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Title
A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data
AuthorFranek, Lucas ; Franek, Marzena ; Maurer, Helmut ; Wagner, Marcus
Published in
Optimal Control Applications and Methods, 2011, Vol. 33, Issue 3, page 276-301
PublishedWiley, 2011
Edition
Preprint
LanguageEnglish
Document typeJournal Article
Keywords (EN)PDE constrained optimization / optimal control problem / direct methods / convergence theorem / image denoising / edge detection
Project-/ReportnumberSFB-MOBIS / Report 2010-003
ISSN0143-2087
URNurn:nbn:at:at-ubg:3-3865 Persistent Identifier (URN)
DOI10.1002/oca.996 
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 The work is publicly available
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A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data [1.6 mb]
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Abstract (English)

The present paper is concerned with the numerical solution of multidimensional control problems of DieudonnéRashevsky type by discretization methods and large-scale optimization techniques. We prove first a convergence theorem wherein the difference of the minimal value and the objective values along a minimizing sequence is estimated by the mesh size of the underlying triangulations. Then we apply the proposed method to the problem of edge detection within raw image data. Instead of using an AmbrosioTortorelli type energy functional, we reformulate the problem as a multidimensional control problem. The edge detector can be built immediately from the control variables. The quality of our numerical results competes well with those obtained by applying variational techniques.

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