A non-invasive alternative to arterial blood sampling for the generation of a blood input function for brain positron emission tomography (PET) studies is presented. The method aims to extract the dimensions of the blood vessel directly from PET images and to simultaneously correct the radioactivity concentration for partial volume and spillover. This involves simulation of the tomographic imaging process to generate images of different blood vessel and background geometries and selecting the one that best fits, in a least-squares sense, the acquired PET image. A phantom experiment was conducted to validate the method which was then applied to eight subjects injected with 6-[18F]fluoro-L-DOPA and one subject injected with [11C]CO-labelled red blood cells. In the phantom study, the diameter of syringes filled with an 11C solution and inserted into a water-filled cylinder were estimated with an accuracy of half a pixel (1 mm). The radioactivity concentration was recovered to 100 +/- 4% in the 8.7 mm diameter syringe, the one that most closely approximated the superior sagittal sinus. In the human studies, the method systematically overestimated the calibre of the superior sagittal sinus by 2-3 mm compared to measurements made in magnetic resonance venograms on the same subjects. Sources of discrepancies related to the anatomy of the blood vessel were found not to be fundamental limitations to the applicability of the method to human subjects. This method has the potential to provide accurate quantification of blood radioactivity concentration from PET images without the need for blood samples, corrections for delay and dispersion, co-registered anatomical images, or manually defined regions of interest.