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Improved optimization methods for image registration problems

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Abstract

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.

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Funding

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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Authors and Affiliations

  1. Centre for Mathematical Imaging Techniques, The University of Liverpool, Merseyside L697ZL, Liverpool, UK

    Ke Chen & Daoping Zhang

  2. Department of Mathematical Sciences, The University of Liverpool, Merseyside L697ZL, Liverpool, UK

    Ke Chen & Daoping Zhang

  3. Departamento de Matemática, Universidade Federal do Paraná, Centro Politécnico, Cx. postal 19.081, 81531-980, Curitiba, Paraná, Brazil

    Geovani Nunes Grapiglia & Jinyun Yuan

Authors
  1. Ke Chen
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  2. Geovani Nunes Grapiglia
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  3. Jinyun Yuan
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  4. Daoping Zhang
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Correspondence to Ke Chen.

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Chen, K., Grapiglia, G.N., Yuan, J. et al. Improved optimization methods for image registration problems. Numer Algor 80, 305–336 (2019). https://doi.org/10.1007/s11075-018-0486-2

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  • DOI: https://doi.org/10.1007/s11075-018-0486-2

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