Vascular segmentation of phase contrast magnetic resonance angiograms based on statistical mixture modeling and local phase coherence

In this paper, we present an approach to segmenting the brain vasculature in phase contrast magnetic resonance angiography (PC-MRA). According to our prior work, we can describe the overall probability density function of a PC-MRA speed image as either a Maxwell-uniform (MU) or Maxwell-Gaussian-uniform (MGU) mixture model. An automatic mechanism based on Kullback-Leibler divergence is proposed for selecting between the MGU and MU models given a speed image volume. A coherence measure, namely local phase coherence (LPC), which incorporates information about the spatial relationships between neighboring flow vectors, is defined and shown to be more robust to noise than previously described coherence measures. A statistical measure from the speed images and the LPC measure from the phase images are combined in a probabilistic framework, based on the maximum a posteriori method and Markov random fields, to estimate the posterior probabilities of vessel and background for classification. It is shown that segmentation based on both measures gives a more accurate segmentation than using either speed or flow coherence information alone. The proposed method is tested on synthetic, flow phantom and clinical datasets. The results show that the method can segment normal vessels and vascular regions with relatively low flow rate and low signal-to-noise ratio, e.g., aneurysms and veins.