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Level set and PDE methods for computer graphics

Published: 08 August 2004 Publication History

Abstract

Level set methods, an important class of partial differential equation (PDE) methods, define dynamic surfaces implicitly as the level set (iso-surface) of a sampled, evolving nD function. The course begins with preparatory material that introduces the concept of using partial differential equations to solve problems in computer graphics, geometric modeling and computer vision. This will include the structure and behavior of several different types of differential equations, e.g. the level set equation and the heat equation, as well as a general approach to developing PDE-based applications. The second stage of the course will describe the numerical methods and algorithms needed to actually implement the mathematics and methods presented in the first stage. The course closes with detailed presentations on several level set/PDE applications, including image/video inpainting, pattern formation, image/volume processing, 3D shape reconstruction, image/volume segmentation, image/shape morphing, geometric modeling, anisotropic diffusion, and natural phenomena simulation.

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    cover image ACM Conferences
    SIGGRAPH '04: ACM SIGGRAPH 2004 Course Notes
    August 2004
    6109 pages
    ISBN:9781450378017
    DOI:10.1145/1103900
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    New York, NY, United States

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    Published: 08 August 2004

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    • (2013)VDBACM Transactions on Graphics10.1145/2487228.248723532:3(1-22)Online publication date: 4-Jul-2013
    • (2009)Adaptively Up-Sampling Point-Sampled ModelsProceedings of the 2009 International Conference on Multimedia Information Networking and Security - Volume 0110.1109/MINES.2009.31(314-318)Online publication date: 18-Nov-2009
    • (2006)Efficient simulation of large bodies of water by coupling two and three dimensional techniquesACM SIGGRAPH 2006 Papers10.1145/1179352.1141959(805-811)Online publication date: 30-Jul-2006
    • (2006)Efficient simulation of large bodies of water by coupling two and three dimensional techniquesACM Transactions on Graphics10.1145/1141911.114195925:3(805-811)Online publication date: 1-Jul-2006
    • (2006)Simplex free adaptive tree fast sweeping and evolution methods for solving level set equations in arbitrary dimensionJournal of Computational Physics10.1016/j.jcp.2005.08.020213:2(458-473)Online publication date: 10-Apr-2006
    • (2006)Dynamic Tubular GridJournal of Scientific Computing10.1007/s10915-005-9062-826:3(261-299)Online publication date: 1-Mar-2006

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