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.
@article{arxiv.2410.21004,
title = {A Continuous and Interpretable Morphometric for Robust Quantification of Dynamic Biological Shapes},
author = {Roua Rouatbi and Juan-Esteban Suarez Cardona and Alba Villaronga-Luque and Jesse V. Veenvliet and Ivo F. Sbalzarini},
journal= {arXiv preprint arXiv:2410.21004},
year = {2025}
}