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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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THE MATHEMATICAL SETTING

THE MATHEMATICAL SETTING

Chapter:
(p.14) 3 THE MATHEMATICAL SETTING
Source:
Numerical Methods for Image Registration
Author(s):

Jan Modersitzki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198528418.003.0003

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as next-neighbour, d-linear, spline, sinc, and wavelet interpolations are discussed. For the functional setting, the square-integrable functions, point evaluation functionals, and various derivative operators are formally introduced. A general setting for image transformations is presented. Using this setting, a formal description of the image registration problem in continuous space is given. Restricted transformations like rigid, affine-linear, polynomial, and B-spline transformations are examined, and the Lagrangian and Eulerian frames for template transformations are discussed.

Keywords:   basic quantities, mathematical preliminaries, image interpolation, image registration, Euler frame, Lagrange frame

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