Pulmonary diseases are frequently associated with changes in lung anatomy. These diseases may change the airway, vessel and lung tissue properties. In order to evaluate the lung in a longitudinal study, a stable reference system is required to identify corresponding parts of the lung. The structure of the airway tree can be used to repeatedly identify the regions of interest. In this study, an improved method for matching of intra-patient airway trees was proposed and evaluated. The association graph method proposed by Pelillo et al. matches free and rooted trees by detecting the maximal sub-tree isomorphism. Tschirren et al. implemented this approach for labeling and matching of human airway trees and reported 92.9% matching accuracy which is the highest among existing methods. However we recognized a few shortcomings of this method. When we tested it on seven normal human cases, we observed that successful matching relies heavily on the accurate labeling of main branchpoints in the trees. Incorrect labeling of main branch points or failure in labeling results in failure to match that branch point. Such matching errors may eventually propagate to sub-trees. On our seven data samples, matching accuracy was found to be as low as 65%. To improve the matching performance, we propose to make matching independent of labeling as well as improve association graph by adding constraint of path-length along with the existing constraints. Furthermore, we would like to redefine the incorrect matches as those matches which are mismatched as well as those that are missed by the matching algorithm. Our results for a total of 27 cases show a significant improvement in accuracy. The accuracy calculated as per the convention without accounting for the branchpoint pairs missed by the algorithm is 92.19% whereas the accuracy calculated as per our definition is 73.98%, with runtime in the range of 0.01-262.81 sec (average runtime is 25.14 sec). We thus propose an improved association graph method which is efficient in matching intra-patient airway trees with good accuracy and within a reasonable time.

Chronic obstructive pulmonary disease (COPD) is a type of obstructive lung disease characterized by chronically poor airflow, which is the result of breakdown of lung tissue (known as emphysema) and small airways disease. It typically worsens over time. Most treatments are limited to the management of symptoms, which makes early detection more valuable to treat the disease etiology itself. With the advancement of computed tomography (CT), it is able to provide high resolution structural and functional imaging to distinguish the lung anatomic structures, as well as characterize their changes over time. Previously, the majority of CT-based measures have focused on quantifying the extent of airway and parenchymal damage. Recent studies suggests that pulmonary vascular dysfunction is an early lesion in COPD and associated with an emphysematous phenotype. Few studies attempted to quantify pulmonary vessel morphology and compared those measures across COPD groups. However, the scope of examined vascular structures in these studies was limited, majorly due to the lack of a standardized method to quantify a broad range of vascular structures. In this thesis, we propose to use anatomically defined airway branches as references to locate and morphologically quantify central pulmonary arteries in different lung regions. Although pulmonary vessel trees have complex topologic and geometric structures, airway tree possesses much simpler and consistent branching patterns and standardized anatomic nomenclatures are available up to sub-segmental levels. It is also well-known that airway and arterial branches have a unique pairing that is established by their spatial proximity and parallel configuration. Therefore, anatomically labeled airway tree provides a robust benchmark to locate consistent arterial segments for both intra- and inter-subjects. New methods have been developed for quantitative assessment of arterial morphology matched and standardized by associated airways at different anatomic branches. First, the skeletons of airway and vessel trees are generated to provide simple and hierarchical representations. Then, topologic and geometric properties of airways and arteries, such as distance, orientation and anatomic positon information, are explored to locate the target arterial segments. Finally, the morphologic properties, e.g. cross-sectional area, of target arterial segments are robustly computed. The developed methods in this thesis provides a standardized framework to assess and compare the vascular measurements in intra- and inter- subjects from a broad range of vessel branches in different lung regions. The work also serves as a practical tool for large longitudinal or cross-sectional studies to explore the pulmonary vessel roles played at the early stage of COPD. The major contribution of this thesis include: (1) developing two novel skeletonization methods that are applicable to airway and pulmonary vessel trees; (2) developing a semi-automatic method to locate and quantify central pulmonary arterial morphology associate to anatomic airway branches; (3) developing a fully automatic method to identify and reconstruct central pulmonary arterial segments associated to anatomic airway branches and quantify their morphology; (4) validating the methods using computerized phantoms, physical phantoms and human subjects; (5) applying the developed methods to two human lung disease studies.

Computed tomography is a very useful technic which allow non-invasive diagnosis in many applications for example is used with success in industry and medicine. However, manual analysis of the interesting structures can be tedious and extremely time consuming, or even impossible due its complexity. Therefore in this thesis we study and develop discrete geometry and topology algorithms suitable for use in many practical applications, especially, in the problem of automatic quantitative analysis of the human airway trees based on computed tomography images. In the first part, we define basic notions used in discrete topology and geometry then we showed that several class of discrete methods like skeletonisation algorithms, medial axes, tunnels closing algorithms and tangent estimators, are widely used in several different practical application. The second part consist of a proposition and theory of a new methods for solving particular problems. We introduced two new medial axis filtering method. The hierarchical scale medial axis which is based on previously proposed scale axis transform, however, is free of drawbacks introduced in the previously proposed method and the discrete adaptive medial axis where the filtering parameter is dynamically adapted to the local size of the object. In this part we also introduced an efficient and parameter less new tangent estimators along three-dimensional discrete curves, called 3D maximal segment tangent direction. Finally, we showed that discrete geometry and topology algorithms can be useful in the problem of quantitative analysis of the human airway trees based on computed tomography images. According to proposed in the literature design of such system we applied discrete topology and geometry algorithms to solve particular problems at each step of the quantitative analysis process. First, we propose a robust method for segmenting airway tree from CT datasets. The method is based on the tunnel closing algorithm and is used as a tool to repair, damaged by acquisition errors, CT images. We also proposed an algorithm for creation of an artificial model of the bronchial tree and we used such model to validate algorithms presented in this work. Then, we compare the quality of different algorithms using set of experiments conducted on computer phantoms and real CT dataset. We show that recently proposed methods which works in cubical complex framework, together with methods introduced in this work can overcome problems reported in the literature and can be a good basis for the further implementation of the system for automatic quantification of bronchial tree properties

