### Abstract

The goal of image registration is to determine a transformation of an image so that the resulting image is close to another image. We use an optimal control approach to determine the transformation. We precisely define the optimal control problem that solves the image registration problem, and state the optimality system corresponding to that control problem. We then define finite element discretizations of the optimality system and derive error estimates for the approximate solutions. We also define and prove the convergence of a gradient iterative method for the solution of the discrete optimality system.

Original language | English |
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Pages (from-to) | 1321-1349 |

Number of pages | 29 |

Journal | SIAM Journal on Numerical Analysis |

Volume | 49 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Sep 19 |

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### All Science Journal Classification (ASJC) codes

- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Numerical Analysis*,

*49*(4), 1321-1349. https://doi.org/10.1137/090767674

}

*SIAM Journal on Numerical Analysis*, vol. 49, no. 4, pp. 1321-1349. https://doi.org/10.1137/090767674

**Analysis of finite element discretizations of an optimal control formulation of the image registration problem.** / Lee, Eunjung; Gunzburger, Max.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analysis of finite element discretizations of an optimal control formulation of the image registration problem

AU - Lee, Eunjung

AU - Gunzburger, Max

PY - 2011/9/19

Y1 - 2011/9/19

N2 - The goal of image registration is to determine a transformation of an image so that the resulting image is close to another image. We use an optimal control approach to determine the transformation. We precisely define the optimal control problem that solves the image registration problem, and state the optimality system corresponding to that control problem. We then define finite element discretizations of the optimality system and derive error estimates for the approximate solutions. We also define and prove the convergence of a gradient iterative method for the solution of the discrete optimality system.

AB - The goal of image registration is to determine a transformation of an image so that the resulting image is close to another image. We use an optimal control approach to determine the transformation. We precisely define the optimal control problem that solves the image registration problem, and state the optimality system corresponding to that control problem. We then define finite element discretizations of the optimality system and derive error estimates for the approximate solutions. We also define and prove the convergence of a gradient iterative method for the solution of the discrete optimality system.

UR - http://www.scopus.com/inward/record.url?scp=80052762936&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052762936&partnerID=8YFLogxK

U2 - 10.1137/090767674

DO - 10.1137/090767674

M3 - Article

AN - SCOPUS:80052762936

VL - 49

SP - 1321

EP - 1349

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 4

ER -