# Single Tensor Cell Segmentation using Scalar Field Representations

arXiv: https://arxiv.org/abs/2511.13947 · HTML: https://mlsanity.com/paper/2511.13947/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Cell Detection with Star-convex Polygons](https://mlsanity.com/paper/1806.03535/) (2018)
- [U-Net and its variants for medical image segmentation: theory and applications](https://mlsanity.com/paper/2011.01118/) (2020)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [MA-Unet: An improved version of Unet based on multi-scale and attention mechanism for medical image segmentation](https://mlsanity.com/paper/2012.10952/) (2020)
- [Multiclass Weighted Loss for Instance Segmentation of Cluttered Cells](https://mlsanity.com/paper/1802.07465/) (2018)
- [Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning](https://mlsanity.com/paper/2501.18708/) (2025)
- [InstanSeg: an embedding-based instance segmentation algorithm optimized for accurate, efficient and portable cell segmentation](https://mlsanity.com/paper/2408.15954/) (2024)
- [IAUNet: Instance-Aware U-Net](https://mlsanity.com/paper/2508.01928/) (2025)

## Abstract (arXiv)

We investigate image segmentation of cells under the lens of scalar fields. Our goal is to learn a continuous scalar field on image domains such that its segmentation produces robust instances for cells present in images. This field is a function parameterized by the trained network, and its segmentation is realized by the watershed method. The fields we experiment with are solutions to the Poisson partial differential equation and a diffusion mimicking the steady-state solution of the heat equation. These solutions are obtained by minimizing just the field residuals, no regularization is needed, providing a robust regression capable of diminishing the adverse impacts of outliers in the training data and allowing for sharp cell boundaries. A single tensor is all that is needed to train a unet thus simplifying implementation, lowering training and inference times, hence reducing energy consumption, and requiring a small memory footprint, all attractive features in edge computing. We present competitive results on public datasets from the literature and show that our novel, simple yet geometrically insightful approach can achieve excellent cell segmentation results.