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The Equivalence of the Taut String Algorithm and BV-Regularization

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Abstract

It is known that discrete BV-regularization and the taut string algorithm are equivalent. In this paper we extend this result to the continuous case. First we derive necessary equations for the solution of both BV-regularization and the taut string algorithm by computing suitable Gateaux derivatives. The equivalence then follows from a uniqueness result.

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Authors and Affiliations

  1. Department of Computer Science, University of Innsbruck, Technikerstr. 21a/2, A–6020, Innsbruck, Austria

    Markus Grasmair

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  1. Markus Grasmair
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Correspondence to Markus Grasmair.

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Markus Grasmair received his MSc degree in Mathematics in 2003 and is now writing his PhD-thesis at the University of Innsbruck under supervision of Prof. Otmar Scherzer. His main research interests lie in the field of variational calculus, in particular with applications to image processing.

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Grasmair, M. The Equivalence of the Taut String Algorithm and BV-Regularization. J Math Imaging Vis 27, 59–66 (2007). https://doi.org/10.1007/s10851-006-9796-4

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  • DOI: https://doi.org/10.1007/s10851-006-9796-4

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