Math @ Duke

Publications [#264773] of Guillermo Sapiro
Papers Published
 Bertalmió, M; Sapiro, G; Cheng, LT; Osher, S, Variational problems and PDEs on implicit surfaces,
Proceedings Ieee Workshop on Variational and Level Set Methods in Computer Vision, Vlsm 2001
(January, 2001),
pp. 186193, IEEE COMPUTER SOC, ISBN 076951278X [Gateway.cgi], [doi]
(last updated on 2019/06/19)
Abstract: © 2001 IEEE. A novel framework for solving variational problems and partial differential equations for scalar and vectorvalued data defined on surfaces is introduced. The key idea is to implicitly represent the surface as the level set of a higher dimensional function, and solve the surface equations in a fixed Cartesian coordinate system using this new embedding function. The equations are then both intrinsic to the surface and defined in the embedding space. This approach thereby eliminates the need for performing complicated and inaccurate computations on triangulated surfaces, as is commonly done in the literature. We describe the framework and present examples in computer graphics and image processing applications, including texture synthesis, flow field visualization, as well as image and vector field intrinsic regularization for data defined on 3D surfaces.


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