Cette thèse traite de la segmentation et du suivi de structures curvilinéaires. La méthodologie proposée est appliquée à la segmentation et au suivi des guide-fils durant les interventions d’angioplastie. Pendant ces opérations, les cardiologues s’assurent que le positionnement des différents outils est correct au moyen d’un système d’imagerie fluoroscopique temps-réel. Les images obtenues sont très bruitées et les guides sont, en conséquence, particulièrement difficiles à segmenter. Les contributions de cette thèse peuvent être regroupées en trois parties. La première est consacrée à la détection des guides, la seconde a leur segmentation et la dernière a leur suivi. La détection partielle des guide-fils est réalisée soit par la sélection d’un opérateur de filtrage approprié soit en utilisant des méthodes modernes d’apprentissage artificiel. Dans un premier temps, un système réalisant un Boosting asymétrique pour entraîner un détecteur de guides est présenté. Par la suite, une méthode renforçant la réponse d’un filtre orientable au moyen d’une variante efficace de vote tensoriel est décrite. Dans la seconde partie, une approche ascendante est proposée, qui consiste à regrouper des points sélectionnés par le détecteur de fil, à extraire des primitives des agrégats obtenus et a les lier. Deux procédures locales de regroupement des points sont étudiées : une reposant sur un clustering de graphe non supervisé suivi d’une extraction de segments de droites ; et l’autre reposant sur un modèle graphique puis une extraction d’axe central. Par la suite, deux méthodes de liaison des primitives sont étudiées : la première repose sur une approche de programmation linéaire, et la seconde sur une heuristique de recherche locale. Dans la dernière partie, des méthodes de recalage sont utilisées pour améliorer la segmentation et pour suivre les fils. Le suivi propos´e couple un suivi iconique avec un suivi géométrique contenant un modèle prédictif. Cette méthode utilise un modèle graphique déterminant à la fois une position du guide-fil (segmentation) et des correspondances (tracking). La solution optimale de ce modèle graphique décrit simultanément les déplacements du guide-fil et les appariements entre points d’intérêt qui en sont extraits, fournissant ainsi une estimation robuste des déformations du fil par rapport aux grands déplacements et au bruit. / This thesis addresses the segmentation and the tracking of thin curvilinear structures. The proposed methodology is applied to the delineation and the tracking of the guide-wires that are used during cardiac angioplasty. During these interventions, cardiologists assess the displacement of the different devices with a real-time fluoroscopic imaging system. The obtained images are very noisy and, as a result, guide-wires are particularly challenging to segment and track. The contributions of this thesis can be grouped into three parts. The first part is devoted to the detection of the guide-wires, the second part addresses their segmentation and the last part focuses on their spatio-temporal tracking. Partial detection of guide-wires is addressed either through the selection of appropriate filter operators or using modern machine learning methods. First, a learning framework using an asymmetric Boosting algorithm for training a guidewire detector is presented. A second method enhancing the output of a steerable filter by using an efficient tensor voting variant is then described. In the second part, a bottom-up method is proposed, that consists in grouping points selected by the wire detector, in extracting primitives from these aggregates and in linking these primitives together. Two local grouping procedures are investigated: one based on unsupervised graph-based clustering followed by a linesegment extraction and one based on a graphical model formulation followed by a graph-based centerline extraction. Subsequently, two variants of linking methods are investigated: one is based on integer programming and one on a local search heuristic. In the last part, registration methods are exploited for improving the segmentation via an image fusion method and then for tracking the wires. This latter is performed by a graph-based iconic tracking method coupled with a graphbased geometric tracking that encodes to certain extend a predictive model. This method uses a coupled graphical model that seeks both optimal position (segmentation) and spatio-temporal correspondences (tracking). The optimal solution of this graphical model simultaneously determines the guide-wire displacements and matches the landmarks that are extracted along it, what provides a robust estimation of the wire deformations with respect to large motion and noise.

