Locally Adaptive Frames in the Roto-Translation Group and their Applications in Medical Imaging

Locally adaptive differential frames (gauge frames) are a well-known effective tool in image analysis, used in differential invariants and PDE-flows. However, at complex structures such as crossings or junctions, these frames are not well-defined. Therefore, we generalize the notion of gauge frames on images to gauge frames on data representations $U:\mathbb{R}^{d} \rtimes S^{d-1} \to \mathbb{R}$ defined on the extended space of positions and orientations, which we relate to data on the roto-translation group $SE(d)$, $d=2,3$. This allows to define multiple frames per position, one per orientation. We compute these frames via exponential curve fits in the extended data representations in $SE(d)$. These curve fits minimize first or second order variational problems which are solved by spectral decomposition of, respectively, a structure tensor or Hessian of data on $SE(d)$. We include these gauge frames in differential invariants and crossing preserving PDE-flows acting on extended data representation $U$ and we show their advantage compared to the standard left-invariant frame on $SE(d)$. Applications include crossing-preserving filtering and improved segmentations of the vascular tree in retinal images, and new 3D extensions of coherence-enhancing diffusion via invertible orientation scores

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

Tensor-cut: A tensor-based graph-cut blood vessel segmentation method and its application to renal artery segmentation

Blood vessel segmentation plays a fundamental role in many computer-aided diagnosis (CAD) systems, such as coronary artery stenosis quantification, cerebral aneurysm quantification, and retinal vascular tree analysis. Fine blood vessel segmentation can help build a more accurate computer-aided diagnosis system and help physicians gain a better understanding of vascular structures. The purpose of this article is to develop a blood vessel segmentation method that can improve segmentation accuracy in tiny blood vessels. In this work, we propose a tensor-based graph-cut method for blood vessel segmentation. With our method, each voxel can be modeled by a second-order tensor, allowing the capture of the intensity information and the geometric information for building a more accurate model for blood vessel segmentation. We compared our proposed method’s accuracy to several state-of-the-art blood vessel segmentation algorithms and performed experiments on both simulated and clinical CT datasets. Both experiments showed that our method achieved better state-of-the-art results than the competing techniques. The mean centerline overlap ratio of our proposed method is 84% on clinical CT data. Our proposed blood vessel segmentation method outperformed other state-of-the-art methods by 10% on clinical CT data. Tiny blood vessels in clinical CT data with a 1-mm radius can be extracted using the proposed technique. The experiments on a clinical dataset showed that the proposed method significantly improved the segmentation accuracy in tiny blood vessels

Vessel tractography using an intensity based tensor model with branch detection

In this paper, we present a tubular structure seg- mentation method that utilizes a second order tensor constructed from directional intensity measurements, which is inspired from diffusion tensor image (DTI) modeling. The constructed anisotropic tensor which is fit inside a vessel drives the segmen- tation analogously to a tractography approach in DTI. Our model is initialized at a single seed point and is capable of capturing whole vessel trees by an automatic branch detection algorithm developed in the same framework. The centerline of the vessel as well as its thickness is extracted. Performance results within the Rotterdam Coronary Artery Algorithm Evaluation framework are provided for comparison with existing techniques. 96.4% average overlap with ground truth delineated by experts is obtained in addition to other measures reported in the paper. Moreover, we demonstrate further quantitative results over synthetic vascular datasets, and we provide quantitative experiments for branch detection on patient Computed Tomography Angiography (CTA) volumes, as well as qualitative evaluations on the same CTA datasets, from visual scores by a cardiologist expert

Vessel tractography using an intensity based tensor model

In the last decade, CAD (Coronary Artery Disease) has been the leading cause of death worldwide [1]. Extraction of arteries is a crucial step for accurate visualization, quantification, and tracking of pathologies. However, coronary artery segmentation is one of the most challenging problems in medical image analysis, since arteries are complex tubular structures with bifurcations, and have possible pathologies. Moreover, appearance of blood vessels and their geometry can be perturbed by stents, calcifications and pathologies such as stenosis. Besides, noise, contrast and resolution artifacts can make the problem more challenging. In this thesis, we present a novel tubular structure segmentation method based on an intensity-based tensor that fits to a vessel, which is inspired from diffusion tensor image (DTI) modeling. The anisotropic tensor inside the vessel drives the segmentation analogously to a tractography approach in DTI. Our model is initialized with a single seed point and it is capable of capturing whole vessel tree by an automatic branch detection algorithm. The centerline of the vessel as well as its thickness is extracted. We demonstrate the performance of our algorithm on 3 complex tubular structured synthetic datasets, and on 8 CTA (Computed Tomography Angiography) datasets (from Rotterdam Coronary Artery Algorithm Evaluation Framework) for quantitative validation. Additionally, extracted arteries from 10 CTA volumes are qualitatively evaluated by a cardiologist expert's visual scores

