Conformal invariants for multiply connected surfaces: Application to landmark curve-based brain morphometry analysis.

Area of Science:

• Neuroimaging
• Computational anatomy
• Medical image analysis

Background:

• Landmark curves are used in neuroimaging for surface correspondence and morphometry.
• Existing methods often focus only on landmark curve shape differences.
• A need exists for quantitative measures of surface deformation and conformal equivalence.

Purpose of the Study:

• To propose conformal invariant-based shape indices for quantitative surface deformation measurement.
• To develop a stable method for computing these indices using surface Ricci flow.
• To assess the utility of these indices in detecting brain abnormalities, particularly in Alzheimer's disease.

Main Methods:

• Computing conformal invariant shape indices based on landmark curve induced boundary lengths.
• Utilizing surface Ricci flow to map surfaces to the Poincaré disk (2D parameter domain).
• Applying Hotelling's T² test for statistical analysis of shape index differences.

Main Results:

• The proposed shape indices are invariant under isometric transformations.
• The method successfully detects brain surface abnormalities in synthetic and 3D MRI data.
• Conformal invariant shape indices revealed significant differences between healthy controls and Alzheimer's disease patients, unlike traditional morphometric features.

Conclusions:

• Novel conformal invariant shape indices provide a succinct, intrinsic, and informative measure of surface deformation.
• These indices offer a sensitive biomarker for detecting brain morphometry abnormalities associated with Alzheimer's disease.
• The method enhances neuroimaging analysis tools for disease diagnosis and prognosis.