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Discontinuity Preserving Phase Unwrapping Using Graph Cuts

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3757))

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Abstract

We present a new algorithm for recovering the absolute phase from modulo-2π phase, the so-called phase unwrapping (PU) problem. PU arises as a key step in several imaging technologies, from which we emphasize interferometric synthetic aperture radar/sonar (InSAR/SAS), magnetic resonance imaging (MRI), and optical interferometry. We adopt a discrete energy minimization viewpoint, where the objective function is a first-order Markov random field. The minimization problem is dealt with via a binary iterative scheme, with each iteration step cast onto a graph cut based optimization problem. For convex clique potentials we provide an exact energy minimization algorithm; namely we solve exactly the PU classical L p norm, with p ≥ 1. For nonconvex clique potentials, it is well known that PU performance is particularly enhanced, namely, the discontinuity preserving ability; however the problem is NP-hard. Accordingly, we provide an approximate algorithm, which is a modified version of the first proposed one. For simplicity we call both algorithms PUMF, for Phase Unwrapping Max-Flow. The state-of-the-art competitiveness of PUMF is illustrated in a series of experiments.

This work was supported by the Fundação para a Ciência e Tecnologia, under the project PDCTE/CPS/49967/2003.

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Authors and Affiliations

  1. Instituto de Telecomunicações, Instituto Superior Técnico, Torre Norte, Piso 10, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    José M. Bioucas-Dias & Gonçalo Valadão

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  1. José M. Bioucas-Dias
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  2. Gonçalo Valadão
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Editors and Affiliations

  1. Department of CISE, University of Florida, Gainesville, FL, USA

    Anand Rangarajan

  2. University of Florida, 32611, Gainesville, FL, USA

    Baba Vemuri

  3. Department of Statistics, University of California, Los Angeles

    Alan L. Yuille

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Bioucas-Dias, J.M., Valadão, G. (2005). Discontinuity Preserving Phase Unwrapping Using Graph Cuts. In: Rangarajan, A., Vemuri, B., Yuille, A.L. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2005. Lecture Notes in Computer Science, vol 3757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11585978_18

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  • DOI: https://doi.org/10.1007/11585978_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30287-2

  • Online ISBN: 978-3-540-32098-2

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