When we scan image data by ultrasound, we have a little information of displayed scene. For understanding content of the image we try to separate the observed objects of interest from the background. Obtaining information of these objects is called a process called segmentation. This work is focused on the segmentation of ultrasound image sequences using geometric active contours solved by the method of level sets. For better representation is also dealing with image preprocessing. The result is an implementation of segmentation methods on simulated and real data.

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This dissertation proposes a novel theoretical framework for the data partitioning problem in computer vision and machine learning. The framework is based on level set methods that are derived from variational calculus and involve a curve-based objective function which integrates both boundary and region based information in a generic form. The proposed approaches within the framework provide original solutions to two important problems in variational methods, namely parameter tuning and information fusion, collectively termed Learning Level Sets in this thesis. Moreover, a novel pattern classification algorithm, namely Level Learning Sets, is proposed to classify any general dataset, including sparse and non sparse data. It is based on the same optimisation process of the objective function directly related to the curve propagation theory used in level set theory. The proposed approach learns the knowledge required for parameter tuning and information fusion in level set methods using machine learning techniques. It uses acquired knowledge to automatically perform parameter tuning and information fusion in level set methods. In the case of pattern classification, variational methods using level set theory optimise decision boundary construction in feature space. Consequently, the optimised values of the objective level set function over the feature space represent the model for pattern classification. The proposed automatic parameter tuning and information fusion method embedded in the level set method framework has been employed to provide original solutions to image segmentation and object extraction in computer vision. On the other hand, the Level Learning Set has been extended and applied to a variety of pattern classification problems". Several experimental results for each of the above methods are provided, demonstrating the effectiveness of the proposed solutions and indicating the potential of the automatic and dynamic tuning and fusion approaches as well as the Level Learning Set model.

This thesis introduces novel ideas in subsurface reservoir model calibration known as History Matching in the reservoir engineering community. The target of history matching is to mimic historical pressure and production data from the producing wells with the output from the reservoir simulator for the sole purpose of reducing uncertainty from such models and improving confidence in production forecast. Ensemble based methods such as the Ensemble Kalman Filter (EnKF) and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) as been proposed for history matching in literature. EnKF/ES-MDA is a Monte Carlo ensemble nature filter where the representation of the covariance is located at the mean of the ensemble of the distribution instead of the uncertain true model. In EnKF/ES-MDA calculation of the gradients is not required, and the mean of the ensemble of the realisations provides the best estimates with the ensemble on its own estimating the probability density. However, because of the inherent assumptions of linearity and Gaussianity of petrophysical properties distribution, EnKF/ES-MDA does not provide an acceptable history-match and characterisation of uncertainty when tasked with calibrating reservoir models with channel like structures. One of the novel methods introduced in this thesis combines a successive parameter and shape reconstruction using level set functions (EnKF/ES-MDA-level set) where the spatial permeability fields' indicator functions are transformed into signed distances. These signed distances functions (better suited to the Gaussian requirement of EnKF/ES-MDA) are then updated during the EnKF/ES-MDA inversion. The method outperforms standard EnKF/ES-MDA in retaining geological realism of channels during and after history matching and also yielded lower Root-Mean-Square function (RMS) as compared to the standard EnKF/ES-MDA. To improve on the petrophysical reconstruction attained with the EnKF/ES-MDA-level set technique, a novel parametrisation incorporating an unsupervised machine learning method for the recovery of the permeability and porosity field is developed. The permeability and porosity fields are posed as a sparse field recovery problem and a novel SELE (Sparsity-Ensemble optimization-Level-set Ensemble optimisation) approach is proposed for the history matching. In SELE some realisations are learned using the K-means clustering Singular Value Decomposition (K-SVD) to generate an overcomplete codebook or dictionary. This dictionary is combined with Orthogonal Matching Pursuit (OMP) to ease the ill-posed nature of the production data inversion, converting our permeability/porosity field into a sparse domain. SELE enforces prior structural information on the model during the history matching and reduces the computational complexity of the Kalman gain matrix, leading to faster attainment of the minimum of the cost function value. From the results shown in the thesis; SELE outperforms conventional EnKF/ES-MDA in matching the historical production data, evident in the lower RMS value and a high geological realism/similarity to the true reservoir model.

