Adaptive smoothing of MR brain images by 3D geometry-driven diffusion

The paper deals with the iterative three-dimensional (3D) smoothing of tomograms acquired by fast Magnetic Resonance (MR) imaging methods. The smoothing method explored, which is aimed basically at the improvement of 3D visualization quality, uses the physical concept of geometry-driven diffusion with a variable conductance function, based on a specific measure of the 3D neighborhood homogeneity. A novel stopping criterion is proposed for iterative 3D diffusion processing. A study of the transition from 2D to 3D algorithms is carried out. The main structure of the program implementation of the smoothing algorithms developed is described. Three smoothing/filtering methods, aimed at the improvement of 3D visualization of MR tomograms of the brain, are quantitatively and visually compared using real 3D MR images. The results of computer simulations with 3D smoothing, segmentation and visualization are presented and discussed.