# Discretely-constrained deep network for weakly supervised segmentation

arXiv: https://arxiv.org/abs/1908.05770 · HTML: https://mlsanity.com/paper/1908.05770/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2019.

## Built on by (most cited first, 12 of 12)

- [Constrained unsupervised anomaly segmentation](https://mlsanity.com/paper/2203.01671/) (2022)
- [Weakly supervised segmentation with cross-modality equivariant constraints](https://mlsanity.com/paper/2104.02488/) (2021)
- [eX-ViT: A Novel eXplainable Vision Transformer for Weakly Supervised Semantic Segmentation](https://mlsanity.com/paper/2207.05358/) (2022)
- [Mixed-UNet: Refined Class Activation Mapping for Weakly-Supervised Semantic Segmentation with Multi-scale Inference](https://mlsanity.com/paper/2205.04227/) (2022)
- [Segmentation with mixed supervision: Confidence maximization helps knowledge distillation](https://mlsanity.com/paper/2109.10902/) (2021)
- [Weakly Supervised Thoracic Disease Localization via Disease Masks](https://mlsanity.com/paper/2101.09915/) (2021)
- [Looking at the whole picture: constrained unsupervised anomaly segmentation](https://mlsanity.com/paper/2109.00482/) (2021)
- [Weakly Supervised Volumetric Segmentation via Self-taught Shape Denoising Model](https://mlsanity.com/paper/2104.13082/) (2021)
- [Bladder segmentation based on deep learning approaches: current limitations and lessons](https://mlsanity.com/paper/2101.06498/) (2021)
- [Context-aware virtual adversarial training for anatomically-plausible segmentation](https://mlsanity.com/paper/2107.05532/) (2021)
- [AI-based Automatic Segmentation of Prostate on Multi-modality Images: A Review](https://mlsanity.com/paper/2407.06612/) (2024)
- [Multi-Context Temporal Consistent Modeling for Referring Video Object Segmentation](https://mlsanity.com/paper/2501.04939/) (2025)

## Abstract (arXiv)

An efficient strategy for weakly-supervised segmentation is to impose constraints or regularization priors on target regions. Recent efforts have focused on incorporating such constraints in the training of convolutional neural networks (CNN), however this has so far been done within a continuous optimization framework. Yet, various segmentation constraints and regularization can be modeled and optimized more efficiently in a discrete formulation. This paper proposes a method, based on the alternating direction method of multipliers (ADMM) algorithm, to train a CNN with discrete constraints and regularization priors. This method is applied to the segmentation of medical images with weak annotations, where both size constraints and boundary length regularization are enforced. Experiments on a benchmark cardiac segmentation dataset show our method to yield a performance near to full supervision.