Math @ Duke

Publications [#264984] of Guillermo Sapiro
Papers Published
 Breen, D; Kirby, M; Lefohn, A; Museth, K; Preusser, T; Sapiro, G; Whitaker, R, Level set and PDE methods for visualization,
Proceedings of the IEEE Visualization Conference
(2005),
pp. 125 [doi]
(last updated on 2018/08/18)
Abstract: Level set methods, an important class of partial differential equation (PDE) methods, define dynamic surfaces implicitly as the level set (isosurface) of a sampled, evolving nD function. This course is targeted for researchers interested in learning about level set and other PDEbased methods, and their application to visualization. The course material will be presented by several of the recognized experts in the field, and will include introductory concepts, practical considerations and extensive details on a variety of level set/PDE applications. The course will begin with preparatory material that introduces the concept of using partial differential equations to solve problems in visualization. This will include the structure and behavior of several different types of differential equations, e.g. the level set, heat and reactiondiffusion equations, as well as a general approach to developing PDEbased applications. The second stage of the course will describe the numerical methods and algorithms needed to implement the mathematics and methods presented in the first stage, including information on implementing the algorithms on GPUs. Throughout the course the technical material will be tied to applications, e.g. image processing, geometric modeling, dataset segmentation, model processing, surface reconstruction, anisotropic geometric diffusion, flow field postprocessing and vector visualization.


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Mathematics Department
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