3D joint Markov-Gibbs model for segmenting the blood vessels from MRA

New techniques for more accurate segmentation of a 3D cerebrovascular system from time-of-flight (TOF) magnetic resonance angiography (MRA) data are proposed. In this paper, we describe TOF-MRA images and desired maps of regions (blood vessels and the other brain tissues) by a joint Markov-Gibbs random field model (MGRF) of independent image signals and interdependent region labels but focus on most accurate model identification. To better specify region borders, each empirical distribution of signals is precisely approximated by a Linear Combination of Discrete Gaussians (LCDG) with positive and negative components. We modify a conventional Expectation-Maximization (EM) algorithm to deal with the LCDG and develop a sequential EM-based technique to get an initial LCDG-approximation for the modified EM algorithm. The initial segmentation based on the LCDG-models is then iteratively refined using a GMRF model with analytically estimated potentials. 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.