—A new method is introduced for joining vessel segments together to form a vessel graph. Using a reference image set from the Sunderland Eye Infirmary, we analysed the retinal bifurcation geometry, to define measurements for the geometrical junction features. These distinctive measurements are employed to resolve the junctions. Self organized feature maps (SOFM) are used to “learn” cost functions for forming bifurcation and bridge forms. The system joins segments depending on their “projective intersections” and the SOFM cost functions. The system includes algorithms to handle overlapping and parallel segments. Transferring the vascular network to a vascular graph provides an opportunity to extract more information and to calculate features that have been not previously calculated, by providing new measurements from graph theory.