Conformal image registration based on constrained optimization

S. Marsland; R. I. McLachlan; M. Y. Tufail

doi:10.21914/anziamj.v62.14516

Authors

S. Marsland Victoria University of Wellington https://orcid.org/0000-0002-9568-848X
R. I. McLachlan Massey University https://orcid.org/0000-0003-0392-4957
M. Y. Tufail NED University of Engineering and Technology https://orcid.org/0000-0002-4113-8183

DOI:

https://doi.org/10.21914/anziamj.v62.14516

Keywords:

conformal diffeomorphisms, image registration, constrained optimization, numerical computation

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.

doi:10.1017/S144618112000022X

Author Biographies

S. Marsland, Victoria University of Wellington

School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand.

R. I. McLachlan, Massey University

School of Fundamental Sciences, Massey University, Palmerston North, New Zealand.

M. Y. Tufail, NED University of Engineering and Technology

Assistant Professor, Department of Mathematics, NED University of Engineering and Technology, Karachi, Pakistan.