Soft tissue contrast on CT is not great, so in general it is hard to constraint region growing. However, this is a special case: the segmented object’s shape is smooth and it is only connected to similar-intensity regions through thin canals, so it is possible to prevent leaking via intensity and spatial connectivity and smoothness constraints implemented in “Local threshold” effect in Segment editor. Once the spinal canal is segmented, centerline extraction is fully automatic. See this video for step-by-step instructions:
What is the clinical application? If spinal canal centerline is only a surrogate and you are actually interested in measuring curvature and torsion of the spinal column then you may consider placing markup points on the facet joints (it should be very quick on volume rendering of bones) and computing the angles from these points.