Globally-convergent iterative numerical schemes for non-linear variational image smoothing and segmentation on a multi-processor machine

Heers, Josef ; Schnörr, Christoph ; Stiehl, H. Siegfried

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URN: urn:nbn:de:bsz:180-madoc-18381
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: Manuskripte / Reihe Informatik ; TR-2000-005
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 68W10 68U10 ,
Subject headings (SWD): Paralleler Algorithmus , Nichtlineare Regelung , Segmentierung
Keywords (English): Adaptive smoothing , variational segmentation , non-linear regularization , images and pde's , auxiliary variables , parallel numerical algorithms
Abstract: We investigate several iterative numerical schemes for nonlinear variational image smoothing and segmentation implemented in parallel. A general iterative framework subsuming these schemes is suggested for which global convergence irrespective of the starting point can be shown. We characterize various edge-preserving regulafization methods from the recent image processing literature involving auxiliary variables as special cases of this general framework. As a by-product, global convergence can be proven under conditions slightly weaker than those stated in the literature. Efficient Krylov subspace solvers for the linear parts of these schemes have been implemented on a multi-processor machine. The performance of these parallel implementations has been assessed and empirical results concerning convergence rates and speed-up factors are reported.
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