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International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2017: Scale Space and Variational Methods in Computer Vision pp 408–420Cite as

An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10302))

Abstract

We propose an efficient algorithm to minimize an anisotropic surface energy generalizing the Geodesic Active Contour model for image segmentation. In this energy, the weight function may depend on the normal of the curve/surface. Our algorithm is Lagrangian, but nonparametric. We only use the node and connectivity information for computations. Our approach provides a flexible scheme, in the sense that it allows to easily incorporate the generalized gradients proposed recently, especially those based on the \(H^1\) scalar product on the surface. However, unlike these approaches, our scheme is applicable in any number of dimensions, such as surfaces in 3d or 4d, and allows weighted \(H^1\) scalar products, with weights may depending on the normal and the curvature. We derive the second shape derivative of the anisotropic surface energy, and use it as the basis for a new weighted \(H^1\) scalar product. In this way, we obtain a Newton-type method that not only gives smoother flows, but also converges in fewer iterations and much shorter time.

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Acknowledgement

This work was performed under the financial assistance award 70NANB16H306 from the U.S. Department of Commerce, National Institute of Standards and Technology.

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Authors and Affiliations

  1. Theiss Research, La Jolla, CA, 92037, USA

    Günay Doğan

  2. National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA

    Günay Doğan

Authors
  1. Günay Doğan
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Correspondence to Günay Doğan .

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Editors and Affiliations

  1. University of Copenhagen , Copenhagen, Denmark

    François Lauze

  2. Technical University of Denmark , Kongens Lyngby, Denmark

    Yiqiu Dong

  3. Technical University of Denmark , Kongens Lyngby, Denmark

    Anders Bjorholm Dahl

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Doğan, G. (2017). An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_33

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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