# GRADE: Gibbs Reaction and Diffusion Equations

 Title: GRADE: Gibbs Reaction and Diffusion Equations Author: Mumford, David Bryant; Zhu, Song Chun Note: Order does not necessarily reflect citation order of authors. Citation: Zhu, Song Chun, and David Bryant Mumford. 1998. GRADE: Gibbs reaction and diffusion equations. In Proceedings of the Sixth International Conference on Computer Vision: January 4 - 7, 1998, Bombay, India, ed. IEEE Computer Society, 847-854. New Delhi: Narosa. Full Text & Related Files: Mumford_GRADE.pdf (1.213Mb; PDF) Abstract: Recently there have been increasing interests in using nonlinear PDEs for applications in computer vision and image processing. In this paper, we propose a general statistical framework for designing a new class of PDEs. For a given application, a Markov random field model $$p(I)$$ is learned according to the minimax entropy principle so that $$p(I)$$ should characterize the ensemble of images in our application. $$P(I)$$ is a Gibbs distribution whose energy terms can be divided into two categories. Subsequently the partial differential equations given by gradient descent on the Gibbs potential are essentially reaction-diffusion equations, where the energy terms in one category produce anisotropic diffusion while the inverted energy terms in the second category produce reaction associated with pattern formation. We call this new class of PDEs the Gibbs Reaction And Diffusion Equations-GRADE and we demonstrate experiments where GRADE are used for texture pattern formation, denoising, image enhancement, and clutter removal. Published Version: doi:10.1109/ICCV.1998.710816 Other Sources: http://www.dam.brown.edu/people/mumford/Papers/DigitizedVisionPapers--forNonCommercialUse/98a--GibbsR-D-Zhu.pdf Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3627275 Downloads of this work: