Cette thèse se propose d'examiner sous un angle particulier quelques aspects de la morphologie mathématique. Nous montrons d'abord comment la notion de convergence d'ensembles fermés et celle d'ensemble aléatoire fermé peuvent être employées en géométrie algorithmique. Nous exposons ensuite une nouvelle technique permettant l'écriture d'algorithmes morphologiques efficace en imagerie binaire au moyen d'un codage de contours sous forme de chaînes et lacets. Les algorithmes concernés sont entre autres l'érosion, la dilatation, la fonction distance, tant dans le cas euclidien que géodésique, la fonction de propagation, en métrique hexagonale et dodécagonale, le labeling, la reconstruction. . . Nous abordons aussi les mesures morphologiques telles que variation diamétrale, diamètre de Ferret, périmètre, nombre d'Euler. . . L'emploi des transformations est alors illustré par la résolution complète d'un problème particulier en sciences des matériaux où nous discutons les qualités respectives d'une dizaine de solutions différentes. Enfin, un essai de formalisation de l'emploi des transformations morphologiques a abouti à l'écriture d'un système de programmation automatique.

<p>Locating and segmenting objects such as bones or internal organs is a common problem in medical imaging. Existing segmentation methods are often cumbersome to use for medical staff, since they require a close initial guess and a range of different parameters to be set appropriately. For this work, we present a two-stage segmentation framework which relies on an initial isosurface interactively extracted by topological analysis. The initial isosurface seldom provides a correct segmentation, so we refine the surface using an iterative level set method to better match the desired object boundary. We present applications and improvements to both the flexible isosurface interface and level set segmentation without edges.</p>

Salient contour detection is an important lowlevel visual process in the human visual system, and has significance towards understanding higher visual and cognitive processes. Salience detection can be investigated by examining the visual cortical response to visual input. Visual response activity in the early stages of visual processing can be approximated by a sequence of convolutions of the input scene with the difference-of-Gaussian (DoG) and the oriented Gabor filters. The filtered responses are unusually high for prominent edge locations in the image, and are uniformly similar across different natural image inputs. Furthermore, such a response follows a power law distribution. The aim of this thesis is to examine how these response properties could be utilized to the problem of salience detection. First, I identify a method to find the best threshold on the response activity (orientation energy) toward the detection of salient contours: compare the response distribution to a Gaussian distribution of equal variance. Second, I justify this comparison by providing an explanation under the framework of Suspicious Coincidence proposed by Barlow [1]. A connection is provided between perceived salience of contours and the neuronal goal of detecting suspiciousness, where salient contours are seen as affording suspicious coincidences by the visual system. Finally, the neural plausibility of such a salience detection mechanism is investigated, and the representational effciency is shown which could potentially explain why the human visual system can effortlessly detect salience.

Ovarian follicles are spherical structures inside the ovaries which contain developing eggs. Monitoring the development of follicles is necessary for both gynecological medicine (ovarian diseases diagnosis and infertility treatment), and veterinary medicine (determining when to introduce superstimulation in cattle, or dividing herds into different stages in the estrous cycle).<p>Ultrasound imaging provides a non-invasive method for monitoring follicles. However, manually detecting follicles from ovarian ultrasound images is time consuming and sensitive to the observer's experience. Existing (semi-) automatic follicle segmentation techniques show the power of automation, but are not widely used due to their limited success.<p>A new automated follicle segmentation method is introduced in this thesis. Human ovarian images acquired <i>in vivo</i> were smoothed using an adaptive neighbourhood median filter. Dark regions were initially segmented using geometric active contour models. Only part of these segmented dark regions were true follicles. A naïve Bayes classifier was applied to determine whether each segmented dark region was a true follicle or not. <p>The Hausdorff distance between contours of the automatically segmented regions and the gold standard was 2.43 ± 1.46 mm per follicle, and the average root mean square distance per follicle was 0.86 ± 0.49 mm. Both the average Hausdorff distance and the root mean square distance were larger than those reported in other follicle segmentation algorithms. The mean absolute distance between contours of the automatically segmented regions and the gold standard was 0.75 ± 0.32 mm, which was below that reported in other follicle segmentation algorithms.<p>The overall follicle recognition rate was 33% to 35%; and the overall image misidentification rate was 23% to 33%. If only follicles with diameter greater than or equal to 3 mm were considered, the follicle recognition rate increased to 60% to 63%, and the follicle misidentification rate increased slightly to 24% to 34%. The proposed follicle segmentation method is proved to be accurate in detecting a large number of follicles with diameter greater than or equal to 3 mm.

