Active Contour Euler Elastica Loss Functions

Official implementations of paper: Learning Euler's Elastica Model for Medical Image Segmentation, and a short version was accepted by ISBI 2021 . * Implemented a novel active contour-based loss function, a combination of region term, length term, and elastica term (mean curvature). * Reimplemented some popular active contour-based loss functions in different ways, such as 3D Active-Contour-Loss based on Sobel filter and max-and min-pool.

Introduction and Some Results

• Pipeline of ACE loss.

  

• 2D results and visualization.

  

• 3D results and visualization.

  

• If you want to use these methods just as constrains (combining with dice loss or ce loss), you can use torch.mean() to replace torch.sum().

Requirements

Some important required packages include: * Pytorch version >= 0.4.1. * Python >= 3.6.

Follow official guidance to install. Pytorch.

Citation

If you find Active Contour Based Loss Functions are useful in your research, please consider to cite:

@inproceedings{chen2020aceloss,
  title={Learning Euler's Elastica Model for Medical Image Segmentation},
  author={Chen, Xu and Luo, Xiangde and Zhao, Yitian and Zhang, Shaoting and Wang, Guotai and Zheng, Yalin},
  journal={arXiv preprint arXiv:2011.00526},
  year={2020}
}

@inproceedings{chen2019learning,
  title={Learning Active Contour Models for Medical Image Segmentation},
  author={Chen, Xu and Williams, Bryan M and Vallabhaneni, Srinivasa R and Czanner, Gabriela and Williams, Rachel and Zheng, Yalin},
  booktitle={Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition},
  pages={11632--11640},
  year={2019}
}

Other Active Contour Based Loss Functions

• Active Contour Loss (ACLoss).
• Geodesic Active Contour Loss (GAC).
• Elastic-Interaction-based Loss (EILoss)

Acknowledgement

• We thank Dr. Jun Ma for instructive discussion of curvature implementation and also thank Mr. Yechong Huang for instructive help during the implementation processing of 3D curvature, Sobel, and Laplace operators.