Representing a 3D shape by a set of one-dimensional curves, that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several applications such as object matching and retrieval, virtual endoscopy, character animation and morphing, medical image analysis of tubular structures, and collision detection.

In this project, we propose a fast, automatic, and robust variational framework for computing continuous, sub-voxel accurate curve skeletons from volumetric objects that are represented by closed manifolds. A reference point inside the object is selected automatically and is considered a point source that transmits two wave fronts of different energies. The first front ( beta-front) divides the object into a set of adjacent clusters from which the salient topological nodes of the shape are computed. The second front (alpha-front) constructs a monotonic shock-free field from which curve skeletons are computed by tracking them from the shape salient nodes until the point source is reached.

Unlike the state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying the skeleton junction points, employs a new energy that does not form medial surfaces, and finally starts curve skeletons from those nodes that correspond to the most prominent parts of the shape, and hence less sensitive to noise. The accuracy and robustness of the proposed framework are validated both quantitatively and qualitatively against competing techniques as well as a database of 3D objects.

Results

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Curve Skeletons of 3D Objects	Visual Comparative Study	Quantitative Comparative Study	Centerlines of 2D Shapes

Curve Skeletons of 3D Objects
 

Curve Skeletons are Superimposed on the Alpha Front Iso-surfaces