Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology.  Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface.  To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization. 
SPHARM
Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biological shape variation and group differences in morphology. 
Procrustes superimposition
Previous SPHARM-MAT techniques use the CALD algorithm to parameterize the mesh surface. 
CALD algorithm
Using Optimal Transport to Improve Spherical Harmonic Quantification of Complex Biological Shapes.The knowledge of the anatomical shape of both gross and microscopic structures is the key to understanding the effects of disease processes on cellular structure.  It starts from initial mapping and performs local and global smoothing methods alternately to control the area and length distortions simultaneously.  However, this parameterization may not be sufficient in complex morphological cases.  To bridge this gap, we propose SPHARM-OT, an enhanced SPHARM surface modeling method using optimal transport (OT) for spherical parameterization.  We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.
OT
Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. 
spherical power diagram