Elsevier

Medical Image Analysis

Volume 32, August 2016, Pages 201-215
Medical Image Analysis

Simultaneous segmentation and anatomical labeling of the cerebral vasculature

https://doi.org/10.1016/j.media.2016.03.006Get rights and content

Highlights

  • We present a novel method for segmentation and anatomical labeling of vasculature.

  • Segmentation and anatomical labeling are performed simultaneously.

  • The problem is formulated as an Integer Program which can be solved optimally.

  • We demonstrate that our approach compares favorably against state-of-the-art methods.

Abstract

We present a novel algorithm for the simultaneous segmentation and anatomical labeling of the cerebral vasculature. Unlike existing approaches that first attempt to obtain a good segmentation and then perform labeling, we optimize for both by simultaneously taking into account the image evidence and the prior knowledge about the geometry and connectivity of the vasculature. This is achieved by first constructing an overcomplete graph capturing the vasculature, and then selecting and labeling the subset of edges that most likely represents the true vasculature. We formulate the latter problem as an Integer Program (IP), which can be solved efficiently to provable optimality. We evaluate our approach on a publicly available dataset of 50 cerebral MRA images, and demonstrate that it compares favorably against state-of-the-art methods.

Introduction

Automated segmentation and anatomical labeling of blood vessels is an important problem with many practical applications. In clinical settings, it can give an interventional radiologist extra guidance when navigating through the vasculature of a patient or enable automatic quantification of specific vessel segments. In a research context, it can be used to detect patterns that may be correlated to the incidence of vascular pathologies.

In this work, we focus on the cerebral vasculature and more specifically on the Circle of Willis (CoW) and its adjacent vessels. The CoW is a circle of arteries at the base of the skull that connects the left and right side of the anterior cerebral circulation with the posterior cerebral circulation (Fig. 1). It is supplied with blood by three large arteries, namely the left and right internal carotid arteries (ICA) and the vertebrobasilar artery (VBA). The CoW plays a crucial role in several vascular pathologies, notably hemorrhagic and ischemic stroke. Cerebral aneurysms are balloon-like bulges on the wall of cerebral vessels and their rupturing is the main cause of subarachnoid hemorrhagic stroke (van Gijn and Rinkel, 2001). About 90 % of all cerebral aneurysms are found on the CoW (Brisman et al., 2006). The specific topology of the CoW determines the redundancy in blood supply to the brain and is associated with the prevalence of border zone infarcts in patients with unilateral ICA stenosis (Hendrikse et al., 2001). Although the CoW has a very characteristic morphology, it is highly variable: less than half of the population has a complete circle because one or more arteries are usually missing (Krabbe-Hartkamp et al., 1998). This variability makes both segmentation and labeling challenging.

In the following section, we provide an overview of the state-of-the-art techniques for vascular segmentation and anatomical labeling. Subsequently, we propose a novel method that tackles both problems simultaneously. Finally, we evaluate our approach and demonstrate its advantage over current techniques.

The problem of anatomical labeling of the vasculature can be posed more generally as labeling of a branched tubular structure. Most existing approaches formulate the problem in a graph-based setting, where the segmented object of interest is represented by a graph. In this graph, the vertices represent the branch and endpoints and the edges represent the branches. In the following, we present an overview of such methods.

A conventional approach to labeling is to anatomically match an unlabeled graph with one or more labeled graphs. This approach was successfully followed by Graham (2006), Buelow et al. (2006) and Feragen et al. (2012) to label the bronchi. However, as remarked by Bogunović et al. (2013), the reported results for approaches that learn a statistical labeling model are generally better.