Medical image segmentation is a challenging problem, and is studied widely. In this thesis, the main goal is to develop automatic segmentation techniques of human mimic muscles and to compare them with ground truth data in order to determine the method that provides best segmentation results. The segmentation methods are based on Bayesian with Markov Random Field (MRF) and Level Set (Active Contour) models. Proposed segmentation methods are multi step processes including preprocess, main muscle segmentation step and post process, and are applied on three types of data: Magnetic Resonance Imaging (MRI) data, Computerized Tomography (CT) data and unified data, in which case, information coming from both modalities are utilized. The methods are applied both in three dimensions (3D) and two dimensions (2D) data cases. A simulation data and two patient data are utilized for tests. The patient data results are compared statistically with ground truth data which was labeled by an expert radiologist.

Στα πλαίσια της παρούσης εργασίας πραγματοποιήθηκε μελέτη της μεθόδου Συνόλων Επιπέδου για την κατάτμηση καροτίδων από τρισδίαστατες εικόνες. Ειδικότερα πραγματοποιήθηκε μελέτη των παθολογιών που συνδέονται με αυτές προκειμένου να καταστούν εμφανή τα κίνητρα της παρούσης εργασίας, όσον αφορά στη συμβολή της στην κλινική σημασία και ιατρική πρακτική. Κατ’αυτόν τον τρόπο, αφού παρουσιάστηκε η ανατομία των καροτίδων και οι δυσκολίες που ενέχει το εγχείρημα της κατάτμησής τους καθώς και μια ανασκόπηση των μεθόδων Συνόλων Επιπέδου (Level-Sets) για κατάτμηση ιατρικής εικόνας και δη καροτίδων, παρουσιάστηκε το γενικό μοντέλο και ο μαθηματικός φορμαλισμός της μεθόδου που χρησιμοποιήθηκε. Εν συνεχεία παρουσιάστηκαν τα τρισδιάστατα δεδομένα και η διαχείρησή τους, οι προγραμματιστικές διαπαφές και υποδομές με τις οποίες υλοποιήθηκαν δύο παραλλαγές της μεθόδου. Επίσης παρουσιάζονται τα αποτελέσματα της μεθόδου οπτικοποιημένα και τέλος συγκρίνονται με αντίστοιχα αποτελέσματα ενός ειδικού ακτινολόγου στη βάση κάποιων κατάλληλων μετρικών. Τέλος παρουσιάζονται τα συμπεράσματα που προέκυψαν καθώς και κάποιες ιδέες για μελλοντική δουλειάπου μπορεί να γίνει στη βάση αυτής που έγινε στα πλαίσια της εν λόγω μεταπτυχιακής διατριβής. / The present thesis outlines the methods we have developed for segmenting both normal and pathological carotid images, acquired with the Computed Tomography (CT) protocol. The layout of the thesis is the following: Chapter 2 analyses the methodological background of the current study. At first, section 2.1 provides an overview to the anatomy of carotids. Section 2.2 reviews the literature of segmentation methods based on level sets for medical images and at last reviews the level set methods developed for segmenting carotids. In addition, section 2.3 presents the conceptual model deployed in the current study, following with the analysis of the particular class we used. Next, section 2.4 treats of the level set method, presenting its basic derivation and furthermore discriminating between the two algorithms used according to their speed function. Chapter 3 refers to the materials and methods. It begins in section 3.1 with a description of the data provided for the experimental demonstration, and the programming interface by deployment of which the experimental procedure took place. Later on, in section 3.2 the implementation of the deployed methods in the programming interface used is presented with an analysis of their components. At last, all intermediate outputs and the final results of each method are illustrated. Chapter 4 presents the evaluation of the results of each method by comparison with a corresponding manual segmentation result on the basis of appropriate metrics. At last, refers to the conclusions occurred and to future work that can be carried out based on the current Msc thesis. In Appendix A some subsidiary methods, for the sake of a coherent flow are stated and analyzed independently.

