if "seconds" is the right answer, you can try for example :
M. Hernández Hoyos, A. Anwander, M. Orkisz, J. P. Roux, P. Douek, and I. E. Magnin, "A deformable vessel model with single point initialization for segmentation, quantification and visualization of blood vessels in 3D MRA", MICCAI, vol. 13, no. 9, Pittsburgh, USA, pp. 735-745, 2000.
You can try tubetk, it's a free software available at: http://public.kitware.com/Wiki/TubeTK where you can extract the centerlines rapidly adding at least one point per branch. It's based on ridge detection, and works fine for us to extract coronaries from CTA, or brain vessels in MRA.
The processing time should be OK. However, only now I realize the particularity of the imaging modality you use : in T1w MRI there is no enhancement of the arterial lumen, is there ? The work I cited used dynamic contrast-enhanced and subtracted MR angiography, where the lumen appeared bright on much darker background. That's why it was quite natural to use inertia moments.
In T1w MRI, the lumen appears darker than the vessel wall region, because it uses blood suppression techniques, but they are not contrast enhanced. So far, I have tried Frangi filter in Matlab, which provides a measure of vesselness as output. Afterwards, I threshold it to obtain a binary image, which is then used for centerline detection. The problem with this approach is that it enhances other structures that are not vessels, but they may appear as vessels due to the noise in the image.
However, I still have not tried TubeTK. I will give it a shot.
You could try VMTK (http://www.vmtk.org), the vascular modeling toolkit, implemented in C++ and with Python wrappings. There you can find frangi and veselness filters, and of course centerline extraction algorithms. There is also a wide and active users list in which you will probably find specific answers to your question.
If you want you can also check this paper: Computational Geometry for Patient-Specific Reconstruction and Meshing of Blood Vessels From MR and CT Angiography, by Luca Antiga (the guy that implemented the vmtk toolkit).