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

Area of Science:

• Continuum mechanics
• Medical image analysis
• Computational imaging

Background:

• Image registration is crucial for analyzing medical images, particularly for understanding cardiac motion.
• Existing methods like hyperelastic warping face challenges with noise and regularization sensitivity.
• A regularization method with a strong mechanical basis is needed for robust cardiac image analysis.

Purpose of the Study:

• To propose a novel continuum finite strain formulation for equilibrium gap regularization in image registration.
• To develop a robust and effective method for cardiac image analysis using mechanical principles.
• To provide a freely available computational tool for researchers.

Main Methods:

• Developed a finite strain formulation for equilibrium gap regularization.
• Applied the finite element method for consistent linearization and discretization.
• Implemented the method using FEniCS & VTK, releasing it as an open-source Python library.

Main Results:

• The equilibrated warping method demonstrates effectiveness and robustness in image registration.
• Minimal impact of regularization strength and image noise on motion tracking was observed.
• The method successfully extracts key deformation features from cardiac MRI, both tagged and untagged.

Conclusions:

• Equilibrated warping offers a mechanically grounded and robust approach to image registration for cardiac analysis.
• This method outperforms traditional strain-based regularization techniques in terms of noise and parameter sensitivity.
• The freely available library facilitates further research and application in cardiac imaging.