Itô diffusions that move on level sets of functions in Rn, which we have called level processes, are an overlooked variant of the classical Itô processes. These processes find themselves nestled between the study of regular Itô diffusions in Rn and diffusions which are bound to smooth manifolds. In this thesis we present how to construct these level processes, in both the plane and n-space, with their properties in the plane being examined. We also show how these processes connect to the Itô diffusions on smooth manifolds. In addition, we derive how to affix a given system of Itô diffusion to a level set, given certain constraints. Lastly, we give a brief overview of three numerical schemes for stochastic differential equations and investigate their applicability to the simulation of level processes. For both the probabilistic and numeric sections, reflections on the work done are given and possible extensions, such as the relaxation of the smoothness condition for the level set, are briefly outlined.

L'imagerie intravasculaire ultrasonore (IVUS) est une technologie médicale par cathéter qui produit des images de coupe des vaisseaux sanguins. Elle permet de quantifier et d'étudier la morphologie de plaques d'athérosclérose en plus de visualiser la structure des vaisseaux sanguins (lumière, intima, plaque, média et adventice) en trois dimensions. Depuis quelques années, cette méthode d'imagerie est devenue un outil de choix en recherche aussi bien qu'en clinique pour l'étude de la maladie athérosclérotique. L'imagerie IVUS est par contre affectée par des artéfacts associés aux caractéristiques des capteurs ultrasonores, par la présence de cônes d'ombre causés par les calcifications ou des artères collatérales, par des plaques dont le rendu est hétérogène ou par le chatoiement ultrasonore (speckle) sanguin. L'analyse automatisée de séquences IVUS de grande taille représente donc un défi important. Une méthode de segmentation en trois dimensions (3D) basée sur l'algorithme du fast-marching à interfaces multiples est présentée. La segmentation utilise des attributs des régions et contours des images IVUS. En effet, une nouvelle fonction de vitesse de propagation des interfaces combinant les fonctions de densité de probabilité des tons de gris des composants de la paroi vasculaire et le gradient des intensités est proposée. La segmentation est grandement automatisée puisque la lumière du vaisseau est détectée de façon entièrement automatique. Dans une procédure d'initialisation originale, un minimum d'interactions est nécessaire lorsque les contours initiaux de la paroi externe du vaisseau calculés automatiquement sont proposés à l'utilisateur pour acceptation ou correction sur un nombre limité d'images de coupe longitudinale. La segmentation a été validée à l'aide de séquences IVUS in vivo provenant d'artères fémorales provenant de différents sous-groupes d'acquisitions, c'est-à-dire pré-angioplastie par ballon, post-intervention et à un examen de contrôle 1 an suivant l'intervention. Les résultats ont été comparés avec des contours étalons tracés manuellement par différents experts en analyse d'images IVUS. Les contours de la lumière et de la paroi externe du vaisseau détectés selon la méthode du fast-marching sont en accord avec les tracés manuels des experts puisque les mesures d'aire sont similaires et les différences point-à-point entre les contours sont faibles. De plus, la segmentation par fast-marching 3D s'est effectuée en un temps grandement réduit comparativement à l'analyse manuelle. Il s'agit de la première étude rapportée dans la littérature qui évalue la performance de la segmentation sur différents types d'acquisition IVUS. En conclusion, la segmentation par fast-marching combinant les informations des distributions de tons de gris et du gradient des intensités des images est précise et efficace pour l'analyse de séquences IVUS de grandes tailles. Un outil de segmentation robuste pourrait devenir largement répandu pour la tâche ardue et fastidieuse qu'est l'analyse de ce type d'images. / Intravascular ultrasound (IVUS) is a catheter based medical imaging technique that produces cross-sectional images of blood vessels. These images provide quantitative assessment of the vascular wall, information about the nature of atherosclerotic lesions as well as the plaque shape and size. Over the past few years, this medical imaging modality has become a useful tool in research and clinical applications, particularly in atherosclerotic disease studies. However, IVUS imaging is subject to catheter ring-down artifacts, missing vessel parts due to calcification shadowing or side-branches, heterogeneously looking plaques and ultrasonic speckle from blood. The