Conformal mapping via metric optimization with application for cortical label fusion

Area of Science:

• Medical Imaging and Computational Anatomy
• Neuroscience
• Differential Geometry

Background:

• Conformal maps are crucial for comparing anatomical surfaces.
• Conventional methods often struggle with feature alignment and metric distortion.
• Laplace-Beltrami (LB) eigenfunctions offer powerful intrinsic geometric descriptors.

Purpose of the Study:

• To develop a novel approach for computing conformal maps between anatomical surfaces.
• To enable alignment of anatomical features and minimize metric distortion.
• To create an automated system for cortical labeling.

Main Methods:

• Computed conformal maps in an embedding space using LB eigenfunctions.
• Utilized LB eigenfunctions for global geometry description and feature alignment.
• Developed a group-wise optimal atlas surface with metric optimization.
• Fused labels from multiple atlas surfaces for automated cortical labeling.

Main Results:

• Demonstrated effective alignment of anatomical features on cortical surfaces.
• Achieved greatly reduced metric distortion compared to conventional methods.
• Validated the automated labeling system's performance using leave-one-out cross-validation on 40 labeled surfaces.
• Showcased robustness and effectiveness in analyzing cortical surfaces from Alzheimer's disease patients and normal controls.

Conclusions:

• The novel LB eigenfunction-based conformal mapping approach effectively aligns anatomical features and reduces distortion.
• The developed automated system provides accurate cortical labeling.
• The method is robust and effective for clinical data analysis, including neurodegenerative diseases like Alzheimer's.