# FourierNet: Compact mask representation for instance segmentation using differentiable shape decoders

arXiv: https://arxiv.org/abs/2002.02709 · HTML: https://mlsanity.com/paper/2002.02709/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2020.

## Built on by (most cited first, 8 of 8)

- [INSTA-YOLO: Real-Time Instance Segmentation](https://mlsanity.com/paper/2102.06777/) (2021)
- [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)
- [SCR: Smooth Contour Regression with Geometric Priors](https://mlsanity.com/paper/2202.03784/) (2022)
- [DPPD: Deformable Polar Polygon Object Detection](https://mlsanity.com/paper/2304.02250/) (2023)
- [FourierLoss: Shape-Aware Loss Function with Fourier Descriptors](https://mlsanity.com/paper/2309.12106/) (2023)
- [FourierMask: Instance Segmentation using Fourier Mapping in Implicit Neural Networks](https://mlsanity.com/paper/2112.12535/) (2021)
- [CenterDisks: Real-time instance segmentation with disk covering](https://mlsanity.com/paper/2403.03296/) (2024)

## Abstract (arXiv)

We present FourierNet, a single shot, anchor-free, fully convolutional instance segmentation method that predicts a shape vector. Consequently, this shape vector is converted into the masks' contour points using a fast numerical transform. Compared to previous methods, we introduce a new training technique, where we utilize a differentiable shape decoder, which manages the automatic weight balancing of the shape vector's coefficients. We used the Fourier series as a shape encoder because of its coefficient interpretability and fast implementation. FourierNet shows promising results compared to polygