The precise three-dimensional (3-D) segmentation of cerebral vessels from magnetic resonance angiography (MRA) images is essential for the detection of cerebrovascular diseases (e.g., occlusion, aneurysm). The complex 3-D structure of cerebral vessels and the low contrast of thin vessels in MRA images make precise segmentation difficult. We present a fast, fully automatic segmentation algorithm based on statistical model analysis and improved curve evolution for extracting the 3-D cerebral vessels from a time-of-flight (TOF) MRA dataset. Cerebral vessels and other tissue (brain tissue, CSF, and bone) in TOF MRA dataset are modeled by Gaussian distribution and combination of Rayleigh with several Gaussian distributions separately. The region distribution combined with gradient information is used in edge-strength of curve evolution as one novel mode. This edge-strength function is able to determine the boundary of thin vessels with low contrast around brain tissue accurately and robustly. Moreover, a fast level set method is developed to implement the curve evolution to assure high efficiency of the cerebrovascular segmentation. Quantitative comparisons with 10 sets of manual segmentation results showed that the average volume sensitivity, the average branch sensitivity, and average mean absolute distance error are 93.6%, 95.98%, and 0.333 mm, respectively. By applying the algorithm to 200 clinical datasets from three hospitals, it is demonstrated that the proposed algorithm can provide good quality segmentation capable of extracting a vessel with a one-voxel diameter in less than 2 min. Its accuracy and speed make this novel algorithm more suitable for a clinical computer-aided diagnosis system. 4 The principle of skeleton-based techniques is the segmentation and reconstruction of vessels by first detecting the centerlines of the vessels from cross-sectional slices. The centerlines can be generated by vessel modeling methods. Several methods have been developed based on this principle. [5] [6] [7] [8] [9] On the other hand, nonskeleton-based techniques extract the vessels in 3-D directly. Non-skeleton-based segmentation techniques have received considerable attention. Wilson et al. , Chung et al. 11, 12 , El-Baz et al. 13,14 , and Hassouna et al. 15 proposed segmentation methods for cerebral vessels based on statistical models using an MRA dataset. The curve evolution theory and level set method have been applied to images to derive object boundaries. Yu et al. , Farag et al. , Yan et al. , Deschamps et al. , and Manniesing et al. 20 developed vessel segmentation methods based on geometric deformable models (level sets). Masutani et al. 21 proposed the segmentation of vessel-like structures using mathematical morphology. In addition, some hybrid methods have been presented. Zana et al. 22 combined morphology and curvature evaluation to segment vessel-like structures. Flasque et al. 23 proposed a method for the detection, representation, and visualization of a cerebral vascular tree using MRA images. The vascular tree is built by iteratively tracking the vessel centerlines using candidate voxels, which is achieved by intensity correction, diffusion filtering, and region growing. Passat et al. 24 introduced an atlas of the whole head to help to segment brain vessels from MRA images using a topology-preserving region-growing algorithm. These existing vascular segmentation methods have at least one of the following limitations: (1) Gaussian distribution is generally assumed to express the probability distribution of the tissues in MRA images. However, this assumption is inconsistent with the truth and results in an error between the proposed model and the clinical data. (2) The maximum intensity gradient, as the only criterion, is frequently employed to determine vascular boundaries, but the gradient magnitudes are not sufficiently high in the boundaries of thin vessels with low contrast. (3) The regulation of parameters in geometric deformable models is difficult or not applicable which greatly influences the segmentation results. (4) User interactions are required to determine the seed region, or the starting and ending points of vessels. (5) The method is time consuming. (6) An evaluation with a limited number of datasets barely proves robustness of the algorithm. Therefore, the development of a fast and fully automatic cerebrovascular segmentation method that uses volumetric MRA data was the prime motivation behind our work. In this paper, we present an algorithm for segmenting a cerebrovascular tree from a time-of-flight (TOF) MRA dataset based on a statistical model analysis and curve evolution method. TOF MRA datasets was modeled by a finite mixture of one Rayleigh and several Gaussian distributions. Cerebral vessels distribution and other tissue (brain tissue, cerebrospinal fluid (CSF), and bone) distribution could be estimated using expectation maximization (EM) algorithm. Then the statistical distribution is integrated with gradient information to form a novel edge-strength for curve evolution. Such curve evolution method embedding the edge information is able to determine the boundary of vessels, particularly thin vessel, more accurately and robustly. Moreover, the curve evolution is implemented by a fast level set so as to able to segment the cerebrovascular structure in a short time. A flow chart for the algorithm is shown in Figure 1 . The database used consisted of 200 TOF MRA studies from three different MRI scanners, including 142 normal cases and 58 abnormal cases (occlusions, unruptured aneurysm). (1) 110 of these MRA studies were performed using a GE Signa Series 1.5 T MRI scanner (TR=29, TE=6.9, flip angle = 20) at the Kizawa Hospital (KH), Japan. The volume was 256×256×80 voxels and the voxel size 0.47×0.47×1.5 mm flip angle = 20) at Gifu University Hospital (GUH), Japan. The volume was 256×256×50 with a spatial resolution of 0.625 × 0.625 × 1.2 mm 3 . All of the acquired MRA data were subsequently converted to isotropic volume data by using tri-linear interpolation. The size of the converted 3-D volume data was 400×400×200 voxels, and the size of each voxel was 0.5×0.5× 0.5 mm 3 . We tested our new segmentation method on the obtained isotropic volume dataset. In addition, 10 sets of volumetric MRA images were selected from the database at random (five sets from KH, four sets from