Optimized conformal parameterization of cortical surfaces using shape based matching of landmark curves

Area of Science:

• Neuroimaging
• Computational Anatomy
• Medical Image Analysis

Background:

• Cortical surface parameterization is crucial for analyzing brain structure and function.
• Existing methods often struggle to maintain anatomical correspondence, especially for landmark features like sulci curves.
• Accurate registration and correspondence are essential for cross-subject data aggregation and comparison.

Purpose of the Study:

• To develop a novel parameterization method for cortical surfaces that incorporates anatomical landmarks.
• To achieve parameterizations that are both conformal and establish shape-based correspondences for landmark curves.
• To ensure consistent alignment of anatomical features for improved neuroimaging data analysis.

Main Methods:

• Proposed a variational energy functional combining harmonic energy of parameterization maps with shape dissimilarity of landmark curves.
• Modeled the search space of maps as flows of smooth vector fields, constrained by landmark curves.
• Utilized local surface geometry on curves to define a shape measure for guaranteed diffeomorphism between landmarks.

Main Results:

• Generated near-conformal parameterizations that provide shape-based correspondence for landmark curves.
• Demonstrated that the computed maps ensure a shape-based diffeomorphism between landmark curves.
• Experimental results on cortical surfaces show effective alignment of sulcal curves without significant loss of conformality.

Conclusions:

• The proposed method offers a robust approach to cortical surface parameterization with guaranteed anatomical feature correspondence.
• This technique facilitates more accurate averaging and comparison of neuroimaging data across subjects.
• The model's ability to align sulcal curves while preserving conformality advances computational neuroanatomy.