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

arXiv: https://arxiv.org/abs/2410.21004 · HTML: https://mlsanity.com/paper/2410.21004/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 23 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 1 of 1)

- [Harmonic Extension](https://mlsanity.com/paper/1509.06458/) (2015)

## Built on by (most cited first, 1 of 1)

- [The Push-Forward Transform for Continuous and Robust Comparison of Dynamic Shapes](https://mlsanity.com/paper/2608.02306/) (2026)

## Abstract (arXiv)

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.