A curve skeleton is a thinned-line representation of a 3D object, which is useful in many visualization tasks. There are many skeleton-extraction methods in the literature, which can be categorized as being either a volumetric approach or a geometric approach.

The proposed algorithm is developed using a vector-field-based method (volumetric approach). Our method creates a vector field from the pseudo-normal vector, which requires less computation time than a typical repulsive force function, while still providing a correct skeleton. Our algorithm consists of two main steps: vector-field creation and skeleton extraction. We develop a novel algorithm for both steps.

1. • For vector field, we proposed the pseudo-normal vector field algorithm. This algorithm estimates a field inside a 3D object created by typical repulsive force field. This algorithm firstly creates a set of normal vectors on the boundary of 3D object, then propagates those normal vectors to the center of the 3D object. In contrast with typical method, which uses a large set of boundary voxels in a calculation of each vector, our method uses only an individual voxel in each calculation. The computation time of our method is significantly less than the one of repulsive force field.
   

2. •  Skeleton-growing algorithm is developed to extract a curve-skeleton from the vector field created in previous step. This algorithms is based on the assumption that the curve-skeleton extracted by connecting critical points in the vector field captures only the central part of the 3D object. Therefore, the proposed algorithm detects a set of high-curvature boundary voxels to identify the high-curvature areas, which should be the end-part of the 3D object. Then, the method detects skeleton-segments and critical points near that high-curvature areas. Our algorithm then uses the detected critical points as seed points to grow a curve-skeleton. All parameters in this algorithm is calculated based on each 3D object without users‘ intervention, which makes this algorithm is easy-to-use by any users. The resulting curve-skeleton is clean and topology-preserving which is suitable for any applications.