Nephroblastoma in MRI Data

The main objective of this work is the mathematical analysis of nephroblastoma in MRI sequences. At the beginning we provide two different datasets for segmentation and classification. Based on the first dataset, we analyze the current clinical practice regarding therapy planning on the basis of annotations of a single radiologist. We can show with our benchmark that this approach is not optimal and that there may be significant differences between human annotators and even radiologists. In addition, we demonstrate that the approximation of the tumor shape currently used is too coarse granular and thus prone to errors. We address this problem and develop a method for interactive segmentation that allows an intuitive and accurate annotation of the tumor. While the first part of this thesis is mainly concerned with the segmentation of Wilms’ tumors, the second part deals with the reliability of diagnosis and the planning of the course of therapy. The second data set we compiled allows us to develop a method that dramatically improves the differential diagnosis between nephroblastoma and its precursor lesion nephroblastomatosis. Finally, we can show that even the standard MRI modality for Wilms’ tumors is sufficient to estimate the developmental tendencies of nephroblastoma under chemotherapy

Image Segmentation using PDE, Variational, Morphological and Probabilistic Methods

The research in this dissertation has focused upon image segmentation and its related areas, using the techniques of partial differential equations, variational methods, mathematical morphological methods and probabilistic methods. An integrated segmentation method using both curve evolution and anisotropic diffusion is presented that utilizes both gradient and region information in images. A bottom-up image segmentation method is proposed to minimize the Mumford-Shah functional. Preferential image segmentation methods are presented that are based on the tree of shapes in mathematical morphologies and the Kullback-Leibler distance in information theory. A thorough evaluation of the morphological preferential image segmentation method is provided, and a web interface is described. A probabilistic model is presented that is based on particle filters for image segmentation. These methods may be incorporated as components of an integrated image processed system. The system utilizes Internet Protocol (IP) cameras for data acquisition. It utilizes image databases to provide prior information and store image processing results. Image preprocessing, image segmentation and object recognition are integrated in one stage in the system, using various methods developed in several areas. Interactions between data acquisition, integrated image processing and image databases are handled smoothly. A framework of the integrated system is implemented using Perl, C++, MySQL and CGI. The integrated system works for various applications such as video tracking, medical image processing and facial image processing. Experimental results on this applications are provided in the dissertation. Efficient computations such as multi-scale computing and parallel computing using graphic processors are also presented

Computing Approximate Solutions to the Art Gallery Problem and Watchman Route Problem by Means of Photon Mapping

Wireless sensor networks (WSNs) can be partitioned component sensor nodes (SNs) who are meant to operate and sense information arriving from multiple spectra in their environment. Determining where to place a single SN or multiple SNs such that the amount of information gained is maximized while the number of SNs used to gain that information is minimized is an instance of solving the art gallery problem (AGP). In order to solve the AGP, we present the Sensor Placement Optimization via Queries (SPOQ) algorithm that uses level sets populated by queries to a photon map in order to find observation points that sense as many photons as possible. Since we are using photon mapping as our means of modeling how information is conveyed, SPOQ can then take into account static or dynamic environmental conditions and can use exploratory or precomputed sensing. Unmanned vehicles can be designated more generally as UxVs where “x” indicates the environment they are expected to operate – either in the air, on the ground, underwater or on the water’s surface. Determining how to plan an optimal route by a single UxV or multiple UxVs operating in their environment such that the amount of information gained is maximized while the cost of gaining that information is minimized is an instance of solving the watchman route problem (WRP). In order to solve the WRP, we present the Photon-mapping-Informed active-Contour Route Designator (PICRD) algorithm. PICRD heuristically solves the WRP by utilizing SPOQ’s AGP-solving vertices and connecting them with the high visibility vertices provided by a photon-mapping informed Chan-Vese segmentation mesh using a shortest-route path-finding algorithm. Since we are using photon-mapping as our foundation for determining sensor coverage by the PICRD algorithm, we can then take into account the behavior of photons as they propagate through the various environmental conditions that might be encountered by a single or multiple UxVs

A discrete graph Laplacian for signal processing

In this thesis we exploit diffusion processes on graphs to effect two fundamental problems of image processing: denoising and segmentation. We treat these two low-level vision problems on the pixel-wise level under a unified framework: a graph embedding. Using this framework opens us up to the possibilities of exploiting recently introduced algorithms from the semi-supervised machine learning literature. We contribute two novel edge-preserving smoothing algorithms to the literature. Furthermore we apply these edge-preserving smoothing algorithms to some computational photography tasks. Many recent computational photography tasks require the decomposition of an image into a smooth base layer containing large scale intensity variations and a residual layer capturing fine details. Edge-preserving smoothing is the main computational mechanism in producing these multi-scale image representations. We, in effect, introduce a new approach to edge-preserving multi-scale image decompositions. Where as prior approaches such as the Bilateral filter and weighted-least squares methods require multiple parameters to tune the response of the filters our method only requires one. This parameter can be interpreted as a scale parameter. We demonstrate the utility of our approach by applying the method to computational photography tasks that utilise multi-scale image decompositions. With minimal modification to these edge-preserving smoothing algorithms we show that we can extend them to produce interactive image segmentation. As a result the operations of segmentation and denoising are conducted under a unified framework. Moreover we discuss how our method is related to region based active contours. We benchmark our proposed interactive segmentation algorithms against those based upon energy-minimisation, specifically graph-cut methods. We demonstrate that we achieve competitive performance

