Computing Center-Lines: An Application of Vector Field Topology
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Curve-skeletons of 3-D objects are medial axes shrunk to a single line. There are several applications for curve-skeletons. For example, animation of 3-D objects, such as an animal or a human, as well as planning of flight paths for virtual colonoscopy. Other applications are the extraction of center lines within blood vessels where center lines are used to quantitatively measure vessel length, vessel diameter, and angles between vessels. The described method computes curve-skeletons based on a vector field that is orthogonal to the object's boundary surface. A topological analysis of this field then yields the center lines of the curve-skeletons. In contrast to previous methods, the vector field does not need to be computed for every sampled point of the entire volume. Instead, the vector field is determined only on the sample points on the boundary surface of the objects. Since most of the computational time was spent on calculating the force field in previous methods, the proposed approach requires significantly less time compared to previous vector-based techniques while still achieving a better accuracy and robustness compared to methods based on Voronoi tessellations.
(2009). Computing Center-Lines: An Application of Vector Field Topology. Topology-Based Methods in Visualization II, 177-190.