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Post Made Community Wiki by Ben Webster♦
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2 | Reversed order of presentation: Ricci 1st, eikonal 2nd. Added Sethian's book. | ||
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Ricci flow has been applied to computer vision (e.g., to 3D shape matching),and to computer graphics (e.g., surface parametrization): Wei Zeng, Samaras, D., Gu, D. , "Ricci Flow for 3D Shape Analysis," IEEE Transactions on Pattern Analysis and Machine Intelligence, 32(4) 2010 662-677. Yang, Guo, Luo, Hu, Gu, "Generalized Discrete Ricci Flow," Computer Graphics Forum, Volume 28, Issue 7, pages 2005–2014, October 2009. "The eikonal equation: some Some results applicable to computer vision,"Ricci flow has also been applied to computer vision (e.g., to 3D shape matching) And in fact Sethian's book, and to computer graphics (e.g., surface parametrization) Level Set Methods: Wei Zeng, Samaras, D.Evolving Interfaces in Geometry, GuFluid Mechanics, D. Computer Vision, "Ricci Flow for 3D Shape Analysis," IEEE Transactions on Pattern Analysis and Machine IntelligenceMaterials Science, 32(4) 2010 662-677 YangCambridge University Press, Guo1996. is filled with applications of the eikonal equation (and its variants):"The text includes applications from physics, Luochemistry, Hufluid mechanics, Gucombustion, "Generalized Discrete Ricci Flow," Computer Graphics Forumimage processing, Volume 28material science, Issue 7seismology, pages 2005–2014fabrication of microelectronic components, October 2009.computer vision and control theory." |
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If you classify the eikonal equation as a geometric evolution equation, then there are many applications to the computer vision problem known as "shape from shading": deriving the 3D shape of an object from shading variation. For example:
Ricci flow has also been applied to computer vision (e.g., to 3D shape matching), and to computer graphics (e.g., surface parametrization):
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