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Numerical Methods for Image Registration$
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Jan Modersitzki

Print publication date: 2003

Print ISBN-13: 9780198528418

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198528418.001.0001

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OPTIMAL LINEAR REGISTRATION

OPTIMAL LINEAR REGISTRATION

Chapter:
(p.55) 6 OPTIMAL LINEAR REGISTRATION
Source:
Numerical Methods for Image Registration
Author(s):

Jan Modersitzki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528418.003.0006

This chapter investigates the question of how to find an optimal linear transformation based on a distance measure. Popular choices for distance measures such as the sum of squared differences, correlation, and mutual information are discussed. Particular attention is paid to the differentiability of the distance measures. The desired transformation is restricted to a parameterizable space, and as such can be expanded in terms of a linear combination of some basis functions. The registration task is considered as an optimization problem, where the objective is to find the optimal coefficient in the expansion while minimizing the distance measure. The well-known Gauss-Newton method is described and used for numerical optimization. Different examples are used to identify similarities and differences of the distance measures.

Keywords:   parametric registration, distance measures, sum of squared differences, correlation, mutual information, optimization

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