Minimal Path Methods for Segmentation and Analysis of 2D and 3D Line Structures

Image segmentation plays a vital role in many applications of computer vision. Segmentation is not only an important task in its own right, but also a prerequisite for many further image analysis steps. Consequently, segmentation is one of the most active research areas of computer vision. In this thesis, line structures are considered, which have quite different characteristics compared to common objects in natural 2D images: Line structures are much thinner and longer, and often they have little color or texture information such as blood vessels in medical images. To cope with these challenges, minimal path methods are commonly used. In this thesis, two new methods are introduced which are extensions of existing minimal path methods. The first method is a novel hybrid approach for automatic 3D segmentation and quantification of high-resolution 7 Tesla magnetic resonance angiography (MRA) images of the human cerebral vasculature. Our approach consists of two main steps. First, a 3D model-based approach is used to segment and quantify thick vessels and most parts of thin vessels. Second, remaining vessel gaps of the first step in low-contrast and noisy regions are completed using a 3D minimal path approach, which exploits directional information. We present two novel minimal path approaches: The first is an explicit approach based on energy minimization using probabilistic sampling, and the second is an implicit approach based on fast marching with anisotropic directional prior. The second method we introduce is a novel minimal path method for the segmentation of 2D and 3D line structures. Minimal path methods perform propagation of a wavefront emanating from a start point at a speed derived from image features, followed by path extraction using backtracing. Usually, the computation of the speed and the propagation of the wave are two separate steps, and point features are used to compute a static speed. We introduce a new continuous minimal path method which steers the wave propagation progressively using dynamic speed based on path features. We present three instances of our method, using an appearance feature of the path, a geometric feature based on the curvature of the path, and a joint appearance and geometric feature based on the tangent of the wavefront. Such features have not been used in previous continuous minimal path methods. We compute the features dynamically during the wave propagation, and also efficiently using a fast numerical scheme and a low-dimensional parameter space. Our method does not suffer from discretization or metrication errors. We conducted quantitative and qualitative experimental evaluations of our methods using 2D and 3D images from different application areas, including synthetic images, retinal images, satellite images of streets, rivers, and bridges, and 3D 7T MRA images of human brain vessels

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

Blood Vessel Segmentation and shape analysis for quantification of Coronary Artery Stenosis in CT Angiography

This thesis presents an automated framework for quantitative vascular shape analysis of the coronary arteries, which constitutes an important and fundamental component of an automated image-based diagnostic system. Firstly, an automated vessel segmentation algorithm is developed to extract the coronary arteries based on the framework of active contours. Both global and local intensity statistics are utilised in the energy functional calculation, which allows for dealing with non-uniform brightness conditions, while evolving the contour towards to the desired boundaries without being trapped in local minima. To suppress kissing vessel artifacts, a slice-by-slice correction scheme, based on multiple regions competition, is proposed to identify and track the kissing vessels throughout the transaxial images of the CTA data. Based on the resulting segmentation, we then present a dedicated algorithm to estimate the geometric parameters of the extracted arteries, with focus on vessel bifurcations. In particular, the centreline and associated reference surface of the coronary arteries, in the vicinity of arterial bifurcations, are determined by registering an elliptical cross sectional tube to the desired constituent branch. The registration problem is solved by a hybrid optimisation method, combining local greedy search and dynamic programming, which ensures the global optimality of the solution and permits the incorporation of any hard constraints posed to the tube model within a natural and direct framework. In contrast with conventional volume domain methods, this technique works directly on the mesh domain, thus alleviating the need for image upsampling. The performance of the proposed framework, in terms of efficiency and accuracy, is demonstrated on both synthetic and clinical image data. Experimental results have shown that our techniques are capable of extracting the major branches of the coronary arteries and estimating the related geometric parameters (i.e., the centreline and the reference surface) with a high degree of agreement to those obtained through manual delineation. Particularly, all of the major branches of coronary arteries are successfully detected by the proposed technique, with a voxel-wise error at 0.73 voxels to the manually delineated ground truth data. Through the application of the slice-by-slice correction scheme, the false positive metric, for those coronary segments affected by kissing vessel artifacts, reduces from 294% to 22.5%. In terms of the capability of the presented framework in defining the location of centrelines across vessel bifurcations, the mean square errors (MSE) of the resulting centreline, with respect to the ground truth data, is reduced by an average of 62.3%, when compared with initial estimation obtained using a topological thinning based algorithm

Vessel Axis Tracking Using Topology Constrained Surface Evolution

An approach to three-dimensional vessel axis tracking based on surface evolution is presented. The main idea is to guide the evolution of the surface by analyzing its skeleton topology during evolution, and imposing shape constraints on the topology. For example, the intermediate topology can be processed such that it represents a single vessel segment, a bifurcation, or a more complex vascular topology. The evolving surface is then re-initialized with the newly found topology. Re-initialization is a crucial step since it creates probing behavior of the evolving front, encourages the segmentation process to extract the vascular structure of interest and reduces the risk on leaking of the curve into the background. The method was evaluated in two computed tomography angiography applications: (i) extracting the internal carotid arteries including the region in which they traverse through the skull base, which is challenging due to the proximity of bone structures and overlap in intensity values, and (ii) extracting the carotid bifurcations including many cases in which they are severely stenosed and contain calcifications. The vessel axis was found in 90% (18/20 internal carotids in ten patients) and 70% (14/20 carotid bifurcations in a different set of ten patients) of the cases

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

Lumen Border Detection of Intravascular Ultrasound via Denoising of Directional Wavelet Representations

