The estimation of probability density functions (PDF) of intensity values plays an important role in medical image analysis. Non-parametric PDF estimation methods have the advantage of generality in their application. The two most popular estimators in image analysis methods to perform the non-parametric PDF estimation task are the histogram and the kernel density estimator. But these popular estimators crucially need to be ‘tuned’ by setting a number of parameters and may be either computationally inefficient or need a large amount of training data. In this thesis, we critically analyse and further develop a recently proposed non-parametric PDF estimation method for signals, called the NP windows method. We propose three new algorithms to compute PDF estimates using the NP windows method. One of these algorithms, called the log-basis algorithm, provides an easier and faster way to compute the NP windows estimate, and allows us to compare the NP windows method with the two existing popular estimators. Results show that the NP windows method is fast and can estimate PDFs with a significantly smaller amount of training data. Moreover, it does not require any additional parameter settings. To demonstrate utility of the NP windows method in image analysis we consider its application to image segmentation. To do this, we first describe the distribution of intensity values in the image with a mixture of non-parametric distributions. We estimate these distributions using the NP windows method. We then use this novel mixture model to evolve curves with the well-known level set framework for image segmentation. We also take into account the partial volume effect that assumes importance in medical image analysis methods. In the final part of the thesis, we apply our non-parametric mixture model (NPMM) based level set segmentation framework to segment colorectal MR images. The segmentation of colorectal MR images is made challenging due to sparsity and ambiguity of features, presence of various artifacts, and complex anatomy of the region. We propose to use the monogenic signal (local energy, phase, and orientation) to overcome the first difficulty, and the NPMM to overcome the remaining two. Results are improved substantially on those that have been reported previously. We also present various ways to visualise clinically useful information obtained with our segmentations in a 3-dimensional manner.

Dans cette these nous nous interessons a l'utilisation des méthodes de chemins minimaux et des méthodes de contours actifs par Ensembles de Niveaux, pour l'extraction de courbes et de surfaces dans des images medicales 3D. Dans un premier temps, nous nous sommes attaches a proposer un éventail varié de techniques d'extraction de chemins minimaux dans des images 2D et 3D, basees sur la résolution de l'équation Eikonal par l'algorithme du Fast Marching. Nous avons montre des resultats de ces techniques appliquees a des problèmes d'imagerie médicale concrets, notamment en construction de trajectoires 3D pour l'endoscopie virtuelle, et en segmentation interactive, avec possibilité d'apprentissage. Dans un deuxieme temps, nous nous sommes interessés a l'extraction de surfaces. Nous avons developpé un algorithme rapide de pré-segmentation, sur la base du formalisme des chemins minimaux. Nous avons étudié en détail la mise en place d'une collaboration entre cette méthode et celle des Ensembles de Niveaux, dont un des avantages communs est de ne pas avoir d'a priori sur la topologie de l'objet a segmenter. Cette méthode collaborative a ensuite ete testée sur des problèmes de segmentation et de visualisation de pathologies telles que les anevrismes cerebraux et les polypes du colon. Dans un troisième temps nous avons fusionné les résultats des deux premières parties pour obtenir l'extraction de surfaces, et des squelettes d'objets anatomiques tubulaires. Les squelettes des surfaces fournissent des trajectoires que nous utilisons pour déplacer des cameras virtuelles, et nous servent a definir les sections des objets lorsque nous voulons mesurer l'étendue d'une pathologie. La dernière partie regroupe des applications de ces méthodes a l'extraction de structures arborescentes. Nous étudions le cas des arbres vasculaires dans des images médicales 3D de produit de contraste, ainsi que le problème plus difficile de l'extraction de l'arbre bronchique sur des images scanners des poumons.

