3D tunnel path, best fit

Hello,

I have a triangulated surface mesh representing a tunnel in 3D space. What I would like to estimate is the 3D path that proceeds through the "center" of the tunnel's cross sections.

This tunnel is always at least 10 times longer than the diameter, but it may bend in 3D slightly: enough that a simple cylindrical least-squares fitting is not valid. I know what the ideal tunnel diameter should be overall, but due to local defects in the drilling/creation of the tunnel there are some deviations in the diameters (~10-20% diameter).

I had the idea of starting at a tunnel aperture and marching a short sample distance along an estimated axis, using a cutting plane at that sample point to find a local cross section, and updating the centroid location iteratively. But I think this would be highly susceptible to noise.

Any other suggestions?

Thank you!