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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 grey and white brain matter. We show that due to a multi-modal 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, and we modify the conventional Expectation-Maximization (EM) algorithm to deal with the LCDG. To validate the accuracy of our algorithm, a special 3D geometrical phantom motivated by statistical analysis of the MRA-TOF data is designed. Experiments with both the phantom and 50 real data sets confirm high accuracy of the proposed approach.

Automatic Cerebrovascular Segmentation by Accurate Probabilistic Modeling of TOF-MRA Images