# Contour Flow Constraint: Preserving Global Shape Similarity for Deep Learning based Image Segmentation

arXiv: https://arxiv.org/abs/2504.09384 · HTML: https://mlsanity.com/paper/2504.09384/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 13 Apr 2025.

## Builds on (most cited first, 26 of 26)

- [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)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [UNet++: A Nested U-Net Architecture for Medical Image Segmentation](https://mlsanity.com/paper/1807.10165/) (2018)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [Kvasir-SEG: A Segmented Polyp Dataset](https://mlsanity.com/paper/1911.07069/) (2019)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Tversky loss function for image segmentation using 3D fully convolutional deep networks](https://mlsanity.com/paper/1706.05721/) (2017)
- [REFUGE Challenge: A Unified Framework for Evaluating Automated Methods for Glaucoma Assessment from Fundus Photographs](https://mlsanity.com/paper/1910.03667/) (2019)
- [Large Kernel Matters -- Improve Semantic Segmentation by Global Convolutional Network](https://mlsanity.com/paper/1703.02719/) (2017)
- [DCAN: Deep Contour-Aware Networks for Accurate Gland Segmentation](https://mlsanity.com/paper/1604.02677/) (2016)
- [Active Boundary Loss for Semantic Segmentation](https://mlsanity.com/paper/2102.02696/) (2021)
- [Deep Convolutional Neural Networks with Spatial Regularization, Volume and Star-shape Priori for Image Segmentation](https://mlsanity.com/paper/2002.03989/) (2020)
- [Psi-Net: Shape and boundary aware joint multi-task deep network for medical image segmentation](https://mlsanity.com/paper/1902.04099/) (2019)
- [Convexity Shape Prior for Level Set based Image Segmentation Method](https://mlsanity.com/paper/1805.08676/) (2018)
- [TopNet: Topology Preserving Metric Learning for Vessel Tree Reconstruction and Labelling](https://mlsanity.com/paper/2009.08674/) (2020)
- [Convexity Shape Constraints for Image Segmentation](https://mlsanity.com/paper/1509.02122/) (2015)
- [Combining Shape Priors with Conditional Adversarial Networks for Improved Scapula Segmentation in MR images](https://mlsanity.com/paper/1910.08963/) (2019)
- [Conv-MCD: A Plug-and-Play Multi-task Module for Medical Image Segmentation](https://mlsanity.com/paper/1908.05311/) (2019)

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

- [Contour Field based Elliptical Shape Prior for the Segment Anything Model](https://mlsanity.com/paper/2504.12556/) (2025)
- [D-Convexity: A Unified Differentiable Convex Shape Prior via Quasi-Concavity for Data-driven Image Segmentation](https://mlsanity.com/paper/2605.19210/) (2026)

## Abstract (arXiv)

For effective image segmentation, it is crucial to employ constraints informed by prior knowledge about the characteristics of the areas to be segmented to yield favorable segmentation outcomes. However, the existing methods have primarily focused on priors of specific properties or shapes, lacking consideration of the general global shape similarity from a Contour Flow (CF) perspective. Furthermore, naturally integrating this contour flow prior image segmentation model into the activation functions of deep convolutional networks through mathematical methods is currently unexplored. In this paper, we establish a concept of global shape similarity based on the premise that two shapes exhibit comparable contours. Furthermore, we mathematically derive a contour flow constraint that ensures the preservation of global shape similarity. We propose two implementations to integrate the constraint with deep neural networks. Firstly, the constraint is converted to a shape loss, which can be seamlessly incorporated into the training phase for any learning-based segmentation framework. Secondly, we add the constraint into a variational segmentation model and derive its iterative schemes for solution. The scheme is then unrolled to get the architecture of the proposed CFSSnet. Validation experiments on diverse datasets are conducted on classic benchmark deep network segmentation models. The results indicate a great improvement in segmentation accuracy and shape similarity for the proposed shape loss, showcasing the general adaptability of the proposed loss term regardless of specific network architectures. CFSSnet shows robustness in segmenting noise-contaminated images, and inherent capability to preserve global shape similarity.