In this thesis, a comparative evaluation of five different wavelet-based filtering techniques in the task of microarray image denoising and enhancement, as well as, a new methodology for the segmentation of microarray images is developed. Clinical material comprised complementary DNA (cDNA) microarray images collected from the Oak Ridge National Laboratory, simulated data produced by using a Microarray Scan Simulator, and a set of two simulated images, each containing 200 spots. Image pre-processing was performed in two stages: In the first stage an Exponential Histogram Equalization filter was applied to real cDNA images in order to increase the contrast between spots and surrounding background. In the second stage, five wavelet-based image filters (Simple Piece-Wise Linear Mapping Filter (SPWLMF), Hard Threshold filter (HTF), Wavelet Enhancement with Noise Suppression filter (WEWNSF), Non Linear Enhancement filter (NLEF) and Sigmoidal Non-linear Enhancement filter (SNLEF)) were implemented for denoising and enhancing gene microarray spots. The enhancing effectiveness of the five filters was assessed by calculating the Mean-Square-Error (MSE) and the Signal-to-MSE ratio. An automatic gridding scheme was applied to both real and simulated cDNA images, for the task of determining spots and their borders (cells). Firstly, the segmentation capability of the Gaussian Mixture Models GMM boosted by the five wavelet based preprocessing filters was evaluated by calculating the segmentation matching factor for each spot. Significant noise suppression was accomplished by the SPWLMP filter, which scored the minimum MSE and the maximum Signal-to-MSE ratio. Optimal segmentation results were obtained by pre-processing the microarray image by all the wavelet-based filters. Finally, a new methodology for spot identification based on the combination of GMM clustering technique with Gradient Vector Flow (GVF) active contours was introduced. According to that method, a GMM clustering algorithm was firstly applied in all individual spot images of the cDNA image. Afterwards, the output of the GMM algorithm was used to utilize a Gradient Vector Flow (GVF) active contour. The major advance of our method is that it overcomes limitations of GMM and deformable models when used individually. For the evaluation of our method, segmentation matching factors, as well as mean intensity value were calculated for every cell using GMM, GVF active contours and GMM and GVF active contours combination. Numerical experiments using simulated cDNA images have also shown that our method was more accurate in measuring mean intensity values and detecting real boundaries of spots with foreground mean intensity value close to the background, compared with GMM and snakes used individually. / Ο σκοπός της παρούσας διπλωματικής εργασίας είναι η συγκριτική αξιολόγηση πέντε διαφορετικών φίλτρων βασισμένα σε μετασχηματισμό κυματιδίου, τα οποία εφαρμόστηκαν σε εικόνες μικροσυστοιχιών. Επίσης, μια νέα μέθοδος για την κατάτμηση των εικόνων αυτών πραγματοποιήθηκε. Ως υλικό, χρησιμοποιήθηκαν εικόνες συμπληρωματικού DNA από το Oak Ridge National Laboratory, απομιμούμενα δεδομένα με την χρήση του Microarray Scan Simulator, καθώς και ένα σετ από δύο απομιμούμενες εικόνες, οι οποίες περιείχαν 200 κηλίδες. Η προεπεξεργασία των εικόνων πραγματοποιήθηκε σε δύο στάδια. Πρώτα, ένα εκθετικό φίλτρο ισοστάθμισης ιστογράμματος εφαρμόστηκε στις πραγματικές εικόνες, με σκοπό την αύξηση της αντίθεσης της εικόνας. Στη συνέχεια, αναπτυχθήκαν και εφαρμόστηκαν τα πέντε φίλτρα βασισμένα σε μετασχηματισμό