Magnetic resonance diffusion tensor imaging (DTI) provides information about fiber local directions in brain white matter. This paper addresses inference of the connectivity induced by fascicles made up of numerous fibers from such diffusion data. The usual fascicle tracking idea, which consists of following locally the direction of highest diffusion, is prone to erroneous forks because of problems induced by fiber crossing. In this paper, this difficulty is partly overcomed by the use of a priori knowledge of the low curvature of most of the fascicles. This knowledge is embedded in a model of the bending energy of a spaghetti plate representation of the white matter used to compute a regularized fascicle direction map. A new tracking algorithm is then proposed to highlight putative fascicle trajectories from this direction map. This algorithm takes into account potential fan shaped junctions between fascicles. A study of the tracking behavior according to the influence given to the a priori knowledge is proposed and concrete tracking results obtained with in vivo human brain data are illustrated. These results include putative trajectories of some pyramidal, commissural, and various association fibers.