Robust centerline extraction framework using level sets

In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (Ps) that transmits a wave front that evolves over time and traverses the object domain. The front propagates at each object point with a speed that is proportional to its Euclidean distance from the boundary. The motion of the front is governed by a nonlinear partial differential equation whose solution is computed efficiently using level set methods. Initially, the P_S transmits a moderate speed wave to explore the object domain and extract its topological information such as merging and extreme points. Then, it transmits a new front that is much faster at centerline points than non central ones. As a consequence, centerlines intersect the propagating fronts at those points of maximum positive curvature. Centerlines are computed by tracking them, starting from each topological point until the Ps is reached, by solving an ordinary differential equation using an efficient numerical scheme. The proposed method is computationally inexpensive, handles efficiently objects with complex topology, and computes centerlines that are centered, connected, one point thick, and less sensitive to boundary noise. In addition, the extracted paths form a tree graph without additional cost. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several 2D and 3D shapes.