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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

To use interdependence between the primary components of the deformation field for smooth and non-smooth registration problems, the channel-by-channel total variation- or standard vectorial total variation (SVTV)-based regularization has been extended to a more flexible and efficient technique, allowing high quality regularization procedures. Based on this method, this paper proposes a fast nonlinear multigrid (NMG) method for solving the underlying Euler-Lagrange system of two coupled second-order nonlinear partial differential equations. Numerical experiments using both synthetic and realistic images not only confirm that the recommended VTV-based regularization yields better registration qualities for a wide range of applications than those of the SVTV-based regularization, but also that the proposed NMG method is fast, accurate, and reliable in delivering visually-pleasing registration results.

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