The objective is to extract the most plausible graph of 2D vascular branches (e.g. with respect to some basic vessel features) or, in other words, to find the best pairing of vascular segments forming these branches. The assumption here is that a previous detection has been carried out which provides the vessel centerlines. The method, based on sparse to dense description, has been designed in order to eliminate irrelevant lines and to extract the most important branches. The key feature of the method is the use of data fusion concepts in a simple but efficient way, capable to later integrate possibilistic or fuzzy decisions. It makes use of local fusion decision at each node (vessel forking, crossing or ending), based on intensity, continuity and shape properties. Several criteria have been explored with hierarchically structured features. A global fusion allows multiple optimal paths to be set and further merged in order to derive a final graph. Local and global fusions are applied by traversing the vessel network form the extremities to the root and vice versa. Segments and branches are defined as objects for any further selection, manipulation and measurements. This method can be used both in pre-operative and intra-operative situations.