Tschirren et al. (2005) label the bronchi of a patient by matching the graph edges with a labeled, probabilistic model containing for each label the mean and standard deviation of geometric properties. They take into account the length and direction of the edges and the angle and distance between pairs of edges. A learnt, fixed topology between the different labels is enforced. van Ginneken et al. (2008) label the bronchi with a probabilistic model that contains for each label the mean and standard deviation of the orientation, radius and angle with the parent edge. For all edges, label probabilities are calculated and the labels are assigned in a top-down fashion to the bronchial segments. Mori et al. published several works about bronchial labeling. Their latest approach (Mori et al., 2009) labels the bronchial branches in an edge matching approach. A trained classifier assigns a probability to each possible pair of edge and label. The algorithm then searches for the globally optimal assignment of edge labels taking into account several topological constraints. In another line of work, they label the abdominal arteries (Mori, Oda, Egusa, Jiang, Kitasaka, Fujiwara, Misawa, 2010, Matsuzaki, Oda, Kitasaka, Hayashi, Misawa, Mori, 2015), which they consider more difficult than labeling bronchi due to the larger variability. They use an application-specific algorithm which they do not expect to work on vasculature of other organs. The method of Bogunović et al. (2011) aims at labeling five bifurcations in the anterior circulation of the CoW. This is done by explicitly enumerating all possible isomorphisms between a given graph and a predetermined atlas, and then calculating a probabilistic cost function, which combines a data term based on bifurcation morphology with a prior term that imposes a certain ordering of the bifurcations. Although the performance of the method is very good, it is not computationally scalable: a preprocessing step is required to prune the graph to about 20 candidate vertices. Robben et al. (2013) label the full CoW by matching vertices to a probabilistic atlas. The approach relies on both unary potentials of the bifurcations and also pairwise potentials between them. Bogunović et al. (2013) also label the full CoW by matching bifurcations to an atlas. They use the bifurcation properties and have several reference graphs to model the topology of the bifurcations. The method is evaluated on ground truth segmentations as it requires topologically correct segmentations without loops, disconnected regions or spurious branches. Bilgel et al. (2013) label the anterior part of the cerebral vasculature using belief propagation on a Bayesian network. Ghanavati et al. (2014) label the complete vasculature of a mouse model. The labeling problem is formulated as a Markov Random Field and the optimal solution is sought through simulated annealing stochastic relaxation. It should be noted that these methods, except Robben et al. (2013), Bogunović et al. (2013) and Ghanavati et al. (2014), assume that the graph is a tree.

All these approaches rely on a pre-existing segmentation in the form of a graph of blood vessels or bronchi. When assigning the anatomical labels, they account for the fact that the vasculature and the airway system are not random sets of tubular structures but organs with specific connectivity patterns. However they do not exploit this knowledge to improve the segmentations. An exception is the work of Lu et al. (2009) where three non-branching coronary arteries are segmented and labeled by generating many possible segmentations and selecting for each label the most likely one, based solely on geometry.

Vascular segmentation refers to estimating both the vessel geometry and topology. The former involves finding vessel centerline points and their associated radii, while the latter involves recovering the connectivity of these points. This kind of segmentation is also called vascular reconstruction and can be contrasted with voxelwise segmentation, where each voxel in a given volume is assigned either to the vasculature or to the background, and where there is no strict notion of connectivity or morphology.

One could attempt to recover the centerlines from a voxelwise segmentation using skeletonization techniques. However, when the distance between the boundaries of two vessels is smaller than the imaging resolution—a phenomenon called kissing vessels—the connectivity of the voxelwise segmentation does not match that of the underlying vasculature. As a result, skeletonization yields erroneous connections.

Other methods aim at extracting the centerlines directly. An overview is given in Lesage et al. (2009, Section 4.4), where two broad categories are distinguished. Tracking methods (Aylward, Bullitt, 2002, Wong, Chung, 2007, Gülsün, Tek, 2008, Friman, Hindennach, Kühnel, Peitgen, 2010) begin at a given starting point and follow the vasculature by iteratively searching an adjacent point on the vessel centerline using local information. Typically heuristic rules detect branch and endpoints. The second category contains minimal path techniques (Deschamps, Cohen, 2001, Hua, Yezzi, 2007). The resulting centerline connects two given points and minimizes the integral of an intensity function along the centerline. Both approaches typically use only local information and are as such prone to creating shortcuts in the presence of kissing vessels.

In a more recent line of research, the vascular centerline segmentation problem is approached in a more global fashion by finding the globally optimal subset of edges in a graph of potential centerlines (Türetken, Blum, González, Fua, 2010, González, Türetken, Fleuret, Fua, 2010, Türetken, Benmansour, Andres, Pfister, Fua, 2013). More specifically, the approach first involves building an overcomplete centerline segmentation by calculating the minimal paths that connect a large set of seed points, i.e. points that have a high probability of lying on the vasculature. Subsequently, the optimal subset of these centerlines is selected according to a cost function that incorporates image evidence and a prior on the presence of junctions. This is done subject to a set of constraints that impose connectedness and—if applicable—the tree-like topology of the resulting solution. Rempfler et al. (2015) extend this approach and make the probability of the presence of a junction depend on its geometric properties as well.

