The methods presented in this study are aimed at the identification of subpopulations (clones) of genetically similar cells within tissue samples through measurement of loci-specific Fluorescence in-situ hybridization (FISH) spot signals for each nucleus and analyzing cell spatial distributions by way of Voronoi tessellation and Delaunay triangulation to robustly define cell neighbourhoods. The motivation for the system is to examine lung cancer patient for subpopulations of Non-Small Cell Lung Cancer (NSCLC) cells with biologically meaningful gene copy-number profiles: patterns of genetic alterations statistically associated with resistance to cis-platinum/vinorelbine doublet chemotherapy treatment. Current technologies for gene-copy number profiling rely on large amount of cellular material, which is not always available and suffers from limited sensitivity to only the most dominant clone in often heterogeneous samples. Thus, through the use of FISH, the detection of gene copy-numbers is possible in unprocessed tissues, allowing identification of specific tumour clones with biologically relevant patterns of genetic aberrations. The tissue-wide characterization of multiplexed loci-specific FISH signals, described herein, is achieved through a fully automated, multicolour fluorescence imaging microscope and object segmentation algorithms to identify cell nuclei and FISH spots within. Related tumour clones are identified through analysis of robustly defined cell neighbourhoods and cell-to-cell connections for regions of cells with homogenous and highly interconnected FISH spot signal characteristics. This study presents experiments which demonstrate the system’s ability to accurately quantify FISH spot signals in various tumour tissues and in up to 5 colours simultaneously or more through multiple rounds of FISH staining. Furthermore, the system’s FISH-based cell classification performance is evaluated at a sensitivity of 84% and specificity 81% and clonal identification algorithm results are determined to be comparable to clone delineation by a human-observer. Additionally, guidelines and procedures to perform anticipated, routine analysis experiments are established. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

In computer graphics, when simulating fractured or cracked objects, most commonly physically based methods or hybrid solutions using physical and procedural methods are used to achieve the result. If only a static representation of a cracked surface, and not a simulation of an object cracking, is desired, these approaches of crack generation are not suitable. Non-physically based methods to generate the cracks or fractured objects has also been used where a fracture pattern is projected onto an object. In this thesis a novel method of generating 3D avalanche slabs directly from a 2D Voronoi pattern, in real-time, without using physically based methods or 3D procedural crack generation is presented. After the slabs are generated, they are placed on the surface of a terrain. To add a more realistic look, snow is added on the mountain around the avalanche slabs. Using this novel method of generating 3D avalanche slabs, separate 3D mesh objects are created directly from the Voronoi pattern, and no 3D model is needed initially to generate them from. The results show that this method can be used in real-time with limitations. With improvements suggested in this thesis, the presented method could be used to generate a large amount of slabs in a fairly large region, and software developers can benefit from using this method in their graphics renderer.

Yes / Background and Objective Corneal endothelial cell abnormalities may be associated with a number of corneal and systemic diseases. Damage to the endothelial cells can significantly affect corneal transparency by altering hydration of the corneal stroma, which can lead to irreversible endothelial cell pathology requiring corneal transplantation. To date, quantitative analysis of endothelial cell abnormalities has been manually performed by ophthalmologists using time consuming and highly subjective semi-automatic tools, which require an operator interaction. We developed and applied a fully-automated and real-time system, termed the Corneal Endothelium Analysis System (CEAS) for the segmentation and computation of endothelial cells in images of the human cornea obtained by in vivo corneal confocal microscopy. Methods First, a Fast Fourier Transform (FFT) Band-pass filter is applied to reduce noise and enhance the image quality to make the cells more visible. Secondly, endothelial cell boundaries are detected using watershed transformations and Voronoi tessellations to accurately quantify the morphological parameters of the human corneal endothelial cells. The performance of the automated segmentation system was tested against manually traced ground-truth images based on a database consisting of 40 corneal confocal endothelial cell images in terms of segmentation accuracy and obtained clinical features. In addition, the robustness and efficiency of the proposed CEAS system were compared with manually obtained cell densities using a separate database of 40 images from controls (n = 11), obese subjects (n = 16) and patients with diabetes (n = 13). Results The Pearson correlation coefficient between automated and manual endothelial cell densities is 0.9 (p < 0.0001) and a Bland–Altman plot shows that 95% of the data are between the 2SD agreement lines. Conclusions We demonstrate the effectiveness and robustness of the CEAS system, and the possibility of utilizing it in a real world clinical setting to enable rapid diagnosis and for patient follow-up, with an execution time of only 6 seconds per image.

