Fast and interpretable quantification of biological shape heterogeneity via stratified Wasserstein kernel

Area of Science:

• Computational Biology
• Biophysics
• Data Science

Background:

• Modern imaging generates large datasets of cellular structures.
• Existing methods for shape comparison are insufficient for large-scale population analysis.
• Principled methods are needed for isometry-invariant shape comparison.

Purpose of the Study:

• Introduce a novel framework for analyzing and comparing shapes from biological imaging.
• Enable statistically rigorous, population-level shape analysis for large datasets.
• Provide a tool for identifying key morphological differences in biological populations.

Main Methods:

• Developed the stratified Wasserstein framework for shape analysis.
• Embedded shapes as point clouds into Euclidean space using ranked local distance profiles.
• Utilized kernel methods for nonparametric hypothesis testing and population analysis.
• Created a sample-based estimator supporting large datasets in near-quadratic time.

Main Results:

• The framework provides an isometry-invariant Euclidean distance and a positive-definite kernel.
• Demonstrated applicability to large-scale 2D cancer cell contour data, quantifying population discrepancies.
• Identified representative cells contributing to observed differences in cancer cell populations.
• Analyzed 3D cell envelope and nucleus volumes to reveal progression patterns and morphological changes.

Conclusions:

• The stratified Wasserstein framework is a simple, principled tool for population-level biological shape analysis.
• The method offers theoretical guarantees and interpretability for shape comparison tasks.
• Potential impact across computational imaging, data science, and diverse biological research domains.