There are two primary sources of motivation for the contents of this thesis. The first is an effort to generalize classical dilation theory, a brief history of which is given in Section 2.1. The second source of motivation is the study of the representation theory of tensor algebras associated to C*-correspondences; these concepts are discussed in Sections 2.2 and 2.4. Although seemingly unrelated, there is a close connection between these two motivating theories. The link between classical dilation theory and the representation theory of tensor algebras over C*-correspondences was established by Muhly and Solel in their 1998 paper Tensor Algebras over C*-Correspondences: Representations, Dilations, and C*-Envelopes. In that paper, the authors not only introduced the concept of (operator-theoretic) tensor algebras – non-selfadjoint operator algebras that generalize algebraic tensor algebras – but they also developed the representation theory of these algebras. In order to do so, they introduced and made extensive use of a generalized dilation theory for contractions on Hilbert space. In analogy with classical dilation theory, they developed notions of “isometric dilation” and “coisometric extension” for completely contractive representations of the tensor algebra. The process of forming isometric dilations proceeded smoothly, but constructing coisometric extensions proved more problematic. In contrast to the classical case, Muhly and Solel showed that there is a high degree of nonuniqueness involved when building coisometric extensions. This lack of uniqueness proved to be an impediment to developing a full generalization of the dilation and model theories of Sz.-Nagy and Foias. In this thesis, we introduce a way to manage the ambiguities that arise when forming coisometric extensions. More specifically, we show that the notion of a transfer operator from classical dynamics can be adapted to this setting, and we prove that when a transfer operator is fixed in advance, every completely contractive representation of the tensor algebra admits a unique coisometric extension that respects the transfer operator in a fashion that we describe in Chapter 5. We also prove a commutant lifting theorem in the context of coisometric extensions.

The Maple V package Vessiot is an extensive set of procedures for performing computations in variational and tensor calculus. Vessiot is an extension of a previous package, Helmholtz, which was written by Cinnamon Hillyard for performing operations in the calculus of variations. The original set of commands included standard operators on differential forms, Euler-Lagrange operators, the Lie bracket operator, Lie derivatives, and homotopy operators. These capabilities are preserved in Vessiot, and enhanced so as to function in a multiple coordinate frame context. In addition, a substantial number of general tensor operations have been added to the package. These include standard algebraic operations such as the tensor product, contraction, raising and lowering of indices, as well covariant and Lie differentiation. Objects such as connections, the Riemannian curvature tensor, and Ricci tensor and scalar may also be easily computed. A synopsis of the command syntax appears in Appendix A on pages 194 through 225, and a complete listing of the Maple procedural code is given in Appendix B, beginning on page 222.

The principal contribution of this dissertation is a theory of Strongly Orthotropic Continuum Mechanics that is derived entirely from an assertion of geometric strain indeterminacy. Implementable into the finite element method, it can resolve widespread kinematic misrepresentations and offer unique and purportedly exact strain-induced energies by removing the assumptions of strain tensor symmetry. This continuum theory births the proposal of a new class of physical tensors described as the Intrinsic Field Tensors capable of generalising the response of most classical mechanical metrics, a number of specialised formulations and the solutions shown to be kinematically intermediate. A series of numerical examples demonstrate Euclidean objectivity, material frame-indifference, patch test satisfaction, and agreement between the subsequent Material Principal Co-rotation and P??I??C decomposition methods that produce the intermediary stress/strain fields. The encompassing theory has wide applicability owing to its fundamental divergence from conventional mechanics, it offers non-trivial outcomes when applied to even very simple problems and its use of not the Eulerian, Lagrangian but the Intrinsic Frame generates previously unreported results in strongly orthotropic continua.

<p>Feature extraction from a tensor based local image representation introduced by Knutsson in [37] is discussed. The tensor representation keeps statements of structure, certainty of statement and energy separate. Further processing for obtaining new features also having these three entities separate is achieved by the use of a new concept, tensor field filtering. Tensor filters for smoothing and for extraction of circular symmetries are presented and discussed in particular. These methods are used for corner detection and extraction of more global features such as lines in images. A novel method for grouping local orientation estimates into global line parameters is introduced. The method is based on a new parameter space, the Möbius Strip parameter space, which has similarities to the Hough transform. A local centroid clustering algorithm is used for classification in this space. The procedure automatically divides curves into line segments with appropriate lengths depending on the curvature. A linked list structure is built up for storing data in an efficient way.</p> / Ogiltigt nummer / annan version: I publ. nr 290:s ISBN: 91-7870-815-X.

<p>The cardiac wall has complex three-dimensional fiber structures and mechanical properties that enable the heart to efficiently pump the blood through the body. By studying the myocardial strains induced during diastole, information about the pumping performance of the heart and what mechanisms that are responsible for this effective blood filling, can be achieved. Two different computation methods for myocardial strain, both based on data acquired from marker technique, were compared using a theoretical cylinder model. The non-homogeneous polynomial fitting method yielded higher accuracy than a homogeneous tetrahedron method, and was further used to investigate cardiac and fiber strains at different wall depths and myocardial regions in normal and ischemic ovine hearts. Large spatial and regional variations were found, as well as alterations, conveyed by ischemic conditions, of fiber mechanisms responsible for the circumferential expansion and wall thinning during diastole.</p>