Curvilinear Structure Enhancement in Biomedical Images

Curvilinear structures can appear in many different areas and at a variety of scales. They can be axons and dendrites in the brain, blood vessels in the fundus, streets, rivers or fractures in buildings, and others. So, it is essential to study curvilinear structures in many fields such as neuroscience, biology, and cartography regarding image processing. Image processing is an important field for the help to aid in biomedical imaging especially the diagnosing the disease. Image enhancement is the early step of image analysis. In this thesis, I focus on the research, development, implementation, and validation of 2D and 3D curvilinear structure enhancement methods, recently established. The proposed methods are based on phase congruency, mathematical morphology, and tensor representation concepts. First, I have introduced a 3D contrast independent phase congruency-based enhancement approach. The obtained results demonstrate the proposed approach is robust against the contrast variations in 3D biomedical images. Second, I have proposed a new mathematical morphology-based approach called the bowler-hat transform. In this approach, I have combined the mathematical morphology with a local tensor representation of curvilinear structures in images. The bowler-hat transform is shown to give better results than comparison methods on challenging data such as retinal/fundus images. The bowler-hat transform is shown to give better results than comparison methods on challenging data such as retinal/fundus images. Especially the proposed method is quite successful while enhancing of curvilinear structures at junctions. Finally, I have extended the bowler-hat approach to the 3D version to prove the applicability, reliability, and ability of it in 3D

Segmentation and Characterization of Small Retinal Vessels in Fundus Images Using the Tensor Voting Approach

