Numerical Algorithms

, Volume 80, Issue 2, pp 305–336 | Cite as

Improved optimization methods for image registration problems

  • Ke ChenEmail author
  • Geovani Nunes Grapiglia
  • Jinyun Yuan
  • Daoping Zhang
Original Paper


In this paper, we propose new multilevel optimization methods for minimizing continuously differentiable functions obtained by discretizing models for image registration problems. These multilevel schemes rely on a novel two-step Gauss-Newton method, in which a second step is computed within each iteration by minimizing a quadratic approximation of the objective function over a certain two-dimensional subspace. Numerical results on image registration problems show that the proposed methods can outperform the standard multilevel Gauss-Newton method.


Image registration Multilevel strategy Gauss-Newton method Subspace methods 


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Funding information

This work was partially supported by UK EPSRC (grants EP/K036939/1 and EP/N014499/1), by the Newton Research Collaboration Programme (grant NRCP 1617/6/187) and by the National Council for Scientific and Technological Development (grant CNPq 406269/2016-5).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre for Mathematical Imaging TechniquesThe University of LiverpoolLiverpoolUK
  2. 2.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK
  3. 3.Departamento de MatemáticaUniversidade Federal do Paraná, Centro PolitécnicoCuritibaBrazil

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