I imagine you are free to define "centre" largely as you please,
though there may well be the constaint that the locus of centres
for your artery should be continuous if the locus of contours is
One reasonable definition would be the centre of mass. I strongly
suspect it has the continuity property, though I lack the linguistic
talents to explain why in a pithy one-liner.
As for the fastest algorithms, this will depend almost entirely on
the manner in which the contour is described. For all I know, you
may be relatively free to choose that, too.