Shape Metamorphism Using p-Laplacian Equation
We present a new approach for shape metamorphism, which is a process of gradually changing a source shape (known) through intermediate shapes (unknown) into a target shape (known). The problem, when represented with implicit scalar function, is under-constrained, and regularization is needed. Using the p-Laplacian equation (PLE), we generalize a series of regularization terms based on the gradient of the implicit function, and we show that the present methods lack additional constraints for a more stable solution. The novelty of our approach is in the deployment of a new regularization term when p --> infinity which leads to the infinite Laplacian equation (ILE). We show that ILE minimizes the supremum of the gradient and prove that it is optimal for metamorphism since intermediate solutions are equally distributed along their normal direction. Applications of the proposed algorithm for 2D and 3D objects are demonstrated.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director. Office of Science. Office of Advanced Scientific Computing Research. Mathematical Information and Computational Sciences Division; National Science Foundation CRCD Grant 0088086 (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 828137
- Report Number(s):
- LBNL-55031; R&D Project: K63040; TRN: US200427%%85
- Resource Relation:
- Conference: International Conference on Pattern Recognition, Oxford (GB), 08/23/2004--08/26/2004; Other Information: PBD: 19 May 2004
- Country of Publication:
- United States
- Language:
- English
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