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

CURL-GRADIENT IMAGE WARPING - Introducing Deformation Potentials for Medical Image Registration using Helmholtz Decomposition
Michael Sass Hansen, Rasmus Larsen, Niels Vorgaard Christensen
Abstract	mage 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.
Type	Conference paper [With referee]
Conference	VISAPP 2009 - Proceedings of the Fourth International Conference on Computer Vision Theory and Applications, Lisboa, Portugal,
Year	2010 Vol. 1 pp. 179-185
BibTeX data	[bibtex]
IMM Group(s)	Image Analysis & Computer Graphics