Regularization of DT-MRI using 3D median filtering methods

DT-MRI (diffusion tensor magnetic resonance imaging) tractography is a method to determine the architecture of axonal fibers in the central nervous system by computing the direction of the principal eigenvectors obtained from tensor matrix, which is different from the conventional isotropic MRI. Tractography based on DT-MRI is known to need many computations and is highly sensitive to noise. Hence, adequate regularization methods, such as image processing techniques, are in demand. Among many regularization methods we are interested in the median filtering method. In this paper, we extended two-dimensional median filters already developed to three-dimensional median filters. We compared four median filtering methods which are two-dimensional simple median method (SM2D), two-dimensional successive Fermat method (SF2D), three-dimensional simple median method (SM3D), and three-dimensional successive Fermat method (SF3D). Three kinds of synthetic data with different altitude angles from axial slices and one kind of human data from MR scanner are considered for numerical implementation by the four filtering methods.