# Lagrange Duality and Compound Multi-Attention Transformer for Semi-Supervised Medical Image Segmentation

arXiv: https://arxiv.org/abs/2409.07793 · HTML: https://mlsanity.com/paper/2409.07793/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 42 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 30 of 34)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Swin-Unet: Unet-like Pure Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2105.05537/) (2021)
- [Multi-Scale Context Aggregation by Dilated Convolutions](https://mlsanity.com/paper/1511.07122/) (2015)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [Self-Supervised Pre-Training of Swin Transformers for 3D Medical Image Analysis](https://mlsanity.com/paper/2111.14791/) (2021)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Semi-Supervised Semantic Segmentation with Cross-Consistency Training](https://mlsanity.com/paper/2003.09005/) (2020)
- [Medical Transformer: Gated Axial-Attention for Medical Image Segmentation](https://mlsanity.com/paper/2102.10662/) (2021)
- [Contrastive learning of global and local features for medical image segmentation with limited annotations](https://mlsanity.com/paper/2006.10511/) (2020)
- [ResUNet-a: a deep learning framework for semantic segmentation of remotely sensed data](https://mlsanity.com/paper/1904.00592/) (2019)
- [TransFuse: Fusing Transformers and CNNs for Medical Image Segmentation](https://mlsanity.com/paper/2102.08005/) (2021)
- [CoTr: Efficiently Bridging CNN and Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.03024/) (2021)
- [nnFormer: Interleaved Transformer for Volumetric Segmentation](https://mlsanity.com/paper/2109.03201/) (2021)
- [Deep Co-Training for Semi-Supervised Image Recognition](https://mlsanity.com/paper/1803.05984/) (2018)
- [SimCVD: Simple Contrastive Voxel-Wise Representation Distillation for Semi-Supervised Medical Image Segmentation](https://mlsanity.com/paper/2108.06227/) (2021)
- [LeViT-UNet: Make Faster Encoders with Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2107.08623/) (2021)
- [ResT: An Efficient Transformer for Visual Recognition](https://mlsanity.com/paper/2105.13677/) (2021)
- [TransAttUnet: Multi-level Attention-guided U-Net with Transformer for Medical Image Segmentation](https://mlsanity.com/paper/2107.05274/) (2021)
- [TransClaw U-Net: Claw U-Net with Transformers for Medical Image Segmentation](https://mlsanity.com/paper/2107.05188/) (2021)

## Built on by (most cited first, 2 of 2)

- [SFormer: SNR-guided Transformer for Underwater Image Enhancement from the Frequency Domain](https://mlsanity.com/paper/2508.18664/) (2025)
- [Forestpest-YOLO: A High-Performance Detection Framework for Small Forestry Pests](https://mlsanity.com/paper/2510.00547/) (2025)

## Abstract (arXiv)

Medical image segmentation, a critical application of semantic segmentation in healthcare, has seen significant advancements through specialized computer vision techniques. While deep learning-based medical image segmentation is essential for assisting in medical diagnosis, the lack of diverse training data causes the long-tail problem. Moreover, most previous hybrid CNN-ViT architectures have limited ability to combine various attentions in different layers of the Convolutional Neural Network. To address these issues, we propose a Lagrange Duality Consistency (LDC) Loss, integrated with Boundary-Aware Contrastive Loss, as the overall training objective for semi-supervised learning to mitigate the long-tail problem. Additionally, we introduce CMAformer, a novel network that synergizes the strengths of ResUNet and Transformer. The cross-attention block in CMAformer effectively integrates spatial attention and channel attention for multi-scale feature fusion. Overall, our results indicate that CMAformer, combined with the feature fusion framework and the new consistency loss, demonstrates strong complementarity in semi-supervised learning ensembles. We achieve state-of-the-art results on multiple public medical image datasets. Example code are available at: urlhttps://github.com/lzeeorno/Lagrange-Duality-and-CMAformer.