RÉSUMÉ La rétine permet de visualiser facilement une partie du réseau vasculaire humain. Elle offre ainsi un aperçu direct sur le développement et le résultat de certaines maladies liées au réseau vasculaire dans son entier. Chaque complication visible sur la rétine peut avoir un impact sur la capacité visuelle du patient. Les plus petits vaisseaux sanguins sont parmi les premières structures anatomiques affectées par la progression d’une maladie, être capable de les analyser est donc crucial. Les changements dans l’état, l’aspect, la morphologie, la fonctionnalité, ou même la croissance des petits vaisseaux indiquent la gravité des maladies. Le diabète est une maladie métabolique qui affecte des millions de personnes autour du monde. Cette maladie affecte le taux de glucose dans le sang et cause des changements pathologiques dans différents organes du corps humain. La rétinopathie diabétique décrit l’en- semble des conditions et conséquences du diabète au niveau de la rétine. Les petits vaisseaux jouent un rôle dans le déclenchement, le développement et les conséquences de la rétinopa- thie. Dans les dernières étapes de cette maladie, la croissance des nouveaux petits vaisseaux, appelée néovascularisation, présente un risque important de provoquer la cécité. Il est donc crucial de détecter tous les changements qui ont lieu dans les petits vaisseaux de la rétine dans le but de caractériser les vaisseaux sains et les vaisseaux anormaux. La caractérisation en elle-même peut faciliter la détection locale d’une rétinopathie spécifique. La segmentation automatique des structures anatomiques comme le réseau vasculaire est une étape cruciale. Ces informations peuvent être fournies à un médecin pour qu’elles soient considérées lors de son diagnostic. Dans les systèmes automatiques d’aide au diagnostic, le rôle des petits vaisseaux est significatif. Ne pas réussir à les détecter automatiquement peut conduire à une sur-segmentation du taux de faux positifs des lésions rouges dans les étapes ultérieures. Les efforts de recherche se sont concentrés jusqu’à présent sur la localisation précise des vaisseaux de taille moyenne. Les modèles existants ont beaucoup plus de difficultés à extraire les petits vaisseaux sanguins. Les modèles existants ne sont pas robustes à la grande variance d’apparence des vaisseaux ainsi qu’à l’interférence avec l’arrière-plan. Les modèles de la littérature existante supposent une forme générale qui n’est pas suffisante pour s’adapter à la largeur étroite et la courbure qui caractérisent les petits vaisseaux sanguins. De plus, le contraste avec l’arrière-plan dans les régions des petits vaisseaux est très faible. Les méthodes de segmentation ou de suivi produisent des résultats fragmentés ou discontinus. Par ailleurs, la segmentation des petits vaisseaux est généralement faite aux dépends de l’amplification du bruit. Les modèles déformables sont inadéquats pour segmenter les petits vaisseaux. Les forces utilisées ne sont pas assez flexibles pour compenser le faible contraste, la largeur, et vii la variance des vaisseaux. Enfin, les approches de type apprentissage machine nécessitent un entraînement avec une base de données étiquetée. Il est très difficile d’obtenir ces bases de données dans le cas des petits vaisseaux. Cette thèse étend les travaux de recherche antérieurs en fournissant une nouvelle mé- thode de segmentation des petits vaisseaux rétiniens. La détection de ligne à échelles multiples (MSLD) est une méthode récente qui démontre une bonne performance de segmentation dans les images de la rétine, tandis que le vote tensoriel est une méthode proposée pour reconnecter les pixels. Une approche combinant un algorithme de détection de ligne et de vote tensoriel est proposée. L’application des détecteurs de lignes a prouvé son efficacité à segmenter les vais- seaux de tailles moyennes. De plus, les approches d’organisation perceptuelle comme le vote tensoriel ont démontré une meilleure robustesse en combinant les informations voisines d’une manière hiérarchique. La méthode de vote tensoriel est plus proche de la perception humain que d’autres modèles standards. Comme démontré dans ce manuscrit, c’est un outil pour segmenter les petits vaisseaux plus puissant que les méthodes existantes. Cette combinaison spécifique nous permet de surmonter les défis de fragmentation éprouvés par les méthodes de type modèle déformable au niveau des petits vaisseaux. Nous proposons également d’utiliser un seuil adaptatif sur la réponse de l’algorithme de détection de ligne pour être plus robuste aux images non-uniformes. Nous illustrons également comment une combinaison des deux méthodes individuelles, à plusieurs échelles, est capable de reconnecter les vaisseaux sur des distances variables. Un algorithme de reconstruction des vaisseaux est également proposé. Cette dernière étape est nécessaire car l’information géométrique complète est requise pour pouvoir utiliser la segmentation dans un système d’aide au diagnostic. La segmentation a été validée sur une base de données d’images de fond d’oeil à haute résolution. Cette base contient des images manifestant une rétinopathie diabétique. La seg- mentation emploie des mesures de désaccord standards et aussi des mesures basées sur la perception. En considérant juste les petits vaisseaux dans les images de la base de données, l’amélioration dans le taux de sensibilité que notre méthode apporte par rapport à la méthode standard de détection multi-niveaux de lignes est de 6.47%. En utilisant les mesures basées sur la perception, l’amélioration est de 7.8%. Dans une seconde partie du manuscrit, nous proposons également une méthode pour caractériser les rétines saines ou anormales. Certaines images contiennent de la néovascula- risation. La caractérisation des vaisseaux en bonne santé ou anormale constitue une étape essentielle pour le développement d’un système d’aide au diagnostic. En plus des défis que posent les petits vaisseaux sains, les néovaisseaux démontrent eux un degré de complexité encore plus élevé. Ceux-ci forment en effet des réseaux de vaisseaux à la morphologie com- plexe et inhabituelle, souvent minces et à fortes courbures. Les travaux existants se limitent viii à l’utilisation de caractéristiques de premier ordre extraites des petits vaisseaux segmentés. Notre contribution est d’utiliser le vote tensoriel pour isoler les jonctions vasculaires et d’uti- liser ces jonctions comme points d’intérêts. Nous utilisons ensuite une statistique spatiale de second ordre calculée sur les jonctions pour caractériser les vaisseaux comme étant sains ou pathologiques. Notre méthode améliore la sensibilité de la caractérisation de 9.09% par rapport à une méthode de l’état de l’art. La méthode développée s’est révélée efficace pour la segmentation des vaisseaux réti- niens. Des tenseurs d’ordre supérieur ainsi que la mise en œuvre d’un vote par tenseur via un filtrage orientable pourraient être étudiés pour réduire davantage le temps d’exécution et résoudre les défis encore présents au niveau des jonctions vasculaires. De plus, la caractéri- sation pourrait être améliorée pour la détection de la rétinopathie proliférative en utilisant un apprentissage supervisé incluant des cas de rétinopathie diabétique non proliférative ou d’autres pathologies. Finalement, l’incorporation des méthodes proposées dans des systèmes d’aide au diagnostic pourrait favoriser le dépistage régulier pour une détection précoce des rétinopathies et d’autres pathologies oculaires dans le but de réduire la cessité au sein de la population.