IEEE Trans Pattern Anal Mach Intell. 2016 Jan;38(1):30-45. doi: 10.1109/TPAMI.2015.2414420.
Computing skeletons of 2D shapes, and medial surface and curve skeletons of 3D shapes, is a challenging task. In particular, there is no unified framework that detects all types of skeletons using a single model, and also produces a multiscale representation which allows to progressively simplify, or regularize, all skeleton types. In this paper, we present such a framework. We model skeleton detection and regularization by a conservative mass transport process from a shape's boundary to its surface skeleton, next to its curve skeleton, and finally to the shape center. The resulting density field can be thresholded to obtain a multiscale representation of progressively simplified surface, or curve, skeletons. We detail a numerical implementation of our framework which is demonstrably stable and has high computational efficiency. We demonstrate our framework on several complex 2D and 3D shapes.
计算二维形状的骨架和三维形状的中表面和曲线骨架是一项具有挑战性的任务。特别是，目前还没有一个统一的框架可以使用单个模型检测所有类型的骨架，并且还可以生成多尺度表示，从而逐步简化或正则化所有骨架类型。在本文中，我们提出了这样一个框架。我们通过从形状的边界到其表面骨架、其次到其曲线骨架、最后到形状中心的保守质量传输过程来对骨架检测和正则化进行建模。得到的密度场可以进行阈值处理，以获得逐步简化的表面或曲线骨架的多尺度表示。我们详细介绍了我们框架的数值实现，该实现具有明显的稳定性和高计算效率。我们在几个复杂的二维和三维形状上演示了我们的框架。