One important topic in medical image analysis is segmenting wall structures from different cardiac medical imaging modalities such as computed tomography (CT) and magnetic resonance imaging (MRI). This task is typically done by radiologists either manually or semi-automatically, which is a very time-consuming process. To reduce the laborious human efforts, automatic methods have become popular in this research. In this thesis, features insensitive to data variations are explored to segment the ventricles from CT images and extract the left atrium from MR images. As applications, the segmentation results are used to facilitate cardiac disease analysis. Specifically, 1. An automatic method is proposed to extract the ventricles from CT images by integrating surface decomposition with contour evolution techniques. In particular, the ventricles are first identified on a surface extracted from patient-specific image data. Then, the contour evolution is employed to refine the identified ventricles. The proposed method is robust to variations of ventricle shapes, volume coverages, and image quality. 2. A variational region-growing method is proposed to segment the left atrium from MR images. Because of the localized property of this formulation, the proposed method is insensitive to data variabilities that are hard to handle by globalized methods. 3. In applications, a geometrical computational framework is proposed to estimate the myocardial mass at risk caused by stenoses. In addition, the segmentation of the left atrium is used to identify scars for MR images of post-ablation.

La segmentación de imágenes es una técnica que tiene como finalidad dividir una imagen en un conjunto de regiones, asignando a cada objeto en la escena una o varias regiones. Para obtener una segmentación correcta, cada una de las regiones debe cumplir con un criterio de homogeneidad impuesto a priori. Cuando se fija un criterio de homogeneidad, lo que implícitamente se esta haciendo es asumir un modelo matemático que caracteriza las regiones.En esta tesis se introduce un nuevo tipo de modelo denominado modelo jerárquico, ya que tiene dos niveles diferentes sobrepuestos uno sobre el otro. El nivel inferior (o subyacente) modela la posición que ocupa cada una de las regiones dentro de la imagen; mientras que, por su parte, el nivel superior (u observable) esta compuesto por un conjunto de submodelos independientes (un submodelo por región) que caracterizan el comportamiento del interior de las regiones. Para el primero se usa un campo aleatorio Markoviano de orden dos que modelara los contornos de las regiones, mientras que para el segundo nivel se usa un modelo Gausiano. En el trabajo se estudian los mejores potenciales que deben asignarse a los tipos de agrupaciones que permiten definir los contornos. Con todo ello la segmentación se realiza buscando la partición más probable (criterio MAP) para una realización concreta (imagen observable).El proceso de búsqueda de la partición optima para imágenes del tamaño habitual seria prácticamente inviable desde un punto de vista de tiempo de cálculo. Para que se pueda realizar debe partirse de una estimación inicial suficientemente buena y de una algoritmo rápido de mejora como es una búsqueda local. Para ello se introduce la técnica de segmentación piramidal (multirresolucion). La pirámide se genera con filtrado Gausiano y diezmado. En el nivel mas alto de la pirámide, al tener pocos píxels, si que se puede encontrar la partición óptima.

This thesis is primarily about the mapping and analyze of the phenomenon of an impinging jet by experimental measurements and numerical simulations by CFD. The mapping shows the characteristics of velocity in and around the impinging jet with different conditions. Additional studies were made by analyzing the pressure along the vertical jet axis, but also weight measurements were part of the investigation. The measurements covered the range from 10 m/s, 20 m/s and 30 m/s, which corresponds to a Reynolds number of 17 000, 34 000 and 50 000. The impinging jet is therefore considered to be highly turbulent. The main difference from previous studies is the use of the ultrasonic anemometer to measure the velocities. These create the ability of measuring the velocities on three coordinates. The jet’s contour was crucial to determine the penetration of ambient air flowing into the jet with an angle of around 88° and the entrainment of the ambient air multiple the jet volume flow. In comparison with CFD, the number of cells in the mesh design and the type of model plays a substantial role. The model k-ε Realized came closest to the experimentally measurements, while the SST k-ω and RNG k-ε EWF had far more entrainment of the ambient air into the impinging jet. / Detta examensarbete handlar om att kartlägga och analysera fenomenet av en ”impinging jet” genom experimentella mätningar samt numeriska simuleringar som CFD. Undersökningen visar karakteristiken av hastigheten i och kring strålen med olika förutsättningar. Kompletterande undersökningar gjordes för trycket i luftstrålens centrum längs den vertikala axeln, men även viktmätningar var del av undersökningen. Mätningarna omfattade hastigheter från 10 m/s, 20 m/s och 30 m/s som motsvarar ett Reynoldstal med 17 000, 34 000 och 50 000. Luftstrålen betraktas därför som turbulent. Det som skiljer sig från tidigare experiment är att hastigheten mättes med en ultrasonic anemometer som egentligen används inom metrologin för att mäta vindhastigheter. Därmed skapades en tredimensionell bild av hastigheten i och kring luftstrålen. Mätområdet sträckte sig från strålens utgångspunkt ner till strax ovanför plattan. Luftstrålens fastställda kontur var avgörande för att bestämma den inträngande omgivningsluften som strömmar in i strålen med en genomsnittlig vinkel av 88°. Denna inströmmande omgivningsluft flerfaldigade strålens volym. I jämförelse med CFD simuleringen visades att antal celler i meshen är avgörande för att skapa liknande och reala förutsättningar. Vid undersökningen av den inträngande omgivningsluften visades även att själva modellen spelar en avgörande roll. Det var modellen k-ε Realized som kom närmast mätningarna. Däremot uppvisade SST k-ω och RNG k-ε EWF modellerna mycket mer inträngande omgivningsluft i jämförelse med mätningarnas resultat.

