Shape Metamorphism Using p-Laplacian Equation

Conference · Wed May 19 04:00:00 EDT 2004

OSTI ID:828137

Cong, Ge ^[1]; Esser, Mehmet; Parvin, Bahram; Bebis, George

---

1. LBNL Library

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: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• 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
• Country of Publication: United States
• Language: English

Related Subjects

60 APPLIED LIFE SCIENCES
ALGORITHMS
LAPLACIAN
METAMORPHISM
PATTERN RECOGNITION
SCALARS
SHAPE
TARGETS