GHSH, one set from GUH), two of which are abnormal (one occlusions, one unruptured aneurysm). The cerebrovascular structures were manually segmented from these 10 datasets under the supervision of two experienced radiologists. The manual segmentations, which were voxel-by-voxel selections, were treated as the ground truth to determine segmentation precision and used for a statistical model analysis of blood vessels. In this section, we show how the statistical model for TOF MRA was derived for the various brain tissues in MRA images and estimate their parameters using the fast EM algorithm (FEM) algorithm. A statistical classification-based method of segmentation for medical images has been proposed 25 . The basic idea behind this method is an assumption that the intensity of a homogeneous region (one anatomical structure) in an image submits to a single statistical model distribution and that the intensity distribution of all the pixels or voxels can be approximated by a finite mixture of statistical model distributions. A statistical model may also be a linear combination of several appropriate probability distribution functions based on the physical specialty of each anatomical structure in a specific imaging modality. It may automatically be determined whether a voxel is an object or background based on the statistical probability of the voxel. This method can be summarized as follows: (1) construct a statistical model with a finite mixture of probability distributions, (2) estimate the parameters for the statistical model, (3) obtain the probability distributions for the objects and background, respectively, and (4) select global threshold values based on the MAP classification rules. A statistical approach-based cerebrovascular segmentation method using MRA images was first developed by Wilson and Noble. 10 In their study, an intensity frequency histogram of a TOF MRA dataset had the property of an adjacent bimodal shape in a low-intensity region and a much lower frequency expansion over a high-intensity region. The lowest intensity region corresponded mainly to CSF (surrounding the brain tissue), bone, and the background air. The next lowest intensity region corresponded to brain tissues (both gray matter and white matter) and parts of the eyes. The highest intensity region consisted of subcutaneous fat and cerebral vessels. Two Gaussian distributions were chosen to model the bimodal shape in the lowest intensity regions respectively while a uniform distribution was used to depict the  distribution of the vessels. El-Baz et al. 14 adopted an adaptive linear combination of a derived model and a number of dominant and subordinate discrete Gaussians distributions rather than a mixture of just three pre-selected Gaussian and uniform distributions to approximate the intensity distribution of voxels in MRA datasets. In the study by Hassouna et al. 15 , one Rayleigh and two Gaussian distributions were used to model CSF and the brain tissue region. One Gaussian distribution corresponded to blood vessels. However, their statistical model for TOF MRA datasets was inadequate for our datasets. The above methods all rescaled the intensity values of the MRA voxels to the range [0,255] which results in the lost of detail information. The intensity value of each voxel in our datasets was a 16-bit positive integer without any rescaling, ensuring accurate intensity information. The plots of the normalized intensity frequency histograms, without smoothing, of three TOF MRA datasets randomly selected from different MRI scanners are shown in Figure 2 (solid line). The normalized intensity frequency histograms for these three datasets have the same shape, two distinct peaks with a long tail over a high-intensity region. We need to construct a further general statistical model suitable for TOF MRA datasets from various MRI scanners. For cerebrovascular segmentation, blood vessels are the object while the background class includes CSF, bone, the background air, brain tissue, and parts of the eyes. The signal from blood vessels is dependent on flow rather than chemical structure in TOF MRA images. Blood vessels are generally regarded as circular vessels, and the intensity characteristics of the vessel voxels are assumed to exhibit a laminar flow pattern for which the vessel intensity is regarded as a uniform distribution. This assumption, however, neglects blood viscosity, turbulence, and changes in the shape of vessels caused by cerebrovascular disease. The intractability of these factors makes it difficult to construct a single accurate statistical model for the intensity distribution of cerebral vessels in MRA images. To acquire a more reasonable statistical model for cerebral vessels, we considered the normalized intensity frequency histograms of 10 sets of manually segmented blood vessels from MRA in turn (see Fig. 3 ). The results predicted that a Gaussian class with large variance could be used to describe a statistical model of cerebral vessels in TOF MRA images. Rayleigh distribution provides a more accurate fit than Gaussian distribution for the lowest intensity region peak of a normalized intensity frequency histogram (peak1). 15 The peak in the next lowest intensity region (peak2) can be Fig. 2 . The normalized intensity frequency histograms, without smoothing, of three TOF MRA datasets from a KH, b GHSH, c GUH, respectively (solid curve); and the fitting results by using the proposed statistical model (dashed curve). GAO ET AL. expressed by a Gaussian distribution. The region between the first peak and second peak in a normalized intensity frequency histogram has an irregular shape, making it difficult to adopt a single probability distribution function to approximate that part of the observed histogram. A linear combination of several Gaussian distributions is able to deal with the problem by adjusting their mean and standard deviation. The total probability density function for the intensity in TOF MRA images is expressed as follows,
For instance, Gao et al. REF introduced a fast automatic segmentation algorithm based on statistical model and also improved curve evolution for extraction the 3D cerebral vessels from MRA dataset.
A Fast and Fully Automatic Method for Cerebrovascular Segmentation on Time-of-Flight (TOF) MRA Image
Journal of Digital Imaging
Journal of Digital Imaging
Computer Science Medicine