<p>Conformal field theories (CFT) constitute an interesting class of twodimensionalquantum field theories, with applications in string theoryas well as condensed matter physics. The symmetries of a CFT can beencoded in the mathematical structure of a conformal vertex algebra.The rational CFT’s are distinguished by the property that the categoryof representations of the vertex algebra is a modular tensor category.The solution of a rational CFT can be split off into two separate tasks, apurely complex analytic and a purely algebraic part.</p><p>The TFT-construction gives a solution to the second part of the problem.This construction gets its name from one of the crucial ingredients,a three-dimensional topological field theory (TFT). The correlators obtainedby the TFT-construction satisfy all consistency conditions of thetheory. Among them are the factorization constraints, whose implicationsfor boundary conditions are the main topic of this thesis.</p><p>The main result reviewed in this thesis is that the factorization constraintsgive rise to a semisimple commutative associative complex algebrawhose irreducible representations are the so-called reflection coefficients.The reflection coefficients capture essential information aboutboundary conditions, such as ground-state degeneracies and Ramond-Ramond charges of string compactifications. We also show that the annuluspartition function can be derived fromthis classifying algebra andits representation theory.</p>

<p>Neuroimaging and neurophysiology techniques were used to study some aspects of cortical sensory and motor system reorganisation in patients in the chronic phase after stroke. Using Diffusion Tensor Imaging, we found that the degree of white matter integrity of the corticofugal tracts (CFT) was positively related to grip strength. Structural changes of the CFT were also associated with functional changes in the corticospinal pathways, measured using Transcranial Magnetic Stimulation. This suggests that structural and functional integrity of the CFT is essential for upper limb function after stroke.</p><p>Using functional magnetic resonance imaging (fMRI), to measure brain activity during slow and fast passive hand movements, we found that velocity-dependent brain activity correlated positively with neural contribution to passive movement resistance in the hand in ipsilateral primary sensory (S1) and motor (M1) cortex in both patients and controls. This suggests a cortical involvement in the hyperactive reflex response of flexor muscles upon fast passive stretch.</p><p>Effects of a four week passive-active movement training programme were evaluated in chronic stroke patients. The group improved in range of motion and upper limb function after the training. The patients also reported improvements in a variety of daily tasks requiring the use of the affected upper limb. </p><p>Finally, we used fMRI to explore if brain activity during passive hand movement is related to time after stroke, and if such activity can be affected with intense training. In patients, reduced activity over time was found in supplementary motor area (SMA), contralateral M1 and prefrontal and parietal association areas along with ipsilateral cerebellum. After training, brain activity increased in SMA, ipsilateral S1 and intraparietal sulcus, and contralateral cerebellum in parallel with functional improvements of the upper limb. The findings suggest a use-dependent modification of cortical activation patterns in the affected hand after stroke. </p>

Exterior tensor products of elliptic operators on smooth manifolds and manifolds with conical singularities are used to obtain examples of elliptic operators on manifolds with edges that do not admit well-posed edge boundary and coboundary conditions.

Earthquake swarms occur frequently in West Bohemia, Central Europe. Their occurrence is correlated with and propably triggered by fluids that escape on the earth's surface near the epicentres. These fluids raise up periodically from a seemingbly deep-seated source in the upper mantle. Moment tensors for swarm events in 1997 indicate tensile faulting. However, they were determined under assumption of seismic isotropy although anisotropy can be observed. Anisotropy may obscure moment tensors and their interpretation. In 2000, more than 10,000 swarm earthquakes occurred near Novy Kostel, West Bohemia. Event triggering by fluid injection is likely. Activity lasted from 28/08 until 31/12/00 (9 phases) with maximum ML=3.2. High quality P-wave seismograms were used to retrieve the source mechanisms for 112 events between 28/08/00 and 30/10/00 using > 20 stations. We determine the source geometry using a new algorithm and different velocity models including anisotropy. From inversions of P waves we observe ML<3.2, strike-slip events on steep N-S oriented faults with additional normal or reverse components. Tensile components seem to be evident for more than 60% of the processed swarm events in West Bohemia during the phases 1-7. Being most significant at great depths and at phases 1-4 during the swarm they are time and location dependent. Although tensile components are reduced when anisotropy is assumed they persist and seem to be important. They can be explained by pore-pressure changes due to the injection of fluids that raise up. Our findings agree with other observations e.g. correlation of fluid transport and seismicity, variations in b-value, forcing rate, and in pore pressure diffusion. Tests of our results show their significance.