This paper presents a method for the detection, representation and visualisation of the cerebral vascular tree and its application to magnetic resonance angiography (MRA) images. The detection method is an iterative tracking of the vessel centreline with subvoxel accuracy and precise orientation estimation. This tracking algorithm deals with forks. Centrelines of the vessels are modelled by second-order B-spline. This method is used to obtain a high-level description of the whole vascular network. Applications to real angiographic data are presented. An MRA sequence has been designed, and a global segmentation of the whole vascular tree is realised in three steps. Applications of this work are accurate 3D representation of the vessel centreline and of the vascular tree, and visualisation. The tracking process is also successfully applied to 3D contrast enhanced MR digital subtracted angiography (3D-CE-MRA) of the inferior member vessels. In addition, detection of artery stenosis for routine clinical use is possible due to the high precision of the tracking algorithm.