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. Geometric morphometric methods, such as Procrustes superimposition, and Spherical Harmonics (SPHARM), have been used to capture the biolo...

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Published in2022 IEEE International Conference on Bioinformatics and Biomedicine (BIBM) Vol. 2022; pp. 1255 - 1261
Main Authors Wang, Zexuan, Yang, Wenxi, Ryan, Katharine, Garai, Sumita, Auerbach, Benjamin M, Shen, Li
Format Conference Proceeding Journal Article
LanguageEnglish
Published United States IEEE 01.12.2022
Subjects
Distortion
Harmonic analysis
Morphology
paranasal sinus
principal component analysis
Shape
shape analysis
Spherical harmonics
spherical optimal transport
Surface morphology
Surface reconstruction
Three-dimensional displays
paranasal sinus
shape analysis
spherical optimal transport
Spherical harmonics
principal component analysis
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Summary: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. 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. 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. First, the genus 0 3D objects are conformally mapped onto a sphere. Then the optimal transport theory via spherical power diagram is introduced to minimize the area distortion. This new algorithm can effectively reduce the area distortion and lead to a better reconstruction result. We demonstrate the effectiveness of the method by applying it to the human sphenoidal paranasal sinuses.
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Z Wang, W Yang and K. Ryan contributed equally to this work.
ISSN:2156-1125
2156-1133
DOI:10.1109/BIBM55620.2022.9995036