An innovative 3D multi-branch tubular structure and centerline extraction method is proposed in this paper. In contrast to classical minimal path techniques that can only detect a single curve between two pre-defined initial points, this method propagates outward from only one initial seed point to detect 3D multi-branch tubular surfaces and centerlines simultaneously. First, instead of only representing the trajectory of a tubular structure as a 3D curve, the surface of the entire structure is represented as a 4D curve along which every point represents a 3D sphere inside the tubular structure. Then, from any given sphere inside the tubular structure, a novel 4D iterative key point searching scheme is applied, in which the minimal action map and the Euclidean length map are calculated with a 4D freezing fast marching evolution. A set of 4D key points is obtained during the front propagation process. Finally, by sliding back from each key point to the previous one via the minimal action map until all the key points are visited, we are able to fully obtain global minimizing multi-branch tubular surfaces. An additional immediate benefit of this method is a natural notion of a multi-branch tube's "central curve" by taking only the first three spatial coordinates of the detected 4D multi-branch curve. Experimental results on 2D/3D medical vascular images illustrate the benefits of this method.