# Cerebrovascular segmentation from TOF using stochastic models.Med Image Anal. 2006 Feb; 10(1):2-18.MI

In this paper, we present an automatic statistical approach for extracting 3D blood vessels from time-of-flight (TOF) magnetic resonance angiography (MRA) data. The voxels of the dataset are classified as either blood vessels or background noise. The observed volume data is modeled by two stochastic processes. The low level process characterizes the intensity distribution of the data, while the high level process characterizes their statistical dependence among neighboring voxels. The low level process of the background signal is modeled by a finite mixture of one Rayleigh and two normal distributions, while the blood vessels are modeled by one normal distribution. The parameters of the low level process are estimated using the expectation maximization (EM) algorithm. Since the convergence of the EM is sensitive to the initial estimate of the model parameters, an automatic method for parameter initialization, based on histogram analysis, is provided. To improve the quality of segmentation achieved by the proposed low level model especially in the regions of significantly vascular signal loss, the high level process is modeled as a Markov random field (MRF). Since MRF is sensitive to edges and the intracranial vessels represent roughly 5% of the intracranial volume, 2D MRF will destroy most of the small and medium sized vessels. Therefore, to reduce this limitation, we employed 3D MRF, whose parameters are estimated using the maximum pseudo likelihood estimator (MPLE), which converges to the true likelihood under large lattice. Our proposed model exhibits a good fit to the clinical data and is extensively tested on different synthetic vessel phantoms and several 2D/3D TOF datasets acquired from two different MRI scanners. Experimental results showed that the proposed model provides good quality of segmentation and is capable of delineating vessels down to 3 voxel diameters.

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*Medical Image Analysis,*vol. 10, no. 1, 2006, pp. 2-18.

*Med Image Anal*. 2006;10(1):2-18.

*Medical Image Analysis*,

*10*(1), 2-18.

*Med Image Anal.*2006;10(1):2-18. PubMed PMID: 15893953.