evaluate our method on 13 deep and shallow sulci of human LPFC in two independent data sets with different age ranges: pediatric (N=60) and adult (N=36) cohorts. We compare the proposed method with a conventional multi-atlas approach and spherical convolutional neural networks without/with rotation data augmentation. In both cohorts, the proposed data augmentation improves labeling accuracy of deep and shallow sulci over the baselines, and the proposed context-aware training offers further improvement in the labeling of shallow sulci over the proposed data augmentation. We share our tools with the field and discuss applications of our results for understanding neuroanatomical-functional organization of LPFC and the rest of cortex (https://github.com/ilwoolyu/SphericalLabeling). ?? 2021 The Author(s

Geodesic Active Fields:A Geometric Framework for Image Registration

Image registration is the concept of mapping homologous points in a pair of images. In other words, one is looking for an underlying deformation field that matches one image to a target image. The spectrum of applications of image registration is extremely large: It ranges from bio-medical imaging and computer vision, to remote sensing or geographic information systems, and even involves consumer electronics. Mathematically, image registration is an inverse problem that is ill-posed, which means that the exact solution might not exist or not be unique. In order to render the problem tractable, it is usual to write the problem as an energy minimization, and to introduce additional regularity constraints on the unknown data. In the case of image registration, one often minimizes an image mismatch energy, and adds an additive penalty on the deformation field regularity as smoothness prior. Here, we focus on the registration of the human cerebral cortex. Precise cortical registration is required, for example, in statistical group studies in functional MR imaging, or in the analysis of brain connectivity. In particular, we work with spherical inflations of the extracted hemispherical surface and associated features, such as cortical mean curvature. Spatial mapping between cortical surfaces can then be achieved by registering the respective spherical feature maps. Despite the simplified spherical geometry, inter-subject registration remains a challenging task, mainly due to the complexity and inter-subject variability of the involved brain structures. In this thesis, we therefore present a registration scheme, which takes the peculiarities of the spherical feature maps into particular consideration. First, we realize that we need an appropriate hierarchical representation, so as to coarsely align based on the important structures with greater inter-subject stability, before taking smaller and more variable details into account. Based on arguments from brain morphogenesis, we propose an anisotropic scale-space of mean-curvature maps, built around the Beltrami framework. Second, inspired by concepts from vision-related elements of psycho-physical Gestalt theory, we hypothesize that anisotropic Beltrami regularization better suits the requirements of image registration regularization, compared to traditional Gaussian filtering. Different objects in an image should be allowed to move separately, and regularization should be limited to within the individual Gestalts. We render the regularization feature-preserving by limiting diffusion across edges in the deformation field, which is in clear contrast to the indifferent linear smoothing. We do so by embedding the deformation field as a manifold in higher-dimensional space, and minimize the associated Beltrami energy which represents the hyperarea of this embedded manifold as measure of deformation field regularity. Further, instead of simply adding this regularity penalty to the image mismatch in lieu of the standard penalty, we propose to incorporate the local image mismatch as weighting function into the Beltrami energy. The image registration problem is thus reformulated as a weighted minimal surface problem. This approach has several appealing aspects, including (1) invariance to re-parametrization and ability to work with images defined on non-flat, Riemannian domains (e.g., curved surfaces, scalespaces), and (2) intrinsic modulation of the local regularization strength as a function of the local image mismatch and/or noise level. On a side note, we show that the proposed scheme can easily keep up with recent trends in image registration towards using diffeomorphic and inverse consistent deformation models. The proposed registration scheme, called Geodesic Active Fields (GAF), is non-linear and non-convex. Therefore we propose an efficient optimization scheme, based on splitting. Data-mismatch and deformation field regularity are optimized over two different deformation fields, which are constrained to be equal. The constraint is addressed using an augmented Lagrangian scheme, and the resulting optimization problem is solved efficiently using alternate minimization of simpler sub-problems. In particular, we show that the proposed method can easily compete with state-of-the-art registration methods, such as Demons. Finally, we provide an implementation of the fast GAF method on the sphere, so as to register the triangulated cortical feature maps. We build an automatic parcellation algorithm for the human cerebral cortex, which combines the delineations available on a set of atlas brains in a Bayesian approach, so as to automatically delineate the corresponding regions on a subject brain given its feature map. In a leave-one-out cross-validation study on 39 brain surfaces with 35 manually delineated gyral regions, we show that the pairwise subject-atlas registration with the proposed spherical registration scheme significantly improves the individual alignment of cortical labels between subject and atlas brains, and, consequently, that the estimated automatic parcellations after label fusion are of better quality