Les matériaux composites occupent une place de plus en plus importante dans l'industrie, en particulier aéronautique. Les composites à matrice thermoplastique suscitent aujourd'hui dans ce secteur un très fort engouement par rapport à leurs concurrents thermodurcissables. Le présent travail de thèse se concentre sur le soudage de matériaux composites à matrice thermoplastique. Le procédé de soudage ultrasons consiste à dissiper un travail mécanique au niveau de l'interface. La température augmente alors localement et entraîne un écoulement dans la zone soudée. Le procédé dit "continu", proposé par EADS IW, permet aujourd'hui d'envisager l'assemblage de structures aéronautiques à l'échelle industrielle par la technique ultrason. Bien évidemment, une bonne compréhension du procédé est un préalable indispensable à une telle application aéronautique. Afin d'étudier la qualité de l'adhésion, la présente étude se situe à l'échelle dite mésoscopique, de quelques millimètres. La problématique consiste à modéliser puis simuler numériquement la thermo-mécanique de l'écoulement à l'interface lors du soudage. L'objectif est de mieux comprendre les liens entre les différents paramètres du procédé, les phénomènes physiques dans la zone soudée et la qualité de la soudure. Après identification des phénomènes physiques prépondérants, la mise en équations de cet écoulement révèle la co-existence de phénomènes rapides (vibration) et lents (écoulement). Une méthode d'homogénéisation temporelle par développements asymptotiques permet alors de modéliser le procédé à l'aide de trois problèmes aux limites couplés. La résolution numérique de ces problèmes nécessite l'utilisation de méthodes particulières permettant de gérer les couplages multiphysiques et les grandes déformations de la géométrie. Finalement, l'outil numérique développé permet une analyse de l'influence des paramètres procédés sur la qualité de l'écoulement et du soudage.

This dissertation presents a fully automatic segmentation algorithm for cardiac MR data. Some of the currently published methods are automatic, but they only work well in 2D and sometimes in 3D and do not perform well near the extremities (apex and base) of the heart. Additionally, they require substantial user input to make them feasible for use in a clinical environment. This dissertation introduces novel approaches to improve the accuracy, robustness, and consistency of existing methods. Segmentation accuracy can be improved by knowing as much about the data as possible. Accordingly, we compute a single 4D active surface that performs segmentation in space and time simultaneously. The segmentation routine can now take advantage of information from neighboring pixels that can be adjacent either spatially or temporally. Robustness is improved further by using confidence labels on shape priors. Shape priors are deduced from manual segmentation of training data. This data may contain imperfections that may impede proper manual segmentation. Confidence labels indicate the level of fidelity of the manual segmentation to the actual data. The contribution of regions with low confidence levels can be attenuated or excluded from the final result. The specific advantages of using the 4D segmentation along with shape priors and regions of confidence are highlighted throughout the thesis dissertation. Performance of the new method is measured by comparing the results to traditional 3D segmentation and to manual segmentation performed by a trained clinician.

In scientific computing, it is very common to visualize the approximate solution obtained by a numerical PDE solver by drawing surface or contour plots of all or some components of the associated approximate solutions. These plots are used to investigate the behavior of the solution and to display important properties or characteristics of the approximate solutions. In this thesis, we consider techniques for drawing such contour plots for the solution of two and three dimensional PDEs. We first present three fast contouring algorithms in two dimensions over an underlying unstructured mesh. Unlike standard contouring algorithms, our algorithms do not require a fine structured approximation. We assume that the underlying PDE solver generates approximations at some scattered data points in the domain of interest. We then generate a piecewise cubic polynomial interpolant (PCI) which approximates the solution of a PDE at off-mesh points based on the DEI (Differential Equation Interpolant) approach. The DEI approach assumes that accurate approximations to the solution and first-order derivatives exist at a set of discrete mesh points. The extra information required to uniquely define the associated piecewise polynomial is determined based on almost satisfying the PDE at a set of collocation points. In the process of generating contour plots, the PCI is used whenever we need an accurate approximation at a point inside the domain. The direct extension of the both DEI-based interpolant and the contouring algorithm to three dimensions is also investigated. The use of the DEI-based interpolant we introduce for visualization can also be used to develop effective Adaptive Mesh Refinement (AMR) techniques and global error estimates. In particular, we introduce and investigate four AMR techniques along with a hybrid mesh refinement technique. Our interest is in investigating how well such a `generic' mesh selection strategy, based on properties of the problem alone, can perform compared with a special-purpose strategy that is designed for a specific PDE method. We also introduce an \`{a} posteriori global error estimator by introducing the solution of a companion PDE defined in terms of the associated PCI.

