# Reformulating Level Sets as Deep Recurrent Neural Network Approach to Semantic Segmentation

arXiv: https://arxiv.org/abs/1704.03593 · HTML: https://mlsanity.com/paper/1704.03593/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2017.

## Built on by (most cited first, 16 of 16)

- [Deep Reinforcement Learning in Computer Vision: A Comprehensive Survey](https://mlsanity.com/paper/2108.11510/) (2021)
- [BiMaL: Bijective Maximum Likelihood Approach to Domain Adaptation in Semantic Scene Segmentation](https://mlsanity.com/paper/2108.03267/) (2021)
- [DirecFormer: A Directed Attention in Transformer Approach to Robust Action Recognition](https://mlsanity.com/paper/2203.10233/) (2022)
- [OTAdapt: Optimal Transport-based Approach For Unsupervised Domain Adaptation](https://mlsanity.com/paper/2205.10738/) (2022)
- [Self-supervised Domain Adaptation in Crowd Counting](https://mlsanity.com/paper/2206.03431/) (2022)
- [Self-Ensembling GAN for Cross-Domain Semantic Segmentation](https://mlsanity.com/paper/2112.07999/) (2021)
- [A hybrid inference system for improved curvature estimation in the level-set method using machine learning](https://mlsanity.com/paper/2104.02951/) (2021)
- [Deep Active Contours Using Locally Controlled Distance Vector Flow](https://mlsanity.com/paper/2105.08447/) (2021)
- [Error-correcting neural networks for semi-Lagrangian advection in the level-set method](https://mlsanity.com/paper/2110.11611/) (2021)
- [Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework](https://mlsanity.com/paper/2505.05806/) (2025)
- [Deep Level Set for Box-supervised Instance Segmentation in Aerial Images](https://mlsanity.com/paper/2112.03451/) (2021)
- [Machine learning algorithms for three-dimensional mean-curvature computation in the level-set method](https://mlsanity.com/paper/2208.09047/) (2022)
- [Bayesian Fusion of Active Contour Models and ConvNet Priors for Standing Dead Tree Segmentation](https://mlsanity.com/paper/2410.07421/) (2024)
- [OmegaSFormer: Dual-Modal Omega-like Super-Resolution Transformer Network for Cross-scale and High-accuracy Terraced Field Vectorization Extraction](https://mlsanity.com/paper/2411.17088/) (2024)
- [Mask Proposal Voting Based on Geodesic Framework for Robust Image Segmentation](https://mlsanity.com/paper/2606.14912/) (2026)
- [FPicker: Topology-Guided Evolution for Filament Tracing in Low-SNR Microscopy](https://mlsanity.com/paper/2609.08305/) (2026)

## Abstract (arXiv)

Variational Level Set (LS) has been a widely used method in medical segmentation. However, it is limited when dealing with multi-instance objects in the real world. In addition, its segmentation results are quite sensitive to initial settings and highly depend on the number of iterations. To address these issues and boost the classic variational LS methods to a new level of the learnable deep learning approaches, we propose a novel definition of contour evolution named Recurrent Level Set (RLS)} to employ Gated Recurrent Unit under the energy minimization of a variational LS functional. The curve deformation process in RLS is formed as a hidden state evolution procedure and updated by minimizing an energy functional composed of fitting forces and contour length. By sharing the convolutional features in a fully end-to-end trainable framework, we extend RLS to Contextual RLS (CRLS) to address semantic segmentation in the wild. The experimental results have shown that our proposed RLS improves both computational time and segmentation accuracy against the classic variations LS-based method, whereas the fully end-to-end system CRLS achieves competitive performance compared to the state-of-the-art semantic segmentation approaches.