Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

Image segmentation is an important step in image processing, with many applications such as pattern recognition, object detection, and medical image analysis. It is a technique that separates objects of interests from the background in an image. Geometric active contour is a recent image segmentation method that overcomes previous problems with snakes. It is an attractive method for medical image segmentation as it is able to capture the object of interest in one continuous curve. The theory and implementation details of geometric active contours are discussed in this work. The robustness of the algorithm is tested through a series of tests, involving both synthetic images and medical images. Curve leaking past boundaries is a common problem in cases of non-ideal edges. Noise is also problematic for the advancement of the curve. Smoothing and parameters selection are discussed as ways to help solve these problems. This work also explores the incorporation of the multi-resolution method of Gaussian pyramids into the algorithm. Multi-resolution methods, used extensively in the areas of denoising and edge-selection, can help capture the spatial structure of an image. Results show that similar to the multi-resolution methods applied to parametric active contours, the multi-resolution can greatly increase the computation without sacrificing performance. In fact, results show that with successive smoothing and sub-sampling, performance often improves. Although smoothing and parameter adjustment help improve the performance of geometric active contours, the edge-based approach is still localized and the improvement is limited. Region-based approaches are recommended for further work on active contours.

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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.

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.

La variation des intensités est souvent exploitée comme une propriété importante du signal ou de l’image par les algorithmes de traitement. La grandeur permettant de représenter et de quantifier cette variation d’intensité est appelée une « mesure de changement », qui est couramment employée dans les méthodes de détection de ruptures d’un signal, dans la détection des contours d’une image, dans les modèles de segmentation basés sur les contours, et dans des méthodes de lissage d’images avec préservation de discontinuités. Dans le traitement des images et signaux biomédicaux, les mesures de changement existantes fournissent des résultats peu précis lorsque le signal ou l’image présentent un fort niveau de bruit ou un fort caractère aléatoire, ce qui conduit à des artefacts indésirables dans le résultat des méthodes basées sur la mesure de changement. D’autre part, de nouvelles techniques d'imagerie médicale produisent de nouveaux types de données dites à valeurs multiples, qui nécessitent le développement de mesures de changement adaptées. Mesurer le changement dans des données de tenseur pose alors de nouveaux problèmes. Dans ce contexte, une mesure de changement, appelée « mesure de non-stationnarité (NSM) », est améliorée et étendue pour permettre de mesurer la non-stationnarité de signaux multidimensionnels quelconques (scalaire, vectoriel, tensoriel) par rapport à un paramètre statistique, et en fait ainsi une mesure générique et robuste. Une méthode de détection de changements basée sur la NSM et une méthode de détection de contours basée sur la NSM sont respectivement proposées et appliquées aux signaux ECG et EEG, ainsi qu’a des images cardiaques pondérées en diffusion (DW). Les résultats expérimentaux montrent que les méthodes de détection basées sur la NSM permettent de fournir la position précise des points de changement et des contours des structures tout en réduisant efficacement les fausses détections. Un modèle de contour actif géométrique basé sur la NSM (NSM-GAC) est proposé et appliqué pour segmenter des images échographiques de la carotide. Les résultats de segmentation montrent que le modèle NSM-GAC permet d’obtenir de meilleurs résultats comparativement aux outils existants avec moins d'itérations et de temps de calcul, et de réduire les faux contours et les ponts. Enfin, et plus important encore, une nouvelle approche de lissage préservant les caractéristiques locales, appelée filtrage adaptatif de non-stationnarité (NAF), est proposée et appliquée pour améliorer les images DW cardiaques. Les résultats expérimentaux montrent que la méthode proposée peut atteindre un meilleur compromis entre le lissage des régions homogènes et la préservation des caractéristiques désirées telles que les bords ou frontières, ce qui conduit à des champs de tenseurs plus homogènes et par conséquent à des fibres cardiaques reconstruites plus cohérentes. / The intensity variation is often used in signal or image processing algorithms after being quantified by a measurement method. The method for measuring and quantifying the intensity variation is called a « change measure », which is commonly used in methods for signal change detection, image edge detection, edge-based segmentation models, feature-preserving smoothing, etc. In these methods, the « change measure » plays such an important role that their performances are greatly affected by the result of the measurement of changes. The existing « change measures » may provide inaccurate information on changes, while processing biomedical images or signals, due to the high noise level or the strong randomness of the signals. This leads to various undesirable phenomena in the results of such methods. On the other hand, new medical imaging techniques bring out new data types and require new change measures. How to robustly measure changes in theos tensor-valued data becomes a new problem in image and signal processing. In this context, a « change measure », called the Non-Stationarity Measure (NSM), is improved and extended to become a general and robust « change measure » able to quantify changes existing in multidimensional data of different types, regarding different statistical parameters. A NSM-based change detection method and a NSM-based edge detection method are proposed and respectively applied to detect changes in ECG and EEG signals, and to detect edges in the cardiac diffusion weighted (DW) images. Experimental results show that the NSM-based detection methods can provide more accurate positions of change points and edges and can effectively reduce false detections. A NSM-based geometric active contour (NSM-GAC) model is proposed and applied to segment the ultrasound images of the carotid. Experimental results show that the NSM-GAC model provides better segmentation results with less iterations that comparative methods and can reduce false contours and leakages. Last and more important, a new feature-preserving smoothing approach called « Nonstationarity adaptive filtering (NAF) » is proposed and applied to enhance human cardiac DW images. Experimental results show that the proposed method achieves a better compromise between the smoothness of the homogeneous regions and the preservation of desirable features such as boundaries, thus leading to homogeneously consistent tensor fields and consequently a more reconstruction of the coherent fibers.