In scientific computing, it is very common to visualize the approximate solution obtained by a numerical PDE solver by drawing surface or contour plots of all or some components of the associated approximate solutions. These plots are used to investigate the behavior of the solution and to display important properties or characteristics of the approximate solutions. In this thesis, we consider techniques for drawing such contour plots for the solution of two and three dimensional PDEs. We first present three fast contouring algorithms in two dimensions over an underlying unstructured mesh. Unlike standard contouring algorithms, our algorithms do not require a fine structured approximation. We assume that the underlying PDE solver generates approximations at some scattered data points in the domain of interest. We then generate a piecewise cubic polynomial interpolant (PCI) which approximates the solution of a PDE at off-mesh points based on the DEI (Differential Equation Interpolant) approach. The DEI approach assumes that accurate approximations to the solution and first-order derivatives exist at a set of discrete mesh points. The extra information required to uniquely define the associated piecewise polynomial is determined based on almost satisfying the PDE at a set of collocation points. In the process of generating contour plots, the PCI is used whenever we need an accurate approximation at a point inside the domain. The direct extension of the both DEI-based interpolant and the contouring algorithm to three dimensions is also investigated. The use of the DEI-based interpolant we introduce for visualization can also be used to develop effective Adaptive Mesh Refinement (AMR) techniques and global error estimates. In particular, we introduce and investigate four AMR techniques along with a hybrid mesh refinement technique. Our interest is in investigating how well such a `generic' mesh selection strategy, based on properties of the problem alone, can perform compared with a special-purpose strategy that is designed for a specific PDE method. We also introduce an \`{a} posteriori global error estimator by introducing the solution of a companion PDE defined in terms of the associated PCI.

Level-set methods have become a valuable and well-established field of visualization over the last decades. Different implementations addressing different design goals and different data types exist. In particular, level sets can be used to extract isosurfaces from scalar volume data that fulfill certain smoothness criteria. Recently, such an approach has been generalized to operate on unstructured point-based volume data, where data points are not arranged on a regular grid nor are they connected in form of a mesh. Utilizing this new development, one can avoid an interpolation to a regular grid which inevitably introduces interpolation errors. However, the global processing of the level-set function can be slow when dealing with unstructured point-based volume data sets containing several million data points. We propose an improved level-set approach that performs the process of the level-set function locally. As for isosurface extraction we are only interested in the zero level set, values are only updated in regions close to the zero level set. In each iteration of the level-set process, the zero level set is extracted using direct isosurface extraction from unstructured point-based volume data and a narrow band around the zero level set is constructed. The band consists of two parts: an inner and an outer band. The inner band contains all data points within a small area around the zero level set. These points are updated when executing the level set step. The outer band encloses the inner band providing all those neighbors of the points of the inner band that are necessary to approximate gradients and mean curvature. Neighborhood information is obtained using an efficient kd-tree scheme, gradients and mean curvature are estimated using a four-dimensional least-squares fitting approach. Comparing ourselves to the global approach, we demonstrate that this local level-set approach for unstructured point-based volume data achieves a significant speed-up of one order of magnitude for data sets in the range of several million data points with equivalent quality and robustness.

This work deals with a fast level-set approach for segmentation of anatomical structures in volumetric medical images. The fast level-set method evolves a closed 3D surface in time propagating the surface form an initial position. The major contribution of this work is the implementation of the level-set method and construction of an interactive tool for segmentation of 3D medical data using this method. The tool is able to interactively change parameters of the evolution during the segmentation process itself. Due to the nature of level-set method, the evolution process can be stopped at any time, or backtracked and restarted from any previous step with a different configuration.

