Using Optimal Transport to Improve Spherical Harmonic Quantification of Complex Biological Shapes

Area of Science:

• Anatomy
• Medical Imaging
• Computational Geometry

Background:

• Understanding anatomical shape is crucial for disease impact assessment.
• Geometric morphometrics, including Spherical Harmonics (SPHARM), analyze shape variations.
• Existing SPHARM parameterization methods may struggle with complex morphologies.

Purpose of the Study:

• To develop an enhanced SPHARM surface modeling method for improved 3D shape analysis.
• To introduce optimal transport (OT) for spherical parameterization in geometric morphometrics.
• To reduce area distortion in surface reconstruction for complex anatomical structures.

Main Methods:

• Proposed SPHARM-OT method utilizing optimal transport theory.
• Conformal mapping of genus 0 3D objects onto a sphere.
• Minimizing area distortion using spherical power diagrams via optimal transport.

Main Results:

• SPHARM-OT effectively reduces area distortion compared to previous methods.
• The enhanced method yields superior reconstruction results for complex shapes.
• Demonstrated application on human sphenoidal paranasal sinuses.

Conclusions:

• SPHARM-OT offers a more robust approach to 3D surface modeling in geometric morphometrics.
• This method enhances the accuracy of shape analysis, particularly for complex anatomical data.
• Improved shape reconstruction has implications for understanding disease effects on cellular structure.