automated analysis of large IVUS data sets thus represents an important challenge. A three-dimensional segmentation algorithm based on the multiple interface fast-marching method is presented. The segmentation is based on region and contour features of the IVUS images: a new speed fonction for the interface propagation that combines the probability density functions (PDFs) of the vessel wall components and the intensity gradients is proposed. The segmentation is highly automated with the detection of the lumen boundary that is fully automatic. Minimal interactions are necessary with a novel initialization procedure since initial contours of the external vessel wall border are also computed automatically on a limited number of longitudinal images and then proposed to the user for acceptance or correction. The segmentation method was validated with in-vivo IVUS data sets acquired from femoral arteries. This database contained 3 subgroups: pullbacks acquired before balloon angioplasty, after the intervention and at a 1 year follow-up examination. Results were compared with validation contours that were manually traced by different experts in IVUS image analysis. The lumen and external wall boundaries detected with the fast-marching method are in agreement with the experts' manually traced contours with similarly found area measurements and small point-to-point contour differences. In addition, the 3D fast-marching segmentation method dramatically reduced the analysis time compared to manual tracing. Such a valdiation study, with comparison between pre- and post-intervention data, has never been reported in the IVUS segmentation literature. In conclusion, the fast-marching method combining the information on the gray level distributions and intensity gradients of the images is precise and efficient to analyze large IVUS sequences. It is hoped that the fast-marching method will become a widely used tool for the fastidious and difficult task of IVUS image processing.

L'imagerie intravasculaire ultrasonore (IVUS) est une technologie médicale par cathéter qui produit des images de coupe des vaisseaux sanguins. Elle permet de quantifier et d'étudier la morphologie de plaques d'athérosclérose en plus de visualiser la structure des vaisseaux sanguins (lumière, intima, plaque, média et adventice) en trois dimensions. Depuis quelques années, cette méthode d'imagerie est devenue un outil de choix en recherche aussi bien qu'en clinique pour l'étude de la maladie athérosclérotique. L'imagerie IVUS est par contre affectée par des artéfacts associés aux caractéristiques des capteurs ultrasonores, par la présence de cônes d'ombre causés par les calcifications ou des artères collatérales, par des plaques dont le rendu est hétérogène ou par le chatoiement ultrasonore (speckle) sanguin. L'analyse automatisée de séquences IVUS de grande taille représente donc un défi important. Une méthode de segmentation en trois dimensions (3D) basée sur l'algorithme du fast-marching à interfaces multiples est présentée. La segmentation utilise des attributs des régions et contours des images IVUS. En effet, une nouvelle fonction de vitesse de propagation des interfaces combinant les fonctions de densité de probabilité des tons de gris des composants de la paroi vasculaire et le gradient des intensités est proposée. La segmentation est grandement automatisée puisque la lumière du vaisseau est détectée de façon entièrement automatique. Dans une procédure d'initialisation originale, un minimum d'interactions est nécessaire lorsque les contours initiaux de la paroi externe du vaisseau calculés automatiquement sont proposés à l'utilisateur pour acceptation ou correction sur un nombre limité d'images de coupe longitudinale. La segmentation a été validée à l'aide de séquences IVUS in vivo provenant d'artères fémorales provenant de différents sous-groupes d'acquisitions, c'est-à-dire pré-angioplastie par ballon, post-intervention et à un examen de contrôle 1 an suivant l'intervention. Les résultats ont été comparés avec des contours étalons tracés manuellement par différents experts en analyse d'images IVUS. Les contours de la lumière et de la paroi externe du vaisseau détectés selon la méthode du fast-marching sont en accord avec les tracés manuels des experts puisque les mesures d'aire sont similaires et les différences point-à-point entre les contours sont faibles. De plus, la segmentation par fast-marching 3D s'est effectuée en un temps grandement réduit comparativement à l'analyse manuelle. Il s'agit de la première étude rapportée dans la littérature qui évalue la performance de la segmentation sur différents types d'acquisition IVUS. En conclusion, la segmentation par fast-marching combinant les informations