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Mathematical Problems in Engineering
Volume 2018, Article ID 6131325, 8 pages
Research Article

Vascular Extraction Using MRA Statistics and Gradient Information

1College of Information Science and Technology, Beijing Normal University, Beijing 100875, China
2Beijing Key Laboratory of Digital Preservation and Virtual Reality for Cultural Heritage, Beijing, China

Correspondence should be addressed to Pengfei Xu; nc.ude.unb@fpux

Received 21 November 2017; Revised 4 January 2018; Accepted 10 January 2018; Published 11 February 2018

Academic Editor: Seungik Baek

Copyright © 2018 Shifeng Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Brain vessel segmentation is a fundamental component of cerebral disease screening systems. However, detecting vessels is still a challenging task owing to their complex appearance and thinning geometry as well as the contrast decrease from the root of the vessel to its thin branches. We present a method for segmentation of the vasculature in Magnetic Resonance Angiography (MRA) images. First, we apply volume projection, 2D segmentation, and back-projection procedures for first stage of background subtraction and vessel reservation. Those labeled as background or vessel voxels are excluded from consideration in later computation. Second, stochastic expectation maximization algorithm (SEM) is used to estimate the probability density function (PDF) of the remaining voxels, which are assumed to be mixture of one Rayleigh and two Gaussian distributions. These voxels can then be classified into background, middle region, or vascular structure. Third, we adapt the -means method which is based on the gradient of remaining voxels to effectively detect true positives around boundaries of vessels. Experimental results on clinical cerebral data demonstrate that using gradient information as a further step improves the mixture model based segmentation of cerebral vasculature, in particular segmentation of the low contrast vasculature.