Equilibrated warping: Finite element image registration with finite strain equilibrium gap regularization

Medical Image Analysis
M GenetS Kozerke

Abstract

In this paper, we propose a novel continuum finite strain formulation of the equilibrium gap regularization for image registration. The equilibrium gap regularization essentially penalizes any deviation from the solution of a hyperelastic body in equilibrium with arbitrary loads prescribed at the boundary. It thus represents a regularization with strong mechanical basis, especially suited for cardiac image analysis. We describe the consistent linearization and discretization of the regularized image registration problem, in the framework of the finite elements method. The method is implemented using FEniCS & VTK, and distributed as a freely available python library. We show that the equilibrated warping method is effective and robust: regularization strength and image noise have minimal impact on motion tracking, especially when compared to strain-based regularization methods such as hyperelastic warping. We also show that equilibrated warping is able to extract main deformation features on both tagged and untagged cardiac magnetic resonance images.

Citations

Nov 2, 2019·American Journal of Physiology. Heart and Circulatory Physiology·Henrik FinsbergSamuel T Wall
Dec 22, 2019·Bioengineering·Wenqiang Liu, Zhijie Wang
Jan 1, 2021·Medical Image Analysis·Luigi E PerottiDaniel B Ennis
Apr 27, 2021·Pediatric Cardiology·Daniel Alexander CastellanosRadomir Chabiniok
Jul 4, 2021·The Canadian Journal of Cardiology·Maria GussevaRadomír Chabiniok

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