CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition

Michael Sass Hansen, Rasmus Larsen, Niels Vorgaard Christensen

2009

Abstract

Image registration is becoming an increasingly important tool in medical image analysis, and the need to understand deformations within and between subjects often requires analysis of obtained deformation fields. The current paper presents a novel representation of the deformation field based on the Helmholtz decomposition of vector fields. The two decomposed potential fields form a curl free field and a divergence free field. The representation has already proven its worth in fluid modelling and electrostatics, and we show it also has desirable features in image registration and morphometry in particular. The potentials are shown to a offer decoupling of the two potential fields in both elastic and fluid image registration. For morphometry applications, we show that when decomposing the deformation field in symmetric and antisymmetric parts, the vector potential alone describes the vorticity, and the scalar gradient potential gives a first-order approximation to the determinant of the Jacobian. We provide some insight into the behavior of curl and divergence representation of the warp field by constructed examples and by a demonstration on real medical image data. Our theoretical findings are readily observable in our empirical experiment, which further illustrates the benefit of the parametrization.

Paper Citation

in Harvard Style

Sass Hansen M., Larsen R. and Christensen N. (2009). CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition . In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009) ISBN 978-989-8111-69-2, pages 178-185. DOI: 10.5220/0001793301780185

in Bibtex Style

@conference{visapp09,
author={Michael Sass Hansen and Rasmus Larsen and Niels Vorgaard Christensen},
title={CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition},
booktitle={Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)},
year={2009},
pages={178-185},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001793301780185},
isbn={978-989-8111-69-2},
}

in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2009)
TI - CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition
SN - 978-989-8111-69-2
AU - Sass Hansen M.
AU - Larsen R.
AU - Christensen N.
PY - 2009
SP - 178
EP - 185
DO - 10.5220/0001793301780185