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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Burger, M., Modersitzki, J., Ruthotto, L.: A hyperelastic regularization energy for image registration. SIAM J. Sci. Comput. 35, B132–B148 (2013)
Cartis, C., Gould, N.I.M., Toint, Ph.L.: On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. SIAM J. Optim. 20, 2833–2852 (2010)
Dolan, E., Moré, J. J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)
Grapiglia, G.N., Yuan, J., Yuan, Y.: Nonlinear stepsize control algorithms: complexity bounds for first-and second-order optimality. J. Optim. Theory Appl. 171, 980–997 (2016)
Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Program. 45, 503–528 (1989)
Modersitzki, J.: Numerical Methods for Image Registration. Oxford University Press, New York (2014)
Modersitzki, J.: FAIR: Flexible Algorithms for Image Registration. SIAM, Philadelphia (2009)
Moré, J. J., Garbow, B.S., Hillstrom, K.E.: Testing unconstrained optimization software. ACM Trans. Math. Softw. 7, 17–41 (1981)
Nesterov, Y u: Introductory Lectures on Convex Optimization: A Basic Course. Applied Optimization. Kluwer, Dordrecht (2004)
Nocedal, J.: Updating quasi-Newton matrices with limited storage. Math. Comput. 35, 773–782 (1980)
Oliveira, F.P.M., Tavares, J.M.R.S.: Medical image registration: a review. Comput. Methods Biomech. Biomed. Engin. 17, 73–93 (2014)
Sun, W., Yuan, Y.: Optimization Theory and Methods: Nonlinear Programming. Springer, Berlin (2006)
Yuan, Y.: A review on subspace methods for nonlinear optimization. In: Proceedings of International Congress of Mathematicians. Seoul (2014)
Zhang, J., Chen, K.: A new curvature-based image registration model and its fast algorithm. Int. J. Numer. Anal. Model. 13, 969–985 (2016)
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).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11075-018-0486-2