Hyperbolic harmonic brain surface registration with curvature-based landmark matching.

Area of Science:

• Neuroimaging
• Computational Anatomy
• Differential Geometry

Background:

• Accurate brain cortical surface registration is crucial for analyzing functional and anatomical data across subjects.
• Harmonic mappings offer stability but can fail to produce diffeomorphic registrations when constrained by landmarks.
• Existing methods struggle with landmark constraints, leading to invalid brain registrations.

Purpose of the Study:

• To develop a robust brain registration method that guarantees diffeomorphic mappings while enforcing landmark constraints.
• To improve the accuracy and reliability of inter-subject brain registration for neuroimaging studies.

Main Methods:

• Utilized hyperbolic geometry by changing the Riemannian metric on the target cortical surface.
• Enforced landmark constraints as boundary matching conditions within the hyperbolic framework.
• Employed computational algorithms based on Ricci flow and hyperbolic heat diffusion.

Main Results:

• The proposed method guarantees diffeomorphic registrations, ensuring valid anatomical mappings.
• Achieved superior landmark alignment compared to traditional methods.
• Demonstrated reduced area distortion and improved overlapping of regions of interest.

Conclusions:

• Employing a hyperbolic metric is a viable strategy to ensure diffeomorphic harmonic mappings in constrained brain registration.
• This approach enhances the quality and validity of inter-subject brain registration for neuroimaging applications.