Title:
Image Sharpening via Sobolev Gradient Flows

dc.contributor.author Calder, J. en_US
dc.contributor.author Mansouri, A. en_US
dc.contributor.author Yezzi, Anthony en_US
dc.contributor.corporatename Queen's University (Kingston, Ont.) . Dept. of Mathematics and Statistics en_US
dc.contributor.corporatename Georgia Institute of Technology. School of Electrical and Computer Engineering en_US
dc.date.accessioned 2013-08-29T20:28:22Z
dc.date.available 2013-08-29T20:28:22Z
dc.date.issued 2010
dc.description © 2010 Society for Industrial and Applied Mathematics en_US
dc.description DOI:10.1137/090771260 en_US
dc.description.abstract Motivated by some recent work in active contour applications, we study the use of Sobolev gradients for PDE-based image diffusion and sharpening. We begin by studying, for the case of isotropic diffusion, the gradient descent/ascent equation obtained by modifying the usual metric on the space of images, which is the L2 metric, to a Sobolev metric. We present existence and uniqueness results for the Sobolev isotropic diffusion, derive a number of maximum principles, and show that the differential equations are stable and well-posed both in the forward and backward directions. This allows us to apply the Sobolev flow in the backward direction for sharpening. Favorable comparisons to the well-known shock filter for sharpening are demonstrated. Finally, we continue to exploit this same well-posed behavior both forward and backward in order to formulate new constrained gradient flows on higher order energy functionals which preserve the first order energy of the original image for interesting combined smoothing and sharpening effects. en_US
dc.identifier.citation J. Calder, A. Mansouri, and A. Yezzi, “Image Sharpening via Sobolev Gradient Flows,” SIAM Journal on Imaging Sciences, vol. 3, 2010, 981-1014. en_US
dc.identifier.doi 10.1137/090771260
dc.identifier.issn 1936-4954
dc.identifier.uri http://hdl.handle.net/1853/48743
dc.language.iso en_US en_US
dc.publisher Georgia Institute of Technology en_US
dc.publisher.original Society for Industrial and Applied Mathematics en_US
dc.subject Image diffusion en_US
dc.subject Partial differential equations en_US
dc.subject Gradient descent en_US
dc.subject Gradient ascent en_US
dc.subject Sobolev spaces en_US
dc.subject Image sharpening en_US
dc.title Image Sharpening via Sobolev Gradient Flows en_US
dc.type Text
dc.type.genre Article
dspace.entity.type Publication
local.contributor.author Yezzi, Anthony
local.contributor.corporatename School of Electrical and Computer Engineering
local.contributor.corporatename College of Engineering
relation.isAuthorOfPublication 53ee63a2-04fd-454f-b094-02a4601962d8
relation.isOrgUnitOfPublication 5b7adef2-447c-4270-b9fc-846bd76f80f2
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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