A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes

TL;DR

The paper introduces PF-SDM, a mathematically smooth, interpretable shape descriptor for biomedical imaging that captures geometric, topological, and dynamic properties, enhancing shape analysis and prediction tasks.

Contribution

It presents the PF-SDM, a novel shape quantification method that encodes geometric and topological features, extends to temporal dynamics, and fuses spatial intensity data for improved biomedical shape analysis.

Findings

Outperforms CNN baseline in accuracy and speed for predicting body-axis formation.

Provides robust, interpretable features for shape comparison and machine learning.

Extends to dynamic and multi-modal shape analysis in biomedical imaging.

Abstract

We introduce the Push-Forward Signed Distance Morphometric (PF-SDM) for shape quantification in biomedical imaging. The PF-SDM compactly encodes geometric and topological properties of closed shapes, including their skeleton and symmetries. This provides robust and interpretable features for shape comparison and machine learning. The PF-SDM is mathematically smooth, providing access to gradients and differential-geometric quantities. It also extends to temporal dynamics and allows fusing spatial intensity distributions, such as genetic markers, with shape dynamics. We present the PF-SDM theory, benchmark it on synthetic data, and apply it to predicting body-axis formation in mouse gastruloids, outperforming a CNN baseline in both accuracy and speed.