Fast, accurate unsupervised segmentation of 3D magnetic resonance angiography

Accurate automatic extraction of a 3D cerebrovascular system from images obtained by time-of-flight (TOF) or phase-contrast (PC) magnetic resonance angiography (MRA) is a challenging segmentation problem due to small size objects of interest (blood vessels) in each 2D MRA slice and complex surrounding anatomical structures, e.g. fat, bones, or gray and white brain matter. We show that due to a multimodal nature of MRA data, blood vessels can be accurately separated from background in each slice by a voxel-wise classification based on precisely identified probability models of voxel intensities. To identify the models, an empirical marginal probability distribution of intensities is closely approximated with a linear combination of discrete Gaussians (LCDG) with alternate signs by using our previous EM-based techniques for precise LCG-approximation adapted to deal with the LCDGs. High accuracy of the proposed approach is experimentally validated on 85 real MRA datasets (50 TOF and 35 PC) as well as synthetic MRA data for special 3D geometrical phantoms of known shapes.