All these approaches use knowledge of the local appearance of blood vessels and possibly some knowledge about their global connectivity. We extend this and we leverage the available anatomical information inherent to many vascular systems to further improve the segmentation performance as we describe in the following.

Our approach performs the segmentation and anatomical labeling of the cerebral vasculature jointly so as to guarantee a result that is biologically plausible. This is achieved by taking into account both the image evidence and the anatomical knowledge about the vascular connectivity simultaneously using probabilistic classifiers that capture both appearance and geometry features, and impose learned connectivity rules.

Not only does this approach yield better results than state-of-the-art methods, such as Türetken et al. (2013), it is also generic and could easily be applied to other curvilinear structures.

This paper extends our earlier work (Robben et al., 2014). We present here an improved derivation for the objective function, which has both theoretical and practical advantages. The objective function has an extra term, taking the directionality of the edges into account. This speeds up the optimization, but more importantly, yields improved segmentation accuracy. Additionally, we propose and compare three different approaches to handling the labeling term introduced previously in Robben et al. (2014). Also, the label classifier uses different features. Finally, we also provide a more thorough experimental evaluation of the approach and its individual components. We propose a new segmentation quality metric that not only looks at overlap of the segmentation but also at its topological correctness. Using this metric, we demonstrate the advantage of the proposed method over existing ones.

Section snippets

Method

Starting from the original image (Fig. 2a), we first compute a directed graph GI, which is an overcomplete segmentation of the vasculature: it is assumed that it includes all the vessels in the image, but it may contain spurious branches that are not part of the vasculature (Fig. 2c). In a second step, we select a subgraph in GI and anatomically label its edges such that it most likely represents the true vasculature. This is done jointly, by optimizing a global objective function that captures

Results

We first evaluate the labeling and the segmentation performance of our algorithm separately, each against a state-of-the-art approach for the respective task, and then report our combined performance. All experiments are done with a leave-one-image-out cross-validation. We use 50 MRA images of the cerebral vasculature of healthy volunteers, originating from a publicly available dataset (Bullitt et al., 2005). The MRA images are acquired on a 3 T MR unit (Allegra, Siemens Medical Systems Inc.,

Discussion and conclusion

We first assessed the performance of anatomical labeling of ground truth centerlines (shown in Table B1). The differences between the three proposed objective functions ((26), (27) and 28) are small, with the third one performing slightly, but not significantly, better than the other two. In comparison with Bogunović et al. (2013), a state of art method for anatomical labeling of the cerebral vasculature, we tend to have a higher precision but a lower recall, resulting in an accuracy that is on

Acknowledgement

David Robben is supported by a Ph.D. fellowship of the Research Foundation - Flanders (FWO). The MRA brain images from healthy volunteers used in this paper were collected and made available by the CASILab at The University of North Carolina at Chapel Hill and were distributed by the MIDAS Data Server at Kitware Inc. We would also like to thank the authors of Bogunović et al. (2013) for sharing their centerline delineations. This work was supported by KU Leuven’s Concerted Research Action

References (42)

  • BogunovićH. et al.

    Anatomical labeling of the circle of willis using maximum a posteriori probability estimation

    IEEE Trans. Med. Imaging

    (2013)
  • BrismanJ.L. et al.

    Cerebral aneurysms

    N. Engl. J. Med.

    (2006)
  • BuelowT. et al.

    Point based methods for automatic bronchial tree matching and labelling

  • FeragenA. et al.

    A hierarchical scheme for geodesic anatomical labeling of airway trees

  • FrangiA. et al.

    Multiscale vessel enhancement filtering

  • GeurtsP. et al.

    Extremely randomized trees

    Mach. Learn.

    (2006)
  • van GijnJ. et al.

    Subarachnoid haemorrhage: diagnosis, causes and management

    Brain

    (2001)
  • van GinnekenB. et al.

    Robust segmentation and anatomical labeling of the airway tree from thoracic CT scans

  • GonzálezG. et al.

    Delineating trees in noisy 2D images and 3D image-stacks

    CVPR

    (2010)
  • GrahamM.

    Robust graph-theoretic methods for matching and labeling anatomical trees

    (2006)
  • GülsünM.A. et al.

    Robust vessel tree modeling

  • Cited by (0)

    View full text