Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension
We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source a...
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| creator | Shafrir, David Sochen, Nir A. Deriche, Rachid |
| description | We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly, as functions of the spatial coordinates. We derive the general implicit differential operators, and show how they can be used to generalize previous results concerning the Beltrami flow and other similar flows.
As examples, We show how these results can be used to regularize gray level and color images on manifolds, and to regularize tangent vector fields and direction fields on manifolds. |
| doi_str_mv | 10.1007/11567646_29 |
| format | Conference Proceeding |
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As examples, We show how these results can be used to regularize gray level and color images on manifolds, and to regularize tangent vector fields and direction fields on manifolds.</description><subject>Applied sciences</subject><subject>Artificial intelligence</subject><subject>Beltrami Flow</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Graph Manifold</subject><subject>Implicit Constraint</subject><subject>Intersection Manifold</subject><subject>Pattern recognition. Digital image processing. Computational geometry</subject><subject>Target Manifold</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540293484</isbn><isbn>3540293485</isbn><isbn>3540321098</isbn><isbn>9783540321095</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>2005</creationdate><recordtype>conference_proceeding</recordtype><recordid>eNpNkE1LxDAQhuMXuK578g_04sFDdSZJk-a4rl8LK4LoTShpkyzRblqaLqK_3pZVcC7D8DwzDC8hZwiXCCCvEDMhBRcFVXvkhGUcGEVQ-T6ZoEBMGePqgMyUzEdGFeM5PyQTYEBTJTk7JrMY32EoRkEgTMjbs11va935b937JiSNSx512_qwjsm17T-tDcly09a-8v1AgndNbeKozbvS953uvpIbv7Ehjts6mGTRmL_5lBw5XUc7--1T8np3-7J4SFdP98vFfJW2FFWfMjCyYrlAp7kUVjMnuaBSGavySmdIq8pI4GC4UpxnSlNqOZbOSMFK6nI2Jee7u62Ola5dp0PlY9F2fjP8V6CkIstBDd7FzosDCmvbFWXTfMQCoRjjLf7Fy34AQXtnlg</recordid><startdate>2005</startdate><enddate>2005</enddate><creator>Shafrir, David</creator><creator>Sochen, Nir A.</creator><creator>Deriche, Rachid</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>IQODW</scope></search><sort><creationdate>2005</creationdate><title>Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension</title><author>Shafrir, David ; Sochen, Nir A. ; Deriche, Rachid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p219t-30d7c3861fa476ea3f746279de98ca512ccd7040d4994459a22e41bfd763b2f83</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Applied sciences</topic><topic>Artificial intelligence</topic><topic>Beltrami Flow</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Graph Manifold</topic><topic>Implicit Constraint</topic><topic>Intersection Manifold</topic><topic>Pattern recognition. Digital image processing. Computational geometry</topic><topic>Target Manifold</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Shafrir, David</creatorcontrib><creatorcontrib>Sochen, Nir A.</creatorcontrib><creatorcontrib>Deriche, Rachid</creatorcontrib><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Shafrir, David</au><au>Sochen, Nir A.</au><au>Deriche, Rachid</au><au>Paragios, Nikos</au><au>Faugeras, Olivier</au><au>Chan, Tony</au><au>Schnörr, Christoph</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension</atitle><btitle>Lecture notes in computer science</btitle><date>2005</date><risdate>2005</risdate><spage>344</spage><epage>355</epage><pages>344-355</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540293484</isbn><isbn>3540293485</isbn><eisbn>3540321098</eisbn><eisbn>9783540321095</eisbn><abstract>We study in this paper the problem of regularization of mappings between manifolds of arbitrary dimension and codimension using variational methods. This is of interest in various applications such as diffusion tensor imaging and EEG processing on the cortex. We consider the cases where the source and target manifold are represented implicitly, using multiple level set functions, or explicitly, as functions of the spatial coordinates. We derive the general implicit differential operators, and show how they can be used to generalize previous results concerning the Beltrami flow and other similar flows.
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| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2005, p.344-355 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_17265809 |
| source | Springer Books |
| subjects | Applied sciences Artificial intelligence Beltrami Flow Computer science control theory systems Exact sciences and technology Graph Manifold Implicit Constraint Intersection Manifold Pattern recognition. Digital image processing. Computational geometry Target Manifold |
| title | Regularization of Mappings Between Implicit Manifolds of Arbitrary Dimension and Codimension |
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