The extraction of the centerlines of tubular objects in two and three-dimensional images is a part of many clinical image analysis tasks. One common approach to tubular object centerline extraction is based on intensity ridge traversal. In this paper, we evaluate the effects of initialization, noise, and singularities on intensity ridge traversal and present multiscale heuristics and optimal-scale measures that minimize these effects. Monte Carlo experiments using simulated and clinical data are used to quantify how these "dynamic-scale" enhancements address clinical needs regarding speed, accuracy, and automation. In particular, we show that dynamic-scale ridge traversal is insensitive to its initial parameter settings, operates with little additional computational overhead, tracks centerlines with subvoxel accuracy, passes branch points, and handles significant image noise. We also illustrate the capabilities of the method for medical applications involving a variety of tubular structures in clinical data from different organs, patients, and imaging modalities.

Vessel segmentation algorithms are the critical components of circulatory blood vessel analysis systems. We present a survey of vessel extraction techniques and algorithms. We put the various vessel extraction approaches and techniques in perspective by means of a classification of the existing research. While we have mainly targeted the extraction of blood vessels, neurosvascular structure in particular, we have also reviewed some of the segmentation methods for the tubular objects that show similar characteristics to vessels. We have divided vessel segmentation algorithms and techniques into six main categories: (1) pattern recognition techniques, (2) model-based approaches, (3) tracking-based approaches, (4) artificial intelligence-based approaches, (5) neural network-based approaches, and (6) miscellaneous tube-like object detection approaches. Some of these categories are further divided into sub- categories. We have also created tables to compare the papers in each category against such criteria as dimensionality, input type, pre-processing, user interaction, and result type.

In this paper, we propose an innovative approach to the segmentation of tubular or vessel-like structures which combines all the benefits of minimal path techniques (global minimizers, fast computation, powerful incorporation of user input) with some of the benefits of active surface techniques (representation of a full 3D tubular surface rather than a just curve). The key is to represent the trajectory of the vessel not as a 3D curve but to go up a dimension and represent the entire vessel as a 4D curve, where each 4D point represents a 3D sphere (three coordinates for the center point and one for the radius). The 3D vessel structure is then obtained as the envelope of the family of spheres traversed along this 4D curve. Because the 3D surface is simply a curve in 4D, we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied end-points in order to reconstruct vessels from noisy or low contrast 3D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3D minimal path techniques, however, we are able to represent the full vessel surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a vessel’s “central curve”, which is obtained by tracing the center points of the family of 3D spheres rather than its envelope. We demonstrate the utility of this approach on 2D images of roads as well as both 2D and 3D MR angiography and CT images. 1.

Abstract. In this paper we propose a Particle Filter-based propagation approach for the segmentation of vascular structures in 3D volumes. Because of pathologies and inhomogeneities, many deterministic methods fail to segment certain types of vessel. Statistical methods represent the solution using a probability density function (pdf). This pdf does not only indicate the best possible solution, but also valuable information about the solution’s variance. Particle Filters are used to learn the variations of direction and appearance of the vessel as the segmentation goes. These variations are used in turn in the particle filters framework to control the perturbations introduced in the Sampling Importance Resampling step (SIR). For the segmentation itself, successive planes of the vessel are modeled as states of a Particle Filter. Such states consist of the orientation, position and appearance (in statistical terms) of the vessel. The shape of the vessel and subsequently the particles pdf are recovered using globally active contours, implemented using circular shortest paths by branch and bound [1] that guarantees the global optimal solution. Promising results on the segmentation of coronary arteries demonstrate the potential of the proposed approach. 1

Precise segmentation of three-dimensional (3D) magnetic resonance angiography (MRA) images can be a very useful computer aided diagnosis (CAD) tool for clinical routines. Level sets based evolution schemes, which have been shown to be effective and easy to implement for many segmentation applications, are being applied to MRA data sets. In this paper, we present a segmentation scheme for accurately extracting vasculature from MRA images. Our proposed algorithm models capillary action and derives a capillary active contour for segmentation of thin vessels. The algorithm is implemented using the level set method and has been applied successfully on real 3D MRA images. Compared with other state-of-the-art MRA segmentation algorithms, experiments show that our method facilitates more accurate segmentation of thin blood vessels.

The Hamilton–Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton–Jacobi method.

In this paper we propose a Particle Filter-based approach for the segmentation of coronary arteries. To this end, successive planes of the vessel are modeled as unknown states of a sequential process. Such states consist of the orientation, position, shape model and appearance (in statistical terms) of the vessel that are recovered in an incremental fashion, using a sequential Bayesian filter (Particle Filter). In order to account for bifurcations and branchings, we consider a Monte Carlo sampling rule that propagates in parallel multiple hypotheses.

In this paper, we use a level set based segmentation algorithm to extract the vascular tree from Phase Contrast Magnetic Resonance Angiography, “PCMRA”. Classification model finds an optimal partition of homogeneous classes with regular interfaces. Regions and their interfaces are represented by level set functions. The algorithm initializes level sets in each image slice using automatic seed initialization and then iteratively, each level set approaches the steady state and contains the vessel or non-vessel area. The results are validated using a phantom that simulates the “PCMRA”. The approach is fast and accurate. Results on various cases demonstrate the accuracy of the approach.

Abstract. In this paper, we use a level set based segmentation algorithm to extract the vascular tree from Magnetic Resonance Angiography (MRA) data sets. The classification approach depends on initializing the level sets in the 3D volume and, the level sets evolve with time to yield the blood vessels. This work introduces a high quality initialization for the level set functions, allowing extraction of the blood vessels in 3D and elimination of non-vessel tissues. A comparison between the 2D and 3D segmentation approaches is made. The results are validated using a phantom that simulates the MRA data and demonstrate good accuracy. 1.

This paper presents a new method to extract a network of vessels centerlines from a medical image. The network is composed of local geodesics over a four-dimensional space that includes local orientation and scale. These shortest paths follow closely the center of tubular structures and can deal robustly with crossings over the image plane. The vessel network is grown by an iterative algorithm that distributes seed points according to a geodesic saliency field. Numerical experiments on a database of synthetic and medical images show the superiority of our approach with respect to several methods based on shortest paths extractions. With a minimum of user interaction, it allows to compute a complex network of vessels over noisy medical. 1