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Improved variational image registration model and a fast algorithm for its numerical approximation

Authors

  • Noppadol Chumchob,

    1. Department of Mathematics, Faculty of Science, Silpakorn University, Nakorn Pathom 73000, Thailand
    2. Centre of Excellence in Mathematics, CHE, Bangkok 10400, Thailand
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    • Both authors are members of the Centre for Mathematical Imaging Techniques.

  • Ke Chen

    Corresponding author
    1. Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, United Kingdom
    • Department of Mathematical Sciences, The University of Liverpool, Peach Street, Liverpool L69 7ZL, United Kingdom
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    • Both authors are members of the Centre for Mathematical Imaging Techniques.


Abstract

In a multimodal image registration scenario, where two given images have similar features, but noncomparable intensity variations, the sum of squared differences is not suitable for inferring image similarities. In this article, we first propose a new variational model based on combining intensity and geometric transformations, as an alternative to use mutual information and an improvement to the work by Modersitzki and Wirtz (Modersitzki and Wirtz, Lect Notes Comput Sci 4057 (2006), 257–263), and then develop a fast multigrid (MG) algorithm for solving the underlying system of fourth-order and nonlinear partial differential equations. We can demonstrate the effective smoothing property of the adopted primal-dual smoother by a local Fourier analysis. Numerical tests will be presented to show both the improvements achieved in image registration quality and MG efficiency. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011

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