Automatic and semi-automatic magnetic resonance angiography (MRA)s segmentation techniques can potentially save radiologists larges amounts of time required for manual segmentation and cans facilitate further data analysis. The proposed MRAs segmentation method uses a mathematical modeling technique whichs is well-suited to the complicated curve-like structure of bloods vessels. We define the segmentation task as ans energy minimization over all 3D curves and use a level set methods to search for a solution. Ours approach is an extension of previous level set segmentations techniques to higher co-dimension.

This thesis introduces geometric dynamic active contours in the context of visual tracking, augmenting geometric curve evolution with physically motivated dynamics. Adding additional state information to an evolving curve lifts the curve evolution problem to space dimensions larger than two and thus forbids the use of classical level set techniques. This thesis therefore develops and explores level set methods for problems of higher codimension, putting an emphasis on the vector distance function based approach. This formalism is very general, it is interesting in its own right and still a challenging topic. Two different implementations for geometric dynamic active contours are explored: the full level set approach as well as a simpler partial level set approach. The full level set approach results in full topological flexibility and can deal with curve intersections in the image plane. However, it is computationally expensive. On the other hand the partial level set approach gives up the topological flexibility (intersecting curves cannot be represented) for increased computational efficiency. Contours colliding with different dynamic information (e.g., objects crossing in the image plane) will be merged in the partial level set approach whereas they will correctly traverse each other in the full level set approach. Both implementations are illustrated on synthetic and real examples. Compared to the traditional static curve evolution case, fundamentally different evolution behaviors can be obtained by propagating additional information along with every point on a curve.

Early detection of breast cancer on screening mammograms is crucial to reduce mortality rates. Computer-aided detection (CADe) systems for mammography are of great importance since they have been shown to positively assist radiologists in detecting early cancer. However, one area where CADe systems for mammography need improvement is in the early detection and annotation of spiculated lesions, which may represent invasive malignancies, and hence, early detection is crucial. Spicule annotation is important since it can yield useful discriminative information about the suspect lesion location on the mammogram and can also provide rich visual evidence to the interpreting radiologist to make the right follow-up decision. However, spicule annotation is a non-trivial task since spicules are fine scale curvilinear structures that are often not clearly visible amidst the surrounding breast parenchyma. The first contribution of this dissertation is an active contour algorithm called snakules for the annotation of spicules on mammography. Observer studies with experienced radiologists to evaluate the performance of snakules demonstrate the potential of the algorithm as an annotation tool that could be used to augment existing spiculated mass CADe systems. Mammography suffers from a major limitation: the 3-D to 2-D projection process results in anatomical noise due to overlapping of out of plane tissue structures, which hinders both radiologists and CADe systems in finding early cancers. This has motivated the development of 3-D breast imaging in the form of breast tomosynthesis, stereoscopic (stereo) mammography, and breast computed tomography (CT) to augment mammography for early cancer detection. Our second contribution is a novel computational stereo model for estimating a dense disparity map from a pair of stereo mammograms. This problem is very important since this is the first step towards elucidating 3-D information that is essential for conducting 3-D digital analysis on the stereo mammogram images. Nearly all of the 3-D structural information of interest on a stereo mammogram exists as a complex network of multi-layered, heavily occluded curvilinear structures, which is unlike what is seen on optical images of the real world. Our proposed stereo model employs a new singularity index as a constraint in a global optimization framework to obtain better estimates of disparity along critical curvilinear structures. The new singularity index is an important contribution of this work. In-depth theoretical analyses and experiments on several real world images demonstrate the efficacy of the index for detecting multi-scale curvilinear structures. Experiments on synthetic images with known ground truth and on real stereo mammograms highlight the advantages of the proposed stereo model over the canonical stereo model. The final contribution of this dissertation is an observer study, which demonstrates the feasibility of viewing breast tomosynthesis projection images stereoscopically. Unlike stereo mammogram images, each tomosynthesis projection image is acquired at a much lower dose. Stereo viewing of tomosynthesis projection images has the potential to reveal the 3-D structure of the breast, unlike the current cine or slice-by slice viewing modes. The results from our study suggest that stereo viewing could be a viable reading mode for breast tomosynthesis data in the future. / text

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

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....