A Well-Posedness Framework for Inpainting Based on Coherence Transport
Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278, 2007 ) introduced a very efficient method, called image inpainting based on coherence transpo...
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| Veröffentlicht in: | Foundations of computational mathematics 2015-08, Vol.15 (4), p.973-1033 |
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| creator | März, Thomas |
| description | Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278,
2007
) introduced a very efficient method, called
image inpainting based on coherence transport
, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions. |
| doi_str_mv | 10.1007/s10208-014-9199-7 |
| format | Article |
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2007
) introduced a very efficient method, called
image inpainting based on coherence transport
, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.</description><identifier>ISSN: 1615-3375</identifier><identifier>EISSN: 1615-3383</identifier><identifier>DOI: 10.1007/s10208-014-9199-7</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Applications of Mathematics ; Computer Science ; Economics ; Image processing ; Inverse functions ; Linear and Multilinear Algebras ; Math Applications in Computer Science ; Mathematical research ; Mathematics ; Mathematics and Statistics ; Matrix Theory ; Numerical Analysis</subject><ispartof>Foundations of computational mathematics, 2015-08, Vol.15 (4), p.973-1033</ispartof><rights>SFoCM 2014</rights><rights>COPYRIGHT 2015 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c460t-f235b070d4ebdf5c6fd63300f907695736d11246fcdee8e7ed82afb1b39b0d2f3</citedby><cites>FETCH-LOGICAL-c460t-f235b070d4ebdf5c6fd63300f907695736d11246fcdee8e7ed82afb1b39b0d2f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10208-014-9199-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10208-014-9199-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>März, Thomas</creatorcontrib><title>A Well-Posedness Framework for Inpainting Based on Coherence Transport</title><title>Foundations of computational mathematics</title><addtitle>Found Comput Math</addtitle><description>Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278,
2007
) introduced a very efficient method, called
image inpainting based on coherence transport
, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.</description><subject>Algorithms</subject><subject>Applications of Mathematics</subject><subject>Computer Science</subject><subject>Economics</subject><subject>Image processing</subject><subject>Inverse functions</subject><subject>Linear and Multilinear Algebras</subject><subject>Math Applications in Computer Science</subject><subject>Mathematical research</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Matrix Theory</subject><subject>Numerical Analysis</subject><issn>1615-3375</issn><issn>1615-3383</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kU1LAzEQhhdRsFZ_gLcFTx5SJ8l-dI-1WC0UFK14DNnNZN26TUqyRf33pqwIhSJzmGF4njnMG0WXFEYUIL_xFBiMCdCEFLQoSH4UDWhGU8L5mB__zXl6Gp15vwKgaUGTQTSbxG_YtuTJelQGvY9nTq7x07qPWFsXz81GNqZrTB3fyoDE1sRT-44OTYXx0knjN9Z159GJlq3Hi98-jF5nd8vpA1k83s-nkwWpkgw6ohlPS8hBJVgqnVaZVhnnALqAPCvSnGeKUpZkulKIY8xRjZnUJS15UYJimg-jq_5uLVsUjdG2c7JaN74Sk4SxlFEOaaDIAapGg0621qBuwnqPHx3gQylcN9VB4XpPCEyHX10tt96L-cvzPkt7tnLWe4dabFyzlu5bUBC77ESfnQjZiV12Ig8O6x0fWFOjEyu7dSZ89h_pB__omU8</recordid><startdate>20150801</startdate><enddate>20150801</enddate><creator>März, Thomas</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20150801</creationdate><title>A Well-Posedness Framework for Inpainting Based on Coherence Transport</title><author>März, Thomas</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c460t-f235b070d4ebdf5c6fd63300f907695736d11246fcdee8e7ed82afb1b39b0d2f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Applications of Mathematics</topic><topic>Computer Science</topic><topic>Economics</topic><topic>Image processing</topic><topic>Inverse functions</topic><topic>Linear and Multilinear Algebras</topic><topic>Math Applications in Computer Science</topic><topic>Mathematical research</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Matrix Theory</topic><topic>Numerical Analysis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>März, Thomas</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Foundations of computational mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>März, Thomas</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Well-Posedness Framework for Inpainting Based on Coherence Transport</atitle><jtitle>Foundations of computational mathematics</jtitle><stitle>Found Comput Math</stitle><date>2015-08-01</date><risdate>2015</risdate><volume>15</volume><issue>4</issue><spage>973</spage><epage>1033</epage><pages>973-1033</pages><issn>1615-3375</issn><eissn>1615-3383</eissn><abstract>Image inpainting is the process of touching up damaged or unwanted portions of a picture and is an important task in image processing. For this purpose Bornemann and März (J Math Imaging Vision, 28:259–278,
2007
) introduced a very efficient method, called
image inpainting based on coherence transport
, that fills the missing region by advecting the image information along integral curves of a coherence vector field from the boundary toward the interior of the hole. The mathematical model behind this method is a first-order functional advection partial differential equation posed on a compact domain with all inflow boundaries. We show that this problem is well posed under certain conditions.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10208-014-9199-7</doi><tpages>61</tpages></addata></record> |
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| subjects | Algorithms Applications of Mathematics Computer Science Economics Image processing Inverse functions Linear and Multilinear Algebras Math Applications in Computer Science Mathematical research Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis |
| title | A Well-Posedness Framework for Inpainting Based on Coherence Transport |
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