The purpose of this study was the hardware implementation of a real time moving object contour extraction.Segmentation of image frames to isolate moving objects followed by contour extraction using digitalmorphology was carried out in this work. Segmentation using temporal difference with median thresholdingapproach was implemented, experimental methods were used to determine the suitable morphological operatorsalong with their structuring elements dimensions to provide the optimum contour extraction.The detector with image resolution of 1280 x1024 pixels and frame rate of 60 Hz was successfully implemented,the results indicate the effect of proper use of morphological operators for post processing and contourextraction on the overall efficiency of the system. An alternative segmentation method based on Stauffer &amp; Grimson algorithm was investigated and proposed which promises better system performance at the expense ofimage resolution and frame rate

The purpose of this study was to explore the efficacy of two existing pulse contour analysis (PCA) models for estimating cardiac stroke volume from the arterial pressure waveform during kicking ergometer exercise and head-up tilt manoeuvres. Secondly, one of the existing models was modified in an attempt to enhance its performance. In part I, seven healthy young adults repeated two submaximal exercise sessions on a kicking ergometer, each with three different sets of steady-state cardiac output comparisons (pulsed Doppler vs. pulse contour). Across all exercise trials regression results were found to be PCA = 1. 23 x Doppler-1. 38 with an r2 = 0. 51. In part II, eight young and eight older male healthy subjects participated in a head-up tilt experiment. Cardiac output comparisons were again performed during the supine and tilt conditions using pulsed Doppler and pulse contour cardiac output. Regression results revealed that PCA performed best during supine conditions and preferentially on the older subjects. In all instances, impedance-calibrated pulse contour analysis will provide reasonable beat-by-beat cardiac output within very narrow confines and will result in a progressively more significant bias as cardiovascular dynamics change. In addition, it appears that heart rate variability negatively influences beat-by-beat pulse contour cardiac output results, further limiting application of existing models.

Ovarian follicles are spherical structures inside the ovaries which contain developing eggs. Monitoring the development of follicles is necessary for both gynecological medicine (ovarian diseases diagnosis and infertility treatment), and veterinary medicine (determining when to introduce superstimulation in cattle, or dividing herds into different stages in the estrous cycle).<p>Ultrasound imaging provides a non-invasive method for monitoring follicles. However, manually detecting follicles from ovarian ultrasound images is time consuming and sensitive to the observer's experience. Existing (semi-) automatic follicle segmentation techniques show the power of automation, but are not widely used due to their limited success.<p>A new automated follicle segmentation method is introduced in this thesis. Human ovarian images acquired <i>in vivo</i> were smoothed using an adaptive neighbourhood median filter. Dark regions were initially segmented using geometric active contour models. Only part of these segmented dark regions were true follicles. A naïve Bayes classifier was applied to determine whether each segmented dark region was a true follicle or not. <p>The Hausdorff distance between contours of the automatically segmented regions and the gold standard was 2.43 ± 1.46 mm per follicle, and the average root mean square distance per follicle was 0.86 ± 0.49 mm. Both the average Hausdorff distance and the root mean square distance were larger than those reported in other follicle segmentation algorithms. The mean absolute distance between contours of the automatically segmented regions and the gold standard was 0.75 ± 0.32 mm, which was below that reported in other follicle segmentation algorithms.<p>The overall follicle recognition rate was 33% to 35%; and the overall image misidentification rate was 23% to 33%. If only follicles with diameter greater than or equal to 3 mm were considered, the follicle recognition rate increased to 60% to 63%, and the follicle misidentification rate increased slightly to 24% to 34%. The proposed follicle segmentation method is proved to be accurate in detecting a large number of follicles with diameter greater than or equal to 3 mm.