Due to increasing demand on deployable surveillance systems in recent years, object tracking and activity recognition are receiving considerable attention in the research community. This thesis contributes to both the tracking and the activity recognition components of a surveillance system. In particular, for the tracking component, we propose two different approaches for tracking objects in video acquired by mobile cameras, each of which uses a different object shape representation. The first approach tracks the centroids of the objects in Forward Looking Infrared Imagery (FLIR) and is suitable for tracking objects that appear small in airborne video. The second approach tracks the complete contours of the objects, and is suitable for higher level vision problems, such as activity recognition, identification and classification. Using the contours tracked by the contour tracker, we propose a novel representation, called the action sketch, for recognizing human activities. Object Tracking in Airborne Imagery: Images obtained from an airborne vehicle generally appear small and can be represented by geometric shapes such as circle or rectangle. After detecting the object position in the first frame, the proposed object tracker models the intensity and the local standard deviation of the object region defined by the shape model. It then tracks the objects by computing the mean-shift vector that minimizes the distance between the kernel distribution for the hypothesized object and its prior. In cases when the ego-motion of the sensor causes the object to move more than the operational limits of the tracking module, a multi-resolution global motion compensation using the Gabor responses of consecutive frames is performed. The experiments performed on the AMCOM FLIR data set show the robustness of the proposed method, which combines automatic model update and global motion compensation into one framework. Contour Tracker: Contour tracking is performed by evolving an initial contour toward the correct object boundaries based on discriminant analysis, which is formulated as a variational calculus problem. Once the contour is initialized, the method generates an online shape model for the object along with the color and the texture priors for both the object and the background regions. A priori texture and color PDFs of the regions are then fused based on the discrimination properties of the features between the object and the background models. The models are then used to compute the posteriori contour likelihood and the evolution is obtained by the Maximum a Posteriori Estimation process, which updates the contour in the gradient ascent direction of the proposed energy functional. During occlusion, the online shape model is used to complete the missing object region. The proposed energy functional unifies commonly used boundary and region based contour approaches into a single framework through a support region defined around the hypothesized object contour. We tested the robustness of the proposed contour tracker using several real sequences and have verified qualitatively that the contours of the objects are perfectly tracked. Behavior Analysis: We propose a novel approach to represent human actions by modeling the dynamics (motion) and the structure (shape) of the objects in video. Both the motion and the shape are modeled using a compact representation, which is called the “action sketch”. An action sketch is a view invariant representation obtained by analyzing important changes that occur during the motion of the objects. When an actor performs an action in 3D, the points on the actor generate space-time trajectories in four dimensions (x, y, z,t). Projection of the world to the imaging coordinates converts the space-time trajectories into the spatiotemporal trajectories in three dimensions (x, y,t). A set of spatio-temporal trajectories constitute a 3D volume, which we call an “action volume”. This volume can be treated as a 3D object in the (x, y,t) space. The action sketch is generated from the action volume by analyzing the differential geometric surface properties, such as peaks, pits, valleys and ridges. These properties reflect the changes in the speed, the motion direction and the shape of the performing actor. We perform action recognition by computing a view invariant distance measure between the sketch generated from the input video and the set of known sketches in the database. Experimental results are provided for twenty eight actions.

Endometriosis is an oestrogen-dependent gynaecological condition defined as the presence of endometrial tissue outside the uterus cavity. The condition is predominantly found in women in their reproductive years, and associated with significant pelvic and abdominal chronic pain and infertility. The disease is believed to affect approximately 33% of women by a recent study. Currently, surgical intervention, often laparoscopic surgery, is the gold standard for diagnosing the disease and it remains an effective and common treatment method for all stages of endometriosis. Magnetic resonance imaging (MRI) of the patient is performed before surgery in order to locate any endometriosis lesions and to determine whether a multidisciplinary surgical team meeting is required. In this dissertation, our goal is to use image processing techniques to aid surgical planning. Specifically, we aim to improve quality of the existing images, and to automatically detect bladder endometriosis lesion in MR images as a form of bladder wall thickening. One of the main problems posed by abdominal MRI is the sparse anisotropic frequency sampling process. As a consequence, the resulting images consist of thick slices and have gaps between those slices. We have devised a method to fuse multi-view MRI consisting of axial/transverse, sagittal and coronal scans, in an attempt to restore an isotropic densely sampled frequency plane of the fused image. In addition, the proposed fusion method is steerable and is able to fuse component images in any orientation. To achieve this, we apply the Riesz transform for image decomposition and reconstruction in the frequency domain, and we propose an adaptive fusion rule to fuse multiple Riesz-components of images in different orientations. The adaptive fusion is parameterised and switches between combining frequency components via the mean and maximum rule, which is effectively a trade-off between smoothing the intrinsically noisy images while retaining the sharp delineation of features. We first validate the method using simulated images, and compare it with another fusion scheme using the discrete wavelet transform. The results show that the proposed method is better in both accuracy and computational time. Improvements of fused clinical images against unfused raw images are also illustrated. For the segmentation of the bladder wall, we investigate the level set approach. While the traditional gradient based feature detection is prone to intensity non-uniformity, we present a novel way to compute phase congruency as a reliable feature representation. In order to avoid the phase wrapping problem with inverse trigonometric functions, we devise a mathematically elegant and efficient way to combine multi-scale image features via geometric algebra. As opposed to the original phase congruency, the proposed method is more robust against noise and hence more suitable for clinical data. To address the practical issues in segmenting the bladder wall, we suggest two coupled level set frameworks to utilise information in two different MRI sequences of the same patients - the T2- and T1-weighted image. The results demonstrate a dramatic decrease in the number of failed segmentations done using a single kind of image. The resulting automated segmentations are finally validated by comparing to manual segmentations done in 2D.