Contributions en optimisation topologique : extension de la méthode adjointe et applications au traitement d'images

De nos jours, l'optimisation topologique a été largement étudiée en optimisation de structure, problème majeur en conception de systèmes mécaniques pour l'industrie et dans les problèmes inverses avec la détection de défauts et d'inclusions. Ce travail se concentre sur les approches de dérivées topologiques et propose une généralisation plus flexible de cette méthode rendant possible l'investigation de nouvelles applications. Dans une première partie, nous étudions des problèmes classiques en traitement d'images (restauration, inpainting), et exposons une formulation commune à ces problèmes. Nous nous concentrons sur la diffusion anisotrope et considérons un nouveau problème : la super-résolution. Notre approche semble meilleure comparée aux autres méthodes. L'utilisation des dérivées topologiques souffre d'inconvénients : elle est limitée à des problèmes simples, nous ne savons pas comment remplir des trous ... Dans une seconde partie, une nouvelle méthode visant à surmonter ces difficultés est présentée. Cette approche, nommée voûte numérique, est une extension de la méthode adjointe. Ce nouvel outil nous permet de considérer de nouveaux champs d'application et de réaliser de nouvelles investigations théoriques dans le domaine des dérivées topologiques.Nowadays, topology optimization has been extensively studied in structural optimization which is a major interest in the design of mechanical systems in the industry and in inverse problems with the detection of defects or inclusions. This work focuses on the topological derivative approach and proposes a more flexible generalization of this method making it possible to address new applications. In a first part, we study classical image processing problems (restoration, inpainting), and give a common framework to theses problems. We focus on anisotropic diffusion and consider a new problem: super-resolution. Our approach seems to be powerful in comparison with other methods. Topological derivative method has some drawbacks: it is limited to simple problems, we do not know how to fill holes, ... In a second part, to overcome these difficulties, an extension of the adjoint method is presented. Named the numerical vault, it allows us to consider new fields of applications and to explore new theoretical investigations in the area of topological derivative

POŁĄCZENIE METODY ELEMENTÓW BRZEGOWYCH I ZBIORÓW POZIOMICOWYCH W ROZWIĄZYWANIU ZAGADNIENIA ODWROTNEGO

The boundary element method and the level set method can be used in order to solve the inverse problem for electric field. In this approach the adjoint equation arises in each iteration step. Results of the numerical calculations show that the boundary element method can be applied successfully to obtain approximate solution of the adjoint equation. The proposed solution algorithm is initialized by using topological sensitivity analysis. Shape derivatives and material derivatives have been incorporated with the level set method to investigate shape optimization problems. The shape derivative measures the sensitivity of boundary perturbations. The coupled algorithm is a relatively new procedure to overcome this problem. Experimental results have demonstrated the efficiency of the proposed approach to achieve the solution of the inverse problem.Metoda elementów brzegowych i metoda zbiorów poziomicowych mogą być wykorzystane to rozwiązania zagadnienia odwrotnego pola elektrycznego. W takim podejściu równanie sprzężone jest rozwiązywane w każdym kroku iteracyjnym. Wyniki obliczeń numerycznych pokazują, że metoda elementów brzegowych może być zastosowana z powodzeniem do uzyskania przybliżonego rozwiązania równania sprzężonego. Proponowany algorytm jest inicjalizowany za pomocą topologicznej analizy wrażliwościowej. Pochodna kształtu i pochodna materialna zostały połączone z metodą zbiorów poziomicowych w celu zbadania problemów optymalizacji kształtu. Pochodna kształtu mierzy wrażliwość perturbacji brzegowych. Zespolony algorytm jest stosunkowo nową procedurą do rozwiązania tego problemu. Wyniki doświadczenia pokazały skuteczność proponowanego podejścia w rozwiązywaniu zagadnienia odwrotnego

