# FCSN: Global Context Aware Segmentation by Learning the Fourier Coefficients of Objects in Medical Images

arXiv: https://arxiv.org/abs/2207.14477 · HTML: https://mlsanity.com/paper/2207.14477/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 36 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [UNETR: Transformers for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.10504/) (2021)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Dilated Residual Networks](https://mlsanity.com/paper/1705.09914/) (2017)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [ParseNet: Looking Wider to See Better](https://mlsanity.com/paper/1506.04579/) (2015)
- [ABCNet: Real-time Scene Text Spotting with Adaptive Bezier-Curve Network](https://mlsanity.com/paper/2002.10200/) (2020)
- [Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation](https://mlsanity.com/paper/1705.08302/) (2017)
- [Numerical Coordinate Regression with Convolutional Neural Networks](https://mlsanity.com/paper/1801.07372/) (2018)
- [Divergence-Regularized Multi-Agent Actor-Critic](https://mlsanity.com/paper/2110.00304/) (2021)
- [A Regularized Convolutional Neural Network for Semantic Image Segmentation](https://mlsanity.com/paper/1907.05287/) (2019)
- [FourierNet: Compact mask representation for instance segmentation using differentiable shape decoders](https://mlsanity.com/paper/2002.02709/) (2020)
- [BezierSeg: Parametric Shape Representation for Fast Object Segmentation in Medical Images](https://mlsanity.com/paper/2108.00760/) (2021)

## Built on by (most cited first, 3 of 3)

- [FourierLoss: Shape-Aware Loss Function with Fourier Descriptors](https://mlsanity.com/paper/2309.12106/) (2023)
- [A Comprehensive Study on Medical Image Segmentation using Deep Neural Networks](https://mlsanity.com/paper/2506.04121/) (2025)
- [PSP: Harnessing Position and Shape Priors for Cross-Domain Few-Shot Medical Image Segmentation](https://mlsanity.com/paper/2606.28799/) (2026)

## Abstract (arXiv)

The encoder-decoder model is a commonly used Deep Neural Network (DNN) model for medical image segmentation. Conventional encoder-decoder models make pixel-wise predictions focusing heavily on local patterns around the pixel. This makes it challenging to give segmentation that preserves the object's shape and topology, which often requires an understanding of the global context of the object. In this work, we propose a Fourier Coefficient Segmentation Network~(FCSN) -- a novel DNN-based model that segments an object by learning the complex Fourier coefficients of the object's masks. The Fourier coefficients are calculated by integrating over the whole contour. Therefore, for our model to make a precise estimation of the coefficients, the model is motivated to incorporate the global context of the object, leading to a more accurate segmentation of the object's shape. This global context awareness also makes our model robust to unseen local perturbations during inference, such as additive noise or motion blur that are prevalent in medical images. When FCSN is compared with other state-of-the-art models (UNet+, DeepLabV3+, UNETR) on 3 medical image segmentation tasks (ISIC2018, RIMCUP, RIMDISC), FCSN attains significantly lower Hausdorff scores of 19.14 (6%), 17.42 (6%), and 9.16 (14%) on the 3 tasks, respectively. Moreover, FCSN is lightweight by discarding the decoder module, which incurs significant computational overhead. FCSN only requires 22.2M parameters, 82M and 10M fewer parameters than UNETR and DeepLabV3+. FCSN attains inference and training speeds of 1.6ms/img and 6.3ms/img, that is 8× and 3× faster than UNet and UNETR.