A direct method for solving an anisotropic mean curvature flow of plane curves with an external force
A new method for solution of the evolution of plane curves satisfying the geometric equation v=β(x,k,ν), where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ⊂ ℝ2 at the point x∈Γ, is proposed. We derive a governing system of partial differential equation...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2004-09, Vol.27 (13), p.1545-1565 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Mikula, Karol S̆evc̆ovic̆, Daniel |
| description | A new method for solution of the evolution of plane curves satisfying the geometric equation v=β(x,k,ν), where v is the normal velocity, k and ν are the curvature and tangential angle of a plane curve Γ ⊂ ℝ2 at the point x∈Γ, is proposed. We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non‐trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd. |
| doi_str_mv | 10.1002/mma.514 |
| format | Article |
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We derive a governing system of partial differential equations for the curvature, tangential angle, local length and position vector of an evolving family of plane curves and prove local in time existence of a classical solution. These equations include a non‐trivial tangential velocity functional governing a uniform redistribution of grid points and thus preventing numerically computed solutions from forming various instabilities. We discretize the governing system of equations in order to find a numerical solution for 2D anisotropic interface motions and image segmentation problems. Copyright © 2004 John Wiley & Sons, Ltd.</description><identifier>ISSN: 0170-4214</identifier><identifier>EISSN: 1099-1476</identifier><identifier>DOI: 10.1002/mma.514</identifier><identifier>CODEN: MMSCDB</identifier><language>eng</language><publisher>Chichester, UK: John Wiley & Sons, Ltd</publisher><subject>anisotropy ; Differential geometry ; Exact sciences and technology ; external force ; Geometry ; image segmentation ; interface ; Lagrangian approach ; Mathematical analysis ; Mathematics ; mean curvature flow ; Numerical analysis ; Numerical analysis. Scientific computation ; Partial differential equations ; Partial differential equations, boundary value problems ; Sciences and techniques of general use ; semi-implicit scheme</subject><ispartof>Mathematical methods in the applied sciences, 2004-09, Vol.27 (13), p.1545-1565</ispartof><rights>Copyright © 2004 John Wiley & Sons, Ltd.</rights><rights>2004 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3274-310db13ce458e5b2f380d750278088f47a717e9646b3dea889f2aac8495b738d3</citedby><cites>FETCH-LOGICAL-c3274-310db13ce458e5b2f380d750278088f47a717e9646b3dea889f2aac8495b738d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fmma.514$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fmma.514$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=15988687$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Mikula, Karol</creatorcontrib><creatorcontrib>S̆evc̆ovic̆, Daniel</creatorcontrib><title>A direct method for solving an anisotropic mean curvature flow of plane curves with an external force</title><title>Mathematical methods in the applied sciences</title><addtitle>Math. 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Copyright © 2004 John Wiley & Sons, Ltd.</description><subject>anisotropy</subject><subject>Differential geometry</subject><subject>Exact sciences and technology</subject><subject>external force</subject><subject>Geometry</subject><subject>image segmentation</subject><subject>interface</subject><subject>Lagrangian approach</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>mean curvature flow</subject><subject>Numerical analysis</subject><subject>Numerical analysis. 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| subjects | anisotropy Differential geometry Exact sciences and technology external force Geometry image segmentation interface Lagrangian approach Mathematical analysis Mathematics mean curvature flow Numerical analysis Numerical analysis. Scientific computation Partial differential equations Partial differential equations, boundary value problems Sciences and techniques of general use semi-implicit scheme |
| title | A direct method for solving an anisotropic mean curvature flow of plane curves with an external force |
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