----------ABSTRACT As an easily accessible site for the direct observation of the circulation system, human retina can offer a unique insight into diseases development or outcome. Retinal vessels are repre- sentative of the general condition of the whole systematic circulation, and thus can act as a "window" to the status of the vascular network in the whole body. Each complication on the retina can have an adverse impact on the patient’s sight. In this direction, small vessels’ relevance is very high as they are among the first anatomical structures that get affected as diseases progress. Moreover, changes in the small vessels’ state, appearance, morphology, functionality, or even growth indicate the severity of the diseases. This thesis will focus on the retinal lesions due to diabetes, a serious metabolic disease affecting millions of people around the world. This disorder disturbs the natural blood glucose levels causing various pathophysiological changes in different systems across the human body. Diabetic retinopathy is the medical term that describes the condition when the fundus and the retinal vessels are affected by diabetes. As in other diseases, small vessels play a crucial role in the onset, the development, and the outcome of the retinopathy. More importantly, at the latest stage, new small vessels, or neovascularizations, growth constitutes a factor of significant risk for blindness. Therefore, there is a need to detect all the changes that occur in the small retinal vessels with the aim of characterizing the vessels to healthy or abnormal. The characterization, in turn, can facilitate the detection of a specific retinopathy locally, like the sight-threatening proliferative diabetic retinopathy. Segmentation techniques can automatically isolate important anatomical structures like the vessels, and provide this information to the physician to assist him in the final decision. In comprehensive systems for the automatization of DR detection, small vessels role is significant as missing them early in a CAD pipeline might lead to an increase in the false positive rate of red lesions in subsequent steps. So far, the efforts have been concentrated mostly on the accurate localization of the medium range vessels. In contrast, the existing models are weak in case of the small vessels. The required generalization to adapt an existing model does not allow the approaches to be flexible, yet robust to compensate for the increased variability in the appearance as well as the interference with the background. So far, the current template models (matched filtering, line detection, and morphological processing) assume a general shape for the vessels that is not enough to approximate the narrow, curved, characteristics of the small vessels. Additionally, due to the weak contrast in the small vessel regions, the current segmentation and the tracking methods produce fragmented or discontinued results. Alternatively, the small vessel segmentation can be accomplished at the expense of x background noise magnification, in the case of using thresholding or the image derivatives methods. Furthermore, the proposed deformable models are not able to propagate a contour to the full extent of the vasculature in order to enclose all the small vessels. The deformable model external forces are ineffective to compensate for the low contrast, the low width, the high variability in the small vessel appearance, as well as the discontinuities. Internal forces, also, are not able to impose a global shape constraint to the contour that could be able to approximate the variability in the appearance of the vasculature in different categories of vessels. Finally, machine learning approaches require the training of a classifier on a labelled set. Those sets are difficult to be obtained, especially in the case of the smallest vessels. In the case of the unsupervised methods, the user has to predefine the number of clusters and perform an effective initialization of the cluster centers in order to converge to the global minimum. This dissertation expanded the previous research work and provides a new segmentation method for the smallest retinal vessels. Multi-scale line detection (MSLD) is a recent method that demonstrates good segmentation performance in the retinal images, while tensor voting is a method first proposed for reconnecting pixels. For the first time, we combined the line detection with the tensor voting framework. The application of the line detectors has been proved an effective way to segment medium-sized vessels. Additionally, perceptual organization approaches like tensor voting, demonstrate increased robustness by combining information coming from the neighborhood in a hierarchical way. Tensor voting is closer than standard models to the way human perception functions. As we show, it is a more powerful tool to segment small vessels than the existing methods. This specific combination allows us to overcome the apparent fragmentation challenge of the template methods at the smallest vessels. Moreover, we thresholded the line detection response adaptively to compensate for non-uniform images. We also combined the two individual methods in a multi-scale scheme in order to reconnect vessels at variable distances. Finally, we reconstructed the vessels from their extracted centerlines based on pixel painting as complete geometric information is required to be able to utilize the segmentation in a CAD system. The segmentation was validated on a high-resolution fundus image database that in- cludes diabetic retinopathy images of varying stages, using standard discrepancy as well as perceptual-based measures. When only the smallest vessels are considered, the improve- ments in the sensitivity rate for the database against the standard multi-scale line detection method is 6.47%. For the perceptual-based measure, the improvement is 7.8% against the basic method. The second objective of the thesis was to implement a method for the characterization of isolated retinal areas into healthy or abnormal cases. Some of the original images, from which xi these patches are extracted, contain neovascularizations. Investigation of image features for the vessels characterization to healthy or abnormal constitutes an essential step in the direction of developing CAD system for the automatization of DR screening. Given that the amount of data will significantly increase under CAD systems, the focus on this category of vessels can facilitate the referral of sight-threatening cases to early treatment. In addition to the challenges that small healthy vessels pose, neovessels demonstrate an even higher degree of complexity as they form networks of convolved, twisted, looped thin vessels. The existing work is limited to the use of first-order characteristics extracted from the small segmented vessels that limits the study of patterns. Our contribution is in using the tensor voting framework to isolate the retinal vascular junctions and in turn using those junctions as points of interests. Second, we exploited second-order statistics computed on the junction spatial distribution to characterize the vessels as healthy or neovascularizations. In fact, the second-order spatial statistics extracted from the junction distribution are combined with widely used features to improve the characterization sensitivity by 9.09% over the state of art. The developed method proved effective for the segmentation of the retinal vessels. Higher order tensors along with the implementation of tensor voting via steerable filtering could be employed to further reduce the execution time, and resolve the challenges at vascular junctions. Moreover, the characterization could be advanced to the detection of prolifera- tive retinopathy by extending the supervised learning to include non-proliferative diabetic retinopathy cases or other pathologies. Ultimately, the incorporation of the methods into CAD systems could facilitate screening for the effective reduction of the vision-threatening diabetic retinopathy rates, or the early detection of other than ocular pathologies