In remote sensing, segmentation is a procedure of partitioning the domain of a remotely sensed dataset into meaningful regions which correspond to different land use and land cover (LULC) classes or part of them. So far, the remotely sensed data segmentation is still one of the most challenging problems addressed by the remote sensing community, partly because of the availability of remotely sensed data from diverse sensors of various platforms with very high spatial resolution (VHSR). Thus, there is a strong motivation to propose a sophisticated data representation that can capture the significant amount of details presented in a VHSR dataset and to search for a more powerful scheme suitable for multiple remotely sensed data segmentations. This thesis focuses on the development of a segmentation framework for multiple VHSR remotely sensed data. The emphases are on VHSR data model and segmentation strategy. Starting with the domain partition of a given remotely sensed dataset, a hierarchical data model characterizing the structures hidden in the dataset locally, regionally and globally is built by three random fields: Markova random field (MRF), strict stationary random field (RF) and label field. After defining prior probability distributions which should capture and characterize general and scene-specific knowledge about model parameters and the contextual structure of accurate segmentations, the Bayesian based segmentation framework, which can lead to algorithmic implementation for multiple remotely sensed data, is developed by integrating both the data model and the prior knowledge. To verify the applicability and effectiveness of the proposed segmentation framework, the segmentation algorithms for different types of remotely sensed data are designed within the proposed segmentation framework. The first application relates to SAR intensity image processing, including segmentation and dark spot detection by marked point process. In the second application, the algorithms for LiDAR point cloud segmentation and building detection are developed. Finally, texture and colour texture segmentation problems are tackled within the segmentation framework. All applications demonstrate that the proposed data model provides efficient representations for hierarchical structures hidden in remotely sensed data and the developed segmentation framework leads to successful data processing algorithms for multiple data and task such as segmentation and object detection.

In remote sensing, segmentation is a procedure of partitioning the domain of a remotely sensed dataset into meaningful regions which correspond to different land use and land cover (LULC) classes or part of them. So far, the remotely sensed data segmentation is still one of the most challenging problems addressed by the remote sensing community, partly because of the availability of remotely sensed data from diverse sensors of various platforms with very high spatial resolution (VHSR). Thus, there is a strong motivation to propose a sophisticated data representation that can capture the significant amount of details presented in a VHSR dataset and to search for a more powerful scheme suitable for multiple remotely sensed data segmentations. This thesis focuses on the development of a segmentation framework for multiple VHSR remotely sensed data. The emphases are on VHSR data model and segmentation strategy. Starting with the domain partition of a given remotely sensed dataset, a hierarchical data model characterizing the structures hidden in the dataset locally, regionally and globally is built by three random fields: Markova random field (MRF), strict stationary random field (RF) and label field. After defining prior probability distributions which should capture and characterize general and scene-specific knowledge about model parameters and the contextual structure of accurate segmentations, the Bayesian based segmentation framework, which can lead to algorithmic implementation for multiple remotely sensed data, is developed by integrating both the data model and the prior knowledge. To verify the applicability and effectiveness of the proposed segmentation framework, the segmentation algorithms for different types of remotely sensed data are designed within the proposed segmentation framework. The first application relates to SAR intensity image processing, including segmentation and dark spot detection by marked point process. In the second application, the algorithms for LiDAR point cloud segmentation and building detection are developed. Finally, texture and colour texture segmentation problems are tackled within the segmentation framework. All applications demonstrate that the proposed data model provides efficient representations for hierarchical structures hidden in remotely sensed data and the developed segmentation framework leads to successful data processing algorithms for multiple data and task such as segmentation and object detection.