La tomodensitométrie est une technique très utile qui permet de mener avec succès des analyses non-invasives dans plusieurs types d'applications, par exemple médicales ou industrielles. L'analyse manuelle des structures d'intérêt présentes dans une image peut prendre beaucoup de temps, être laborieuse et parfois même impossible à faire en raison de sa complexité. C'est pour cela que dans cette thèse, nous proposons et développons des algorithmes nécessaires à cette analyse, basés sur la géométrie discrète et la topologie. Ces algorithmes peuvent servir dans de nombreuses applications, et en particulier au niveau de l'analyse quantitative automatique de l'arbre bronchique humain, sur la base d'images de tomodensitométrie. La première partie introduit les notions fondamentales de la topologie et de la géométrie discrètes utiles dans cette thèse. Ensuite, nous présentons le principe de méthodes utilisées dans de nombreuses applications : les algorithmes de squelettisation, de calcul de l'axe médian, les algorithmes de fermeture de tunnels et les estimateurs de tangentes. La deuxième partie présente les nouvelles méthodes que nous proposons et qui permettent de résoudre des problèmes particuliers. Nous avons introduit deux méthodes nouvelles de filtrage d'axe médian. La première, que nous appelons "hierarchical scale medial axis", est inspirée du "scale axis transform", sans les inconvénients qui sont propres à la méthode originale. La deuxième est une méthode nommée "discrete adaptive medial axis", où le paramètre de filtrage est adapté dynamiquement aux dimensions locales de l'objet. Dans cette partie, nous introduisons également des estimateurs de tangente nouveaux et efficaces, agissant sur des courbes discrètes tridimensionnelles, et que nous appelons "3Dlambda maximal segment tangent direction". Enfin, nous avons montré que la géométrie discrète et les algorithmes topologiques pouvaient être utiles dans le problème de l'analyse quantitative de l'arbre bronchique humain à partir d'images tomodensitométriques. Dans une chaîne de traitements de structure classique par rapport à l'état de l'art, nous avons appliqué des méthodes de topologie et de géométrie discrète afin de résoudre des problèmes particuliers dans chaque étape du processus de l'analyse quantitative. Nous proposons une méthode robuste pour segmenter l'arbre bronchique à partir d'un ensemble de données tomographiques (CT). La méthode est basée sur un algorithme de fermeture de tunnels qui est utilisé comme outil pour réparer des images CT abîmées par les erreurs d'acquisition. Nous avons aussi proposé un algorithme qui sert à créer un modèle artificiel d'arbre bronchique. Ce modèle est utilisé pour la validation des algorithmes présentés dans cette thèse. Ensuite nous comparons la qualité des différents algorithmes en utilisant un ensemble de test constitué de fantômes (informatiques) et d'un ensemble de données CT réelles. Nous montrons que les méthodes récemment présentées dans le cadre des complexes cubiques, combinées avec les méthodes présentées dans cette thèse, permettent de surmonter des problèmes indiqués par la littérature et peuvent être un bon fondement pour l'implémentation future des systèmes de quantification automatique des particularités de l'arbre bronchique / Computed tomography is a very useful technic which allow non-invasive diagnosis in many applications for example is used with success in industry and medicine. However, manual analysis of the interesting structures can be tedious and extremely time consuming, or even impossible due its complexity. Therefore in this thesis we study and develop discrete geometry and topology algorithms suitable for use in many practical applications, especially, in the problem of automatic quantitative analysis of the human airway trees based on computed tomography images. In the first part, we define basic notions used in discrete topology and geometry then we showed that several class of discrete methods like skeletonisation algorithms, medial axes, tunnels closing algorithms and tangent estimators, are widely used in several different practical application. The second part consist of a proposition and theory of a new methods for solving particular problems. We introduced two new medial axis filtering method. The hierarchical scale medial axis which is based on previously proposed scale axis transform, however, is free of drawbacks introduced in the previously proposed method and the discrete adaptive medial axis where the filtering parameter is dynamically adapted to the local size of the object. In this part we also introduced an efficient and parameter less new tangent estimators along three-dimensional discrete curves, called 3D maximal segment tangent direction. Finally, we showed that discrete geometry and topology algorithms can be useful in the problem of quantitative analysis of the human airway trees based on computed tomography images. According to proposed in the literature design of such system we applied discrete topology and geometry algorithms to solve particular problems at each step of the quantitative analysis process. First, we propose a robust method for segmenting airway tree from CT datasets. The method is based on the tunnel closing algorithm and is used as a tool to repair, damaged by acquisition errors, CT images. We also proposed an algorithm for creation of an artificial model of the bronchial tree and we used such model to validate algorithms presented in this work. Then, we compare the quality of different algorithms using set of experiments conducted on computer phantoms and real CT dataset. We show that recently proposed methods which works in cubical complex framework, together with methods introduced in this work can overcome problems reported in the literature and can be a good basis for the further implementation of the system for automatic quantification of bronchial tree properties

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