# FourierLoss: Shape-Aware Loss Function with Fourier Descriptors

arXiv: https://arxiv.org/abs/2309.12106 · HTML: https://mlsanity.com/paper/2309.12106/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 21 Sep 2023.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [The Liver Tumor Segmentation Benchmark (LiTS)](https://mlsanity.com/paper/1901.04056/) (2019)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [ABCNet: Real-time Scene Text Spotting with Adaptive Bezier-Curve Network](https://mlsanity.com/paper/2002.10200/) (2020)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [Deep Distance Transform for Tubular Structure Segmentation in CT Scans](https://mlsanity.com/paper/1912.03383/) (2019)
- [Explicit Shape Encoding for Real-Time Instance Segmentation](https://mlsanity.com/paper/1908.04067/) (2019)
- [Shape-Aware Organ Segmentation by Predicting Signed Distance Maps](https://mlsanity.com/paper/1912.03849/) (2019)
- [Psi-Net: Shape and boundary aware joint multi-task deep network for medical image segmentation](https://mlsanity.com/paper/1902.04099/) (2019)
- [Automatic Liver and Tumor Segmentation of CT and MRI Volumes using Cascaded Fully Convolutional Neural Networks](https://mlsanity.com/paper/1702.05970/) (2017)
- [ShapePU: A New PU Learning Framework Regularized by Global Consistency for Scribble Supervised Cardiac Segmentation](https://mlsanity.com/paper/2206.02118/) (2022)
- [FourierNet: Compact mask representation for instance segmentation using differentiable shape decoders](https://mlsanity.com/paper/2002.02709/) (2020)
- [Prior Information Guided Regularized Deep Learning for Cell Nucleus Detection](https://mlsanity.com/paper/1901.07061/) (2019)
- [BezierSeg: Parametric Shape Representation for Fast Object Segmentation in Medical Images](https://mlsanity.com/paper/2108.00760/) (2021)
- [FCSN: Global Context Aware Segmentation by Learning the Fourier Coefficients of Objects in Medical Images](https://mlsanity.com/paper/2207.14477/) (2022)
- [FourierNet: Shape-Preserving Network for Henle's Fiber Layer Segmentation in Optical Coherence Tomography Images](https://mlsanity.com/paper/2201.06435/) (2022)

## Built on by (most cited first, 1 of 1)

- [Privacy-enhancing Sclera Segmentation Benchmarking Competition: SSBC 2025](https://mlsanity.com/paper/2508.10737/) (2025)

## Abstract (arXiv)

Encoder-decoder networks become a popular choice for various medical image segmentation tasks. When they are trained with a standard loss function, these networks are not explicitly enforced to preserve the shape integrity of an object in an image. However, this ability of the network is important to obtain more accurate results, especially when there is a low-contrast difference between the object and its surroundings. In response to this issue, this work introduces a new shape-aware loss function, which we name FourierLoss. This loss function relies on quantifying the shape dissimilarity between the ground truth and the predicted segmentation maps through the Fourier descriptors calculated on their objects, and penalizing this dissimilarity in network training. Different than the previous studies, FourierLoss offers an adaptive loss function with trainable hyperparameters that control the importance of the level of the shape details that the network is enforced to learn in the training process. This control is achieved by the proposed adaptive loss update mechanism, which end-to-end learns the hyperparameters simultaneously with the network weights by backpropagation. As a result of using this mechanism, the network can dynamically change its attention from learning the general outline of an object to learning the details of its contour points, or vice versa, in different training epochs. Working on 2879 computed tomography images of 93 subjects, our experiments revealed that the proposed adaptive shape-aware loss function led to statistically significantly better results for liver segmentation, compared to its counterparts.