κυματιδίου (Simple Piece-Wise Linear Mapping Filter (SPWLMF), Hard Threshold filter (HTF), Wavelet Enhancement with Noise Suppression filter (WEWNSF), Non Linear Enhancement filter (NLEF) and Sigmoidal Non-linear Enhancement filter (SNLEF)) με σκοπό την αύξηση της αντίθεσης. Ποσοτικά, η ικανότητα βελτίωσης των πέντε παραπάνω αλγορίθμων μετρήθηκε με το Mean-Square-Error (MSE) και το Signal-to-MSE. Ένα αυτόματο σύστημα διευθυνσιοδότησης εφαρμόστηκε στις πραγματικές και τις απομιμούμενες εικόνες με σκοπό την ανίχνευση των κηλίδων. Στην συνέχεια εφαρμόστηκαν αλγόριθμοι κατάτμησης μίξης Γκαουσιανών μοντέλων (GMM). Η αξιολόγηση πραγματοποιήθηκε με τη βοήθεια του παράγοντα ταυτοποίησης κατάτμησης. Σημαντική μείωση του θορύβου πραγματοποιήθηκε από το φίλτρο SPWLMF, το οποίο πέτυχε το μικρότερο MSE και το μεγαλύτερο S/MSE. Επίσης, καλύτερα αποτελέσματα πάρθηκαν από τις εικόνες οι οποίες είχαν προεπεξεργαστεί από τα φίλτρα μετασχηματισμού κυαμτιδίου. Στη συνέχεια, υλοποιήθηκε μια νέα τεχνική κατάτμησης βασισμένη στο συνδυασμό GMM και Gradient Vector Flow (GVF) ενεργών περιγραμμάτων. Σύμφωνα με τη μέθοδο αυτή, ο αλγόριθμος GMM εφαρμόζεται και δημιουργείτε μια δυαδική εικόνα η οποία περιέχει το περίγραμμα της κηλίδας. Στην συνέχεια, αυτό το περίγραμμα χρησιμοποιείται για την εκκίνηση ενός GVF ενεργού περιγράμματος. Το κυριότερο πλεονέκτημα αυτής της τεχνικής είναι ότι ξεπερνά περιορισμούς των δύο αυτών αλγορίθμων, όταν αυτοί χρησιμοποιούνται μεμονωμένα. Για την αξιολόγηση της μεθόδου υπολογίστηκε ο παράγοντα ταυτοποίησης κατάτμησης, καθώς και η μέση τιμή για κάθε κηλίδα, χρησιμοποιώντας τον αλγόριθμο GMM, τον αλγόριθμο GVF ενεργών περιγραμμάτων καθώς και το υβριδικό μοντέλο GMM και GVF ενεργού περιγράμματος. Αριθμητικά αποτελέσματα σε απομιμούμενες εικόνες απέδειξαν ότι η μέθοδος μας είναι πιο αποτελεσματική στο να βρίσκει τα όρια των κηλίδων, κυρίως σε αυτές στις οποίες η τιμή της έντασης βρίσκεται πολύ κοντά στο φόντο.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / A identificaÃÃo correta do ventrÃculo esquerdo em imagens de ecocardiograma constitui uma importante ferramenta no auxÃlio ao diagnÃstico precoce de doenÃas cardiovasculares. No entanto, limitaÃÃes inerentes ao processo de aquisiÃÃo das imagens, como baixa relaÃÃo sinal-ruÃdo e presenÃa de sombras acÃsticas, tornam essa identificaÃÃo uma tarefa complexa. Neste trabalho, com o objetivo de segmentar o ventrÃculo esquerdo, contornos ativos geomÃtricos e paramÃtricos sÃo aplicados sobre imagens de ecocardiografia. Uma nova variaÃÃo dos contornos ativos paramÃtricos, o mÃtodo dos contornos ativos algÃbricos, e duas modalidades de mÃtodo level-set, uma baseada no gradiente e outra baseada em regiÃes, sÃo testadas e comparadas. SÃo propostas, neste trabalho, quatro contribuiÃÃes à literatura. Uma à a filtragem do Hamiltoniano por uma janela gaussiana a afim de acelerar o movimento do contorno. Outra à uma funÃÃo sinal, que permite que o contorno mude sua direÃÃo radial automaticamente. AlÃm disso, a prÃpria concepÃÃo do mÃtodo dos contornos ativos algÃbricos à uma das contribuiÃÃes. Finalmente, a ultima à a superposiÃÃo de mapas de contorno, que aumenta a Ãrea de influÃncia do contorno ativo sem perda de precisÃo. Conclui-se que, apesar da capacidade dos contornos ativos geomÃtricos de dividirem-se e unificarem-se independentemente de novas parametrizaÃÃes, o mÃtodo dos contornos ativos algÃbricos Ã, dentre os avaliados, o Ãnico capaz de realizar a segmentaÃÃo do ventrÃculo esquerdo nas imagens de ecocardiografia conforme o padrÃo-ouro fornecido pelos especialistas.