Visual Exploration And Information Analytics Of High-Dimensional Medical Images

Data visualization has transformed how we analyze increasingly large and complex data sets. Advanced visual tools logically represent data in a way that communicates the most important information inherent within it and culminate the analysis with an insightful conclusion. Automated analysis disciplines - such as data mining, machine learning, and statistics - have traditionally been the most dominant fields for data analysis. It has been complemented with a near-ubiquitous adoption of specialized hardware and software environments that handle the storage, retrieval, and pre- and postprocessing of digital data. The addition of interactive visualization tools allows an active human participant in the model creation process. The advantage is a data-driven approach where the constraints and assumptions of the model can be explored and chosen based on human insight and confirmed on demand by the analytic system. This translates to a better understanding of data and a more effective knowledge discovery. This trend has become very popular across various domains, not limited to machine learning, simulation, computer vision, genetics, stock market, data mining, and geography. In this dissertation, we highlight the role of visualization within the context of medical image analysis in the field of neuroimaging. The analysis of brain images has uncovered amazing traits about its underlying dynamics. Multiple image modalities capture qualitatively different internal brain mechanisms and abstract it within the information space of that modality. Computational studies based on these modalities help correlate the high-level brain function measurements with abnormal human behavior. These functional maps are easily projected in the physical space through accurate 3-D brain reconstructions and visualized in excellent detail from different anatomical vantage points. Statistical models built for comparative analysis across subject groups test for significant variance within the features and localize abnormal behaviors contextualizing the high-level brain activity. Currently, the task of identifying the features is based on empirical evidence, and preparing data for testing is time-consuming. Correlations among features are usually ignored due to lack of insight. With a multitude of features available and with new emerging modalities appearing, the process of identifying the salient features and their interdependencies becomes more difficult to perceive. This limits the analysis only to certain discernible features, thus limiting human judgments regarding the most important process that governs the symptom and hinders prediction. These shortcomings can be addressed using an analytical system that leverages data-driven techniques for guiding the user toward discovering relevant hypotheses. The research contributions within this dissertation encompass multidisciplinary fields of study not limited to geometry processing, computer vision, and 3-D visualization. However, the principal achievement of this research is the design and development of an interactive system for multimodality integration of medical images. The research proceeds in various stages, which are important to reach the desired goal. The different stages are briefly described as follows: First, we develop a rigorous geometry computation framework for brain surface matching. The brain is a highly convoluted structure of closed topology. Surface parameterization explicitly captures the non-Euclidean geometry of the cortical surface and helps derive a more accurate registration of brain surfaces. We describe a technique based on conformal parameterization that creates a bijective mapping to the canonical domain, where surface operations can be performed with improved efficiency and feasibility. Subdividing the brain into a finite set of anatomical elements provides the structural basis for a categorical division of anatomical view points and a spatial context for statistical analysis. We present statistically significant results of our analysis into functional and morphological features for a variety of brain disorders. Second, we design and develop an intelligent and interactive system for visual analysis of brain disorders by utilizing the complete feature space across all modalities. Each subdivided anatomical unit is specialized by a vector of features that overlap within that element. The analytical framework provides the necessary interactivity for exploration of salient features and discovering relevant hypotheses. It provides visualization tools for confirming model results and an easy-to-use interface for manipulating parameters for feature selection and filtering. It provides coordinated display views for visualizing multiple features across multiple subject groups, visual representations for highlighting interdependencies and correlations between features, and an efficient data-management solution for maintaining provenance and issuing formal data queries to the back end

Deformable Medical Image Registration: A Survey

Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this technical report, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this technical report is to provide an extensive account of registration techniques in a systematic manner.Le recalage déformable d'images est une des tâches les plus fondamentales dans l'imagerie médicale. Parmi ses applications les plus importantes, on compte: i) la fusion d' information provenant des différents types de modalités a n de faciliter le diagnostic et la planification du traitement; ii) les études longitudinales, oú des changements structurels ou anatomiques sont étudiées en fonction du temps; et iii) la modélisation de la variabilité anatomique normale d'une population et les atlas statistiques. Dans ce rapport de recherche, nous essayons de donner un aperçu des différentes méthodes du recalage déformables, en mettant l'accent sur les avancées les plus récentes du domaine. Nous avons particulièrement insisté sur les techniques appliquées aux images médicales. A n d'étudier les méthodes du recalage d'images, leurs composants principales sont d'abord identifiés puis étudiées de manière indépendante, les techniques les plus récentes étant classifiées en suivant un schéma logique déterminé. La contribution de ce rapport de recherche est de fournir un compte rendu détaillé des techniques de recalage d'une manière systématique

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