Navier-Stokes Modelling of Non-Newtonian Blood Flow in Cerebral Arterial Circulation and its Dynamic Impact on Electrical Conductivity in a Realistic Multi-Compartment Head Model

Background and Objective: This study aims to evaluate the dynamic effect of non-Newtonian cerebral arterial circulation on electrical conductivity distribution (ECD) in a realistic multi-compartment head model. It addresses the importance and challenges associated with electrophysiological modalities, such as transcranial electrical stimulation, electro-magnetoencephalography, and electrical impedance tomography. Factors such as electrical conductivity's impact on forward modeling accuracy, complex vessel networks, data acquisition limitations (especially in MRI), and blood flow phenomena are considered. Methods: The Navier-Stokes equations (NSEs) govern the non-Newtonian flow model used in this study. The solver comprises two stages: the first solves the pressure field using a dynamical pressure-Poisson equation derived from NSEs, and the second updates the velocity field using Leray regularization and the pressure distribution from the first stage. The Carreau-Yasuda model establishes the connection between blood velocity and viscosity. Blood concentration in microvessels is approximated using Fick's law of diffusion, and conductivity mapping is obtained via Archie's law. The head model used corresponds to an open 7 Tesla MRI dataset, differentiating arterial vessels from other structures. Results: The results suggest the establishment of a dynamic model of cerebral blood flow for arterial and microcirculation. Blood pressure and conductivity distributions are obtained through numerically simulated pulse sequences, enabling approximation of blood concentration and conductivity within the brain. Conclusions: This model provides an approximation of dynamic blood flow and corresponding ECD in different brain regions. The advantage lies in its applicability with limited a priori information about blood flow and compatibility with arbitrary head models that distinguish arteries.Comment: 13 pages; 8 figures; 2 tabl