# Placental Flattening via Volumetric Parameterization

arXiv: https://arxiv.org/abs/1903.05044 · HTML: https://mlsanity.com/paper/1903.05044/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2019.

## Built on by (most cited first, 7 of 7)

- [Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamics](https://mlsanity.com/paper/2304.14369/) (2023)
- [Volumetric Parameterization of the Placenta to a Flattened Template](https://mlsanity.com/paper/2111.07900/) (2021)
- [Consistency Regularization Improves Placenta Segmentation in Fetal EPI MRI Time Series](https://mlsanity.com/paper/2310.03870/) (2023)
- [Shape-aware Segmentation of the Placenta in BOLD Fetal MRI Time Series](https://mlsanity.com/paper/2312.05148/) (2023)
- [Automatic 3D Multi-modal Ultrasound Segmentation of Human Placenta using Fusion Strategies and Deep Learning](https://mlsanity.com/paper/2401.09638/) (2024)
- [Aligning Fetal Anatomy with Kinematic Tree Log-Euclidean PolyRigid Transforms](https://mlsanity.com/paper/2603.02371/) (2026)
- [Volumetrically Consistent Implicit Atlas Learning via Neural Diffeomorphic Flow for Placenta MRI](https://mlsanity.com/paper/2603.16078/) (2026)

## Abstract (arXiv)

We present a volumetric mesh-based algorithm for flattening the placenta to a canonical template to enable effective visualization of local anatomy and function. Monitoring placental function in vivo promises to support pregnancy assessment and to improve care outcomes. We aim to alleviate visualization and interpretation challenges presented by the shape of the placenta when it is attached to the curved uterine wall. To do so, we flatten the volumetric mesh that captures placental shape to resemble the well-studied ex vivo shape. We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume. Local injectivity is enforced via constrained line search during gradient descent. We evaluate the proposed method on 28 placenta shapes extracted from MRI images in a clinical study of placental function. We achieve sub-voxel accuracy in mapping the boundary of the placenta to the template while successfully controlling distortion throughout the volume. We illustrate how the resulting mapping of the placenta enhances visualization of placental anatomy and function. Our code is freely available at https://github.com/mabulnaga/placenta-flattening .