# Neural ODEs for Image Segmentation with Level Sets

arXiv: https://arxiv.org/abs/1912.11683 · HTML: https://mlsanity.com/paper/1912.11683/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [SegStitch: Multidimensional Transformer for Robust and Efficient Medical Imaging Segmentation](https://mlsanity.com/paper/2408.00496/) (2024)
- [Semantic Segmentation using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2209.08667/) (2022)
- [Differential Motion Evolution for Fine-Grained Motion Deformation in Unsupervised Image Animation](https://mlsanity.com/paper/2110.04658/) (2021)
- [A Neural Ordinary Differential Equation Model for Visualizing Deep Neural Network Behaviors in Multi-Parametric MRI based Glioma Segmentation](https://mlsanity.com/paper/2203.00628/) (2022)

## Abstract (arXiv)

We propose a novel approach for image segmentation that combines Neural Ordinary Differential Equations (NODEs) and the Level Set method. Our approach parametrizes the evolution of an initial contour with a NODE that implicitly learns from data a speed function describing the evolution. In addition, for cases where an initial contour is not available and to alleviate the need for careful choice or design of contour embedding functions, we propose a NODE-based method that evolves an image embedding into a dense per-pixel semantic label space. We evaluate our methods on kidney segmentation (KiTS19) and on salient object detection (PASCAL-S, ECSSD and HKU-IS). In addition to improving initial contours provided by deep learning models while using a fraction of their number of parameters, our approach achieves F scores that are higher than several state-of-the-art deep learning algorithms.