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CONFORMAL IMAGE REGISTRATION BASED ON CONSTRAINED OPTIMIZATION

Published online by Cambridge University Press:  12 January 2021

S. MARSLAND Open the ORCID record for S. MARSLAND [Opens in a new window] ,
R. I. MCLACHLAN Open the ORCID record for R. I. MCLACHLAN [Opens in a new window]  and
M. Y. TUFAIL Open the ORCID record for M. Y. TUFAIL [Opens in a new window]
S. MARSLAND
Affiliation:
School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand; e-mail: stephen.marsland@vuw.ac.nz.
R. I. MCLACHLAN
Affiliation:
School of Fundamental Sciences, Massey University, Palmerston North, New Zealand; e-mail: r.mclachlan@massey.ac.nz.
M. Y. TUFAIL*
Affiliation:
Department of Mathematics, NED University of Engineering and Technology, Karachi, Pakistan.
*
e-mail: tufail@neduet.edu.pk
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Abstract

Image registration is the process of finding an alignment between two or more images so that their appearances match. It has been widely studied and applied to several fields, including medical imaging and biology, where it is related to morphometrics. In this paper, we present a construction of conformal diffeomorphisms which is based on constrained optimization. We consider a set of different penalty terms that aim to enforce conformality, based on discretizations of the Cauchy–Riemann equations and geometric principles, and demonstrate them experimentally on a variety of images.

Keywords

conformal diffeomorphismsimage registrationconstrained optimizationnumerical computation

MSC classification

Primary: 68U10: Image processing
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 3 , July 2020 , pp. 235 - 255
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Copyright
© Australian Mathematical Society 2021

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