des distributions de tons de gris et du gradient des intensités des images est précise et efficace pour l'analyse de séquences IVUS de grandes tailles. Un outil de segmentation robuste pourrait devenir largement répandu pour la tâche ardue et fastidieuse qu'est l'analyse de ce type d'images. / Intravascular ultrasound (IVUS) is a catheter based medical imaging technique that produces cross-sectional images of blood vessels. These images provide quantitative assessment of the vascular wall, information about the nature of atherosclerotic lesions as well as the plaque shape and size. Over the past few years, this medical imaging modality has become a useful tool in research and clinical applications, particularly in atherosclerotic disease studies. However, IVUS imaging is subject to catheter ring-down artifacts, missing vessel parts due to calcification shadowing or side-branches, heterogeneously looking plaques and ultrasonic speckle from blood. The automated analysis of large IVUS data sets thus represents an important challenge. A three-dimensional segmentation algorithm based on the multiple interface fast-marching method is presented. The segmentation is based on region and contour features of the IVUS images: a new speed fonction for the interface propagation that combines the probability density functions (PDFs) of the vessel wall components and the intensity gradients is proposed. The segmentation is highly automated with the detection of the lumen boundary that is fully automatic. Minimal interactions are necessary with a novel initialization procedure since initial contours of the external vessel wall border are also computed automatically on a limited number of longitudinal images and then proposed to the user for acceptance or correction. The segmentation method was validated with in-vivo IVUS data sets acquired from femoral arteries. This database contained 3 subgroups: pullbacks acquired before balloon angioplasty, after the intervention and at a 1 year follow-up examination. Results were compared with validation contours that were manually traced by different experts in IVUS image analysis. The lumen and external wall boundaries detected with the fast-marching method are in agreement with the experts' manually traced contours with similarly found area measurements and small point-to-point contour differences. In addition, the 3D fast-marching segmentation method dramatically reduced the analysis time compared to manual tracing. Such a valdiation study, with comparison between pre- and post-intervention data, has never been reported in the IVUS segmentation literature. In conclusion, the fast-marching method combining the information on the gray level distributions and intensity gradients of the images is precise and efficient to analyze large IVUS sequences. It is hoped that the fast-marching method will become a widely used tool for the fastidious and difficult task of IVUS image processing.

In this dissertation, level set methods are employed to segment masses in digital mammographic images and to classify land cover classes in hyperspectral data. For the mammography computer aided diagnosis (CAD) application, level set-based segmentation methods are designed and validated for mass periphery segmentation, spiculation segmentation, and core segmentation. The proposed periphery segmentation uses the narrowband level set method in conjunction with an adaptive speed function based on a measure of the boundary complexity in the polar domain. The boundary complexity term is shown to be beneficial for delineating challenging masses with ill-defined and irregularly shaped borders. The proposed method is shown to outperform periphery segmentation methods currently reported in the literature. The proposed mass spiculation segmentation uses a generalized form of the Dixon and Taylor Line Operator along with narrowband level sets using a customized speed function. The resulting spiculation features are shown to be very beneficial for classifying the mass as benign or malignant. For example, when using patient age and texture features combined with a maximum likelihood (ML) classifier, the spiculation segmentation method increases the overall accuracy to 92% with 2 false negatives as compared to 87% with 4 false negatives when using periphery segmentation approaches. The proposed mass core segmentation uses the Chan-Vese level set method with a minimal variance criterion. The resulting core features are shown to be effective and comparable to periphery features, and are shown to reduce the number of false negatives in some cases. Most mammographic CAD systems use only a periphery segmentation, so those systems could potentially benefit from core features.