Este trabalho representa continuidade no desenvolvimento de trabalhos na área de neurociência computacional, em particular na área de neuromorfometria e no relacionamento da forma-função. Os objetivos principais são a investigação e a simulação de modelos dinâmicos para o desenvolvimento de células neurais, e a caracterização da sua morfometria em termos de atributos. A tese apresenta um histórico sobre a neurociência, e uma breve revisão sobre a biologia do neurônio e sobre fatores que influenciam na variação na sua forma. Seguimos com a apresentação dos principais modelos computacionais de simulação neural, funcionais e de crescimento neural, com uma descrição mais detalhada de um modelo de crescimento baseado na atuação do cálcio como agente morfogênico e também na polimerização de actinas. Como uma introdução à modelagem neural, discutimos técnicas computacionais de evolução de contornos que podem ser utilizadas na simulação do desenvolvimento neural, propagação de frentes e contornos ativos. Apresentamos também medidas neuromorfométricas tais como a dimensão fractal multiescala, e medidas extraídas a partir do esqueleto da imagem do neurônio, tais como largura, espessura, número de ramos e curvatura das ramificações. Apresentamos os resultados obtidos em diferentes hipóteses de desenvolvimento de células neurais. Foram propostos crescimentos baseados na normal (velocidade na direção normal a curva), convolução, thin plate splines e dinâmica da polimerização da actina. Além disso, foi proposta uma nova abordagem para a evolução da membrana neural baseada em contornos, utilizando a formulação de contornos ativos sob a ação do campo elétrico externo e a curvatura da forma, o que possibilitou a geração de estruturas com características muito semelhantes a do neurônio, inclusive com ramificações. Finalizamos o trabalho apresentando os resultados e conclusões obtidas para os modelos de desenvolvimento. / In this thesis we report the investigation and simulation of dynamic models of neural growing, and their characterization using shape features, considering the form function relationship and neuromorphometry. The thesis begins by presenting an overview about neuroscience, neural cell biology and the biological factors that affects the neuron form developments, followed by the presentation of computational neuronal models based on electrophisiological measures and development models of internal structures as actin and microtubules. Special attention is devoted to a neuron growth model based on calcium as a morphogen, whose main characteristic is its electric activity at the membrane. Regarding mathematical models of neural development, two different approaches of contour evolutions are presented, Level Set Methods and Active Contours. Some neuromorphometric measures are implemented and discussed as features for classification and neural evolution, including the multiscale fractal dimension, and dendrite measurements are obtained by using neuron skeletons. In agreement with biological form influences, some hypotheses about development of neuron growth are proposed based on evolution rules, such as: normal evolution (based in normal velocity), convolution, thin plate splines and actin polimerization. A new approach about neuron development is also proposed: a contour based technique that makes use of active contour formulation, Snake Balloon, where the membrane velocity and direction suffers influences of internal and external factors, such as electrical field with diferent geometries, and contour curvature. Both hypotheses are in accordance with the biological factors that influences the neuron form. The simulation produces similar neuron-like structures, even with ramification of certain dendrites