Interactive Segmentation of 3D Medical Images with Implicit Surfaces

To cope with a variety of clinical applications, research in medical image processing has led to a large spectrum of segmentation techniques that extract anatomical structures from volumetric data acquired with 3D imaging modalities. Despite continuing advances in mathematical models for automatic segmentation, many medical practitioners still rely on 2D manual delineation, due to the lack of intuitive semi-automatic tools in 3D. In this thesis, we propose a methodology and associated numerical schemes enabling the development of 3D image segmentation tools that are reliable, fast and interactive. These properties are key factors for clinical acceptance. Our approach derives from the framework of variational methods: segmentation is obtained by solving an optimization problem that translates the expected properties of target objects in mathematical terms. Such variational methods involve three essential components that constitute our main research axes: an objective criterion, a shape representation and an optional set of constraints. As objective criterion, we propose a unified formulation that extends existing homogeneity measures in order to model the spatial variations of statistical properties that are frequently encountered in medical images, without compromising efficiency. Within this formulation, we explore several shape representations based on implicit surfaces with the objective to cover a broad range of typical anatomical structures. Firstly, to model tubular shapes in vascular imaging, we introduce convolution surfaces in the variational context of image segmentation. Secondly, compact shapes such as lesions are described with a new representation that generalizes Radial Basis Functions with non-Euclidean distances, which enables the design of basis functions that naturally align with salient image features. Finally, we estimate geometric non-rigid deformations of prior templates to recover structures that have a predictable shape such as whole organs. Interactivity is ensured by restricting admissible solutions with additional constraints. Translating user input into constraints on the sign of the implicit representation at prescribed points in the image leads us to consider inequality-constrained optimization

A collaborative approach to image segmentation and behavior recognition from image sequences

Visual behavior recognition is currently a highly active research area. This is due both to the scientific challenge posed by the complexity of the task, and to the growing interest in its applications, such as automated visual surveillance, human-computer interaction, medical diagnosis or video indexing/retrieval. A large number of different approaches have been developed, whose complexity and underlying models depend on the goals of the particular application which is targeted. The general trend followed by these approaches is the separation of the behavior recognition task into two sequential processes. The first one is a feature extraction process, where features which are considered relevant for the recognition task are extracted from the input image sequence. The second one is the actual recognition process, where the extracted features are classified in terms of the pre-defined behavior classes. One problematic issue of such a two-pass procedure is that the recognition process is highly dependent on the feature extraction process, and does not have the possibility to influence it. Consequently, a failure of the feature extraction process may impair correct recognition. The focus of our thesis is on the recognition of single object behavior from monocular image sequences. We propose a general framework where feature extraction and behavior recognition are performed jointly, thereby allowing the two tasks to mutually improve their results through collaboration and sharing of existing knowledge. The intended collaboration is achieved by introducing a probabilistic temporal model based on a Hidden Markov Model (HMM). In our formulation, behavior is decomposed into a sequence of simple actions and each action is associated with a different probability of observing a particular set of object attributes within the image at a given time. Moreover, our model includes a probabilistic formulation of attribute (feature) extraction in terms of image segmentation. Contrary to existing approaches, segmentation is achieved by taking into account the relative probabilities of each action, which are provided by the underlying HMM. In this context, we solve the joint problem of attribute extraction and behavior recognition by developing a variation of the Viterbi decoding algorithm, adapted to our model. Within the algorithm derivation, we translate the probabilistic attribute extraction formulation into a variational segmentation model. The proposed model is defined as a combination of typical image- and contour-dependent energy terms with a term which encapsulates prior information, offered by the collaborating recognition process. This prior information is introduced by means of a competition between multiple prior terms, corresponding to the different action classes which may have generated the current image. As a result of our algorithm, the recognized behavior is represented as a succession of action classes corresponding to the images in the given sequence. Furthermore, we develop an extension of our general framework, that allows us to deal with a common situation encountered in applications. Namely, we treat the case where behavior is specified in terms of a discrete set of behavior types, made up of different successions of actions, which belong to a shared set of action classes. Therefore, the recognition of behavior requires the estimation of the most probable behavior type and of the corresponding most probable succession of action classes which explains the observed image sequence. To this end, we modify our initial model and develop a corresponding Viterbi decoding algorithm. Both our initial framework and its extension are defined in general terms, involving several free parameters which can be chosen so as to obtain suitable implementations for the targeted applications. In this thesis, we demonstrate the viability of the proposed framework by developing particular implementations for two applications. Both applications belong to the field of gesture recognition and concern finger-counting and finger-spelling. For the finger-counting application, we use our original framework, whereas for the finger-spelling application, we use its proposed extension. For both applications, we instantiate the free parameters of the respective frameworks with particular models and quantities. Then, we explain the training of the obtained models from specific training data. Finally, we present the results obtained by testing our trained models on new image sequences. The test results show the robustness of our models in difficult cases, including noisy images, occlusions of the gesturing hand and cluttered background. For the finger-spelling application, a comparison with the traditional sequential approach to image segmentation and behavior recognition illustrates the superiority of our collaborative model