A Simple and Stable Centeredness Measure for 3D Curve Skeleton Extraction

Existing methods for extracting 3D curve skeletons mostly suffer from the difficulty of finding the center points of 3D shapes and tedious manual adjustments of the thresholds for pruning spurious branches due to the influence of shape boundary perturbations. In this article, we present a method based on medial surfaces of 3D shapes for the convenient and fast extraction of high-quality curve skeletons. Our main contribution is a simple and stable centeredness measure. It is based on simulating fire propagation via the scheme of inside-out evolution from the interior to the boundary, differentiating it from existing methods that use the scheme of outside-in evolution from the boundary to the interior. Thus, our measure is much more localized, and it can be implemented with a high degree of parallelism. In addition, we propose measures to effectively suppress the influence of details to obtain a stable measurement, and employ minimum set covers to optimize the center points to generate compact skeletons, which enables spurious branches to be effectively excluded without the tedious work of manually adjusting thresholds. Our experiments show the superiority of our method over existing methods, including its convenient generation of clean, compact and centered curve skeletons while running much faster than state-of-the-art methods.