In this paper, intravascular ultrasound (IVUS) grayscale images, acquired with a single-element mechanically rotating transducer, are processed with wavelet denoising and region-based segmentation to extract various layers of lumen contours and plaques. First, IVUS volumetric data is expanded on complex exponential wavelet-like basis functions, also known as Brushlets, which are well localized in time and frequency domains. Brushlets denoising have demonstrated in the past a great aptitude for denoising ultrasound data and removal of blood speckles. A region-based segmentation framework is then applied for detection of lumen border layers, which remains one of the most challenging problems in IVUS image analysis for images acquired with a single element, mechanically rotating 45 MHz transducer. We evaluated hard thresholding for Brushlet denoising, and compared segmentation results to manually traced lumen borders. We observed good agreement and suggest that the proposed algorithm has a great potential to be used as a reliable pre-processing step for accurate lumen border detection

Geodesic tractography segmentation for directional medical image analysis

Acknowledgements page removed per author's request, 01/06/2014.Geodesic Tractography Segmentation is the two component approach presented in this thesis for the analysis of imagery in oriented domains, with emphasis on the application to diffusion-weighted magnetic resonance imagery (DW-MRI). The computeraided analysis of DW-MRI data presents a new set of problems and opportunities for the application of mathematical and computer vision techniques. The goal is to develop a set of tools that enable clinicians to better understand DW-MRI data and ultimately shed new light on biological processes. This thesis presents a few techniques and tools which may be used to automatically find and segment major neural fiber bundles from DW-MRI data. For each technique, we provide a brief overview of the advantages and limitations of our approach relative to other available approaches.Ph.D.Committee Chair: Tannenbaum, Allen; Committee Member: Barnes, Christopher F.; Committee Member: Niethammer, Marc; Committee Member: Shamma, Jeff; Committee Member: Vela, Patrici

Geodesic Tracking via New Data-driven Connections of Cartan Type for Vascular Tree Tracking

We introduce a data-driven version of the plus Cartan connection on the homogeneous space $\mathbb{M}_2$ of 2D positions and orientations. We formulate a theorem that describes all shortest and straight curves (parallel velocity and parallel momentum, respectively) with respect to this new data-driven connection and corresponding Riemannian manifold. Then we use these shortest curves for geodesic tracking of complex vasculature in multi-orientation image representations defined on $\mathbb{M}_{2}$. The data-driven Cartan connection characterizes the Hamiltonian flow of all geodesics. It also allows for improved adaptation to curvature and misalignment of the (lifted) vessel structure that we track via globally optimal geodesics. We compute these geodesics numerically via steepest descent on distance maps on $\mathbb{M}_2$ that we compute by a new modified anisotropic fast-marching method. Our experiments range from tracking single blood vessels with fixed endpoints to tracking complete vascular trees in retinal images. Single vessel tracking is performed in a single run in the multi-orientation image representation, where we project the resulting geodesics back onto the underlying image. The complete vascular tree tracking requires only two runs and avoids prior segmentation, placement of extra anchor points, and dynamic switching between geodesic models. Altogether we provide a geodesic tracking method using a single, flexible, transparent, data-driven geodesic model providing globally optimal curves which correctly follow highly complex vascular structures in retinal images. All experiments in this article can be reproduced via documented Mathematica notebooks available at GitHub (https://github.com/NickyvdBerg/DataDrivenTracking)

The optimal connection model for blood vessels segmentation and the MEA-Net

Vascular diseases have long been regarded as a significant health concern. Accurately detecting the location, shape, and afflicted regions of blood vessels from a diverse range of medical images has proven to be a major challenge. Obtaining blood vessels that retain their correct topological structures is currently a crucial research issue. Numerous efforts have sought to reinforce neural networks' learning of vascular geometric features, including measures to ensure the correct topological structure of the segmentation result's vessel centerline. Typically, these methods extract topological features from the network's segmentation result and then apply regular constraints to reinforce the accuracy of critical components and the overall topological structure. However, as blood vessels are three-dimensional structures, it is essential to achieve complete local vessel segmentation, which necessitates enhancing the segmentation of vessel boundaries. Furthermore, current methods are limited to handling 2D blood vessel fragmentation cases. Our proposed boundary attention module directly extracts boundary voxels from the network's segmentation result. Additionally, we have established an optimal connection model based on minimal surfaces to determine the connection order between blood vessels. Our method achieves state-of-the-art performance in 3D multi-class vascular segmentation tasks, as evidenced by the high values of Dice Similarity Coefficient (DSC) and Normalized Surface Dice (NSD) metrics. Furthermore, our approach improves the Betti error, LR error, and BR error indicators of vessel richness and structural integrity by more than 10% compared to other methods, and effectively addresses vessel fragmentation and yields blood vessels with a more precise topological structure.Comment: 19 page

Vascular Tree Structure: Fast Curvature Regularization and Validation

This work addresses the challenging problem of accurate vessel structure analysis in high resolution 3D biomedical images. Typical segmentation methods fail on recent micro-CT data sets resolving near-capillary vessels due to limitations of standard first-order regularization models. While regularization is needed to address noise and partial volume issues in the data, we argue that extraction of thin tubular structures requires higher-order curvature-based regularization. There are no standard segmentation methods regularizing surface curvature in 3D that could be applied to large 3D volumes. However, we observe that standard measures for vessels structure are more concerned with topology, bifurcation angles, and other parameters that can be directly addressed without segmentation. We propose a novel methodology reconstructing tree structure of the vessels using a new centerline curvature regularization technique. Our high-order regularization model is based on a recent curvature estimation method. We developed a Levenberg-Marquardt optimization scheme and an efficient GPU-based implementation of our algorithm. We also propose a validation mechanism based on synthetic vessel images. Our preliminary results on real ultra-resolution micro CT volumes are promising