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An Efficient Curve Evolution Algorithm for Multiphase Image Segmentation

  • Conference paper
Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8932))

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Abstract

We propose a novel iterative algorithm for multiphase image segmentation by curve evolution. Specifically, we address a multiphase version of the Chan-Vese piecewise constant segmentation energy. Our algorithm is efficient: it is based on an explicit Lagrangian representation of the curves and it converges in a relatively small number of iterations. We devise a stable curvature-free semi-implicit velocity computation scheme. This enables us to take large steps to achieve sharp decreases in the multiphase segmentation energy when possible. The velocity and curve computations are linear with respect to the number of nodes on the curves, thanks to a finite element discretization of the curve and the gradient descent equations, yielding essentially tridiagonal linear systems. The step size at each iteration is selected using a nonmonotone line search algorithm ensuring rapid progress and convergence. Thus, the user does not need to specify fixed step sizes or iteration numbers. We also introduce a novel dynamic stopping criterion, robust to various imaging conditions, to decide when to stop the iterations. Our implementation can handle topological changes of curves, such as merging and splitting as well. This is a distinct advantage of our approach, because we do not need to know the number of phases in advance. The curves can merge and split during the evolution to detect the correct regions, especially the number of phases.

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Author information

Authors and Affiliations

  1. Theiss Research, National Institute of Standards and Technology, 100 Bureau Dr., Stop 8910, Gaithersburg, MD, 20899-8910, USA

    Günay Doğan

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  1. Günay Doğan
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, 7800, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  3. The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, S.A.R.

    Tony F. Chan

  4. Telemark University College, Postboks 203, 3901, Porsgrunn, Norway

    Marius Lysaker

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© 2015 Springer International Publishing Switzerland

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Doğan, G. (2015). An Efficient Curve Evolution Algorithm for Multiphase Image Segmentation. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_22

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  • DOI: https://doi.org/10.1007/978-3-319-14612-6_22

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14611-9

  • Online ISBN: 978-3-319-14612-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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