Multi-agent systems are extensively used in several applications. An important class of applications involves the optimal spatial distribution of a group of mobile robots on a given area, where the optimality refers to the assignment of subregions to the robots, in such a way that a suitable coverage metric is maximized. Typically the coverage metric encodes a risk distribution defined on the area, and a measure of the performance of individual robots with respect to points inside the region of interest. The coverage metric will be maximized when the set of mobile robots configure themselves as the centroids of the Voronoi tessellation dictated by the risk density. In this work we advance on this result by considering a generalized area control problem in which the coverage metric is non-autonomous, that coverage metric is time varying independently of the states of the robots. This generalization is motivated by the study of coverage control problems in which the coordinated motion of a set of mobile robots accounts for the kinematics of objects penetrating from the outside. Asymptotic convergence and optimality of the non-autonmous system are studied by means of Barbalat's Lemma, and connections with the kinematics of the moving intruders is established. Several numerical simulation results are used to illustrate theoretical predictions.

Une mosaïque de Poisson-Voronoï est une partition aléatoire de l'espace euclidien en polyèdres, appelés cellules, obtenue à partir d'un ensemble aléatoire discret de points appelés germes. A chaque germe correspond une cellule, qui est l'ensemble des points de l'espace qui sont plus proches de ce germes que des autres germes. Ces modèles sont souvent utilisées dans divers domaines tels que la biologie, les télécommunications, l'astronomie, etc. Les caractéristiques de ces mosaïques et des cellules associées ont été largement étudiées dans l'espace euclidien mais les travaux sur les mosaïques de Voronoï dans un cadre non-euclidien sont rares.Dans cette thèse, on étend la définition de mosaïque de Voronoï à une variétériemannienne de dimension finie et on s'intéresse aux caractéristiques des cellules associées. Plus précisément, on mesure dans un premier temps l'influence que peut avoir la géométrie locale de la variété, c'est-à-dire les courbures sur les caractéristiques moyennes d'une cellule, comme son volume ou son nombre de sommets, en calculant des développements asymptotiques des ces caractéristiques moyennes à grande intensité. Dans un deuxième temps, on s'interroge sur la possibilité de retrouver la géométrie locale de la variété à partir des caractéristiques combinatoires de la mosaïque sur la variété. En particulier, on établit desthéorèmes limites, quand l'intensité du processus des germes tend vers l'infini, pour le nombre de sommets de la mosaïque dans une fenêtre, ce qui permet de construire un estimateur de la courbure et d'en donner quelques propriétés.Les principaux résultats de cette thèse reposent sur la combinaison de méthodesprobabilistes et de techniques issues de la géométrie différentielle. / A Poisson-Voronoi tessellation is a random partition of the Euclidean space intopolytopes, called cells, obtained from a discrete set of points called germs. To each germ corresponds a cell which is the set of the points of the space which are closer to this germ than to the other germs. These models are often used in several domains such as biology, telecommunication, astronomy, etc. The caracteristics of these tessellations and cells have been widely studied in the Euclidean space but only a few works concerns non-Euclidean Voronoi tessellation. In this thesis, we extend the definition of Poisson-Voronoi tessellation to a Riemannian manifold with finite dimension and we study the caracteristics of the associated cells. More precisely, we first measure the influence of the local geometry of the manifold, namely the curvatures, on the caracteristics of the cells, e.g. the mean volume or the mean number of vertices. Second, we aim to recover the local geometry of the manifold from the combinatorial properties of the tessellation on the manifolds. In particular, we establish limit theorems for the number of vertices of the tessellation, when the intensity of the process of the germs tends to infinity. This leads to the construction of an estimator of the curvature of the manifold and makes it possible to derive some properties of it. The main results of this thesis relies on the combination of stochastic methods and techniques from the differential geometry theory.

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Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.

Dado um processo de Poisson d-dimensional, construímos funções harmônicas na triangulação de Delaunay associada, com comportamento assintótico linear, como limite de um processo de harness sem ruído. Tais funções permitem que construamos uma nova imersão da triangulação de Delaunay, que denominaremos de deformação harmônica. / Given a d-dimensional Poisson point process, we construct harmonic functions on the associated Delaunay triangulation, with linear assymptotic behaviour, as the limit of a noiseless harness process. These mappings allow us to find a new embedding for the Delaunay triangulation. We call it harmonic deformation of the graph.