Authors:
Michael Sass Hansen
1
;
Rasmus Larsen
1
and
Niels Vorgaard Christensen
2
Affiliations:
1
Technical University of Denmark, Denmark
;
2
University of Copenhagen, Denmark
Keyword(s):
Image registration, Morphometry, Helmholtz decomposition.
Related
Ontology
Subjects/Areas/Topics:
Computer Vision, Visualization and Computer Graphics
;
Feature Extraction
;
Features Extraction
;
Image and Video Analysis
;
Image Registration
;
Informatics in Control, Automation and Robotics
;
Signal Processing, Sensors, Systems Modeling and Control
;
Statistical Approach
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.
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