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Brownian Warps for Non-Rigid Registration

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Abstract

A Brownian motion model in the group of diffeomorphisms has been introduced as inducing a least committed prior on warps. This prior is source-destination symmetric, fulfills a natural semi-group property for warps, and with probability 1 creates invertible warps. Using this as a least committed prior, we formulate a Partial Differential Equation for obtaining the maximally likely warp given matching constraints derived from the images. We solve for the free boundary conditions, and the bias toward smaller areas in the finite domain setting. Furthermore, we demonstrate the technique on 2D images, and show that the obtained warps are also in practice source-destination symmetric and in an example on X-ray spine registration provides extrapolations from landmark point superior to those of spline solutions.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Mads Nielsen, Peter Johansen & Søren Hauberg

  2. Nordic Bioscience A/S, Herlev Hovedgadde 207, 2730, Herlev, Denmark

    Mads Nielsen

  3. Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen, Denmark

    Andrew D. Jackson & Benny Lautrup

Authors
  1. Mads Nielsen
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  2. Peter Johansen
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  3. Andrew D. Jackson
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  4. Benny Lautrup
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  5. Søren Hauberg
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Corresponding author

Correspondence to Søren Hauberg.

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Nielsen, M., Johansen, P., Jackson, A.D. et al. Brownian Warps for Non-Rigid Registration. J Math Imaging Vis 31, 221–231 (2008). https://doi.org/10.1007/s10851-008-0083-4

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  • DOI: https://doi.org/10.1007/s10851-008-0083-4

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