PDE-Based Medial Axis Extraction and Shape Manipulation of Arbitrary Meshes

Shape skeletonization (i.e., medial axis extraction) is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D solids represented by polygonal meshes based on their differential properties. It offers an alternative but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects. This research was supported in part by the National Science Foundation (NSF) Information Technology Research under Grant No. IIS-0082035, the NSF under Grant No. IIS-0097646, Alfred P. Sloan Fellowship, Honda Initiation Award, and an appointment of Haixia Du to the NLM Research Participation Program sponsored by the National Library of Medicine and administered by the Oak Ridge Institute for Science and Education.