Optimization and planning of radiation therapy is performed in a treatment planning system. This includes the definition of target structures to be irradiated and organs at risk to be protected, typically performed by contouring structures slice by slice in the image data. Conversions between contours and their volume representations are needed for visualizations and computations, but will however introduce a loss of information due to the sampling to a uniform voxel grid. The number of conversions performed can be large, causing errors to accumulate. The aim of this thesis is to examine volume reconstruction methods and sparse voxel representations for the purpose of volume reconstruction and representation with better accuracy than currently used algorithms in treatment planning systems. A prototype has been shown to be more accurate on contours and potentially cheaper in memory compared to the current method in RayStation in the case where contours represent non-smooth objects.

Active contours have been proven to be a powerful semiautomatic image segmentation approach, that seems to cope with many applications and different image modalities. However, they exhibit inherent drawbacks, including the sensibility to contour initialization due to the limited capture range of image edges and problems with concave boundary regions. The Gradient Vector Flow replaces the traditional image force and provides an enlarged capture range as well as enhanced concavity extraction capabilities, but it involves an expensive computational effort and considerably increased memory requirements at the time of computation. In this paper, we present an enhancement of the active contour model to facilitate semiautomatic contour detection in huge images. We propose a tile-based image decomposition accompanying an image force computation scheme on demand in order to minimize both computational and memory requirements. We show an efficient implementation of this approach on the basis of general purpose GPU processing providing for continuous active contour deformation without a considerable delay.

Interest in hippocampus increased sharply after his significance in the process of learning and retention of information was published. In particular, considerable interest was in its volume changes and their effect on Alzheimer’s disease. Understanding the structure and function hippocampus would contribute to a more accurate diagnosis of this disease. In this work was created a method of hippocampal segmentation using active contours. With its help, the data composed of both healthy and a diseased patients was segmented and the results were then statistically analyzed using statistical methods such as Kruskal-Walis test, Mann-Whitney test. The level of significance given by results of analysis supports alternative hypothesis that attaches significance of the difference in volume of the hippocampus between studied groups.

This thesis focuses on cell tracking in image sequences acquired using a multimodal holographic microscope (MHM). The principles of holographic microscopy are described together with the application in cells acquisition. The main part of the thesis describes a complete approach for segmentation and tracking of single cells in acquired in long-term sequences. The approach is designed based on parametric active contour models with specific modifications to achieve reasonable precision and robustness. The implemented method is described in detail, including the evaluation and demonstration of results.

Název práce: Segmentace mikroskopických snímků pomocí level-set metod Autor: Zuzana Bílková Katedra: Katedra numerické matematiky Vedoucí diplomové práce: RNDr. Václav Kučera, Ph.D., KNM, MFF UK Konzultant: RNDr. Jindřich Soukup, ÚTIA, AV ČR Abstrakt: Tato diplomová práce představuje novou metodu pro segmentaci snímků pořízených mikroskopem s fázovým konrastem. Cílem je oddělit buňky od pozadí. Algoritmus je založen na variační formulaci level set metod, tedy na minimalizaci funkcionálu popisujícího level set funkci. Funkcionál je minimalizován gradientním tokem popsaným evoluční parciální diferenciální rovnicí. Nejdůležitější nové myšlenky jsou inicializace pomocí prahování a nové členy ve funkcionálu, které zrychlují konvergenci a zpřesňují výsledky. Také jsme použili nové funkce napsané v jazyce C k počítání gradientu a Laplaceova operátoru. Tato implementace je třikrát rychlejší než standardní funkce v MATLABu. Dosáhli jsme lepších výsledků než algoritmy, se kterými jsme metodu porovnávali. Klíčová slova: Segmentace, level set metody, aktivní kontury Title: Segmentation of microscopic images using level set methods Author: Zuzana Bílková Department: Department of Numerical Mathematics Supervisor: RNDr....

Aim of this report is the investigation of suitable operational conditions for the drif{}t chambers MDC III installed in the HADES setup. The simulations performed showed that operating the drif{}t chambers in a mode with nearly constant electron drif{}t velocity in a predominant part of the cell allows a more precise and fast tracking. This is particularly important for electrons and positrons; here the invariant dilepton mass must be reconstructed with high precision to get a resolution of $\Delta M/M\approx 1\%$ for the $\omega$ and $\phi$ mass peaks and thus a chance to verify also small in-medium mass shif{}ts. This helps to realize the physics program at HADES which focuses on the search for such mass shif{}ts to get insight into the in-medium behaviour of hadrons in dense strongly interacting matter.

This thesis explores the boundaries and transitions within architecture. What makes a solid boundary? And what blurs the lines of transition in between? Possibilities were explored and limits pushed through the studying of elements such as thickness, transparency, material, texture, and light. The result is an architectural space in which a person can experience nature, while being separate from it. The building becomes a transition into nature while also a part of the landscape. The intent of this thesis is to bring the site together with the thesis idea and program in a cohesive way. / Master of Architecture