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PDE-based medial axis extraction and shape manipulation of arbitrary meshes.

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Du H, Yoo TS, Qin H
Journal of Systems Science and Complexity. 2008 Dec;21(4):601-17.
Abstract: 

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, we 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, our 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, our 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.

Du H, Yoo TS, Qin H. PDE-based medial axis extraction and shape manipulation of arbitrary meshes. Journal of Systems Science and Complexity. 2008 Dec;21(4):601-17.