How to apply 2D active contours (snakes) in 3D image?

Hi, I am trying to apply a snake method on a 3D image with no sucess. To my understanding, MATLAB's "activecontours" can be applied to 3D images but it seems that it fits a surface (balloon) into an object, instead of a single contour (snake). Or at least it seems to repeat the seed contour slice by slice, instead of fitting a single countour into a 3D object, because the end result is the whole 3D image segmented. I am looking for an active contour that has 3D awareness, as suggested by the following figure:

If the seed contour is the blue contour (slightly in perspective as to see it is a contour), I want the final snake to be the green one, as it fits the closest and easiest edge, instead of the red one, which would happen if I simply applied a 2D snake onto a slice of the 3D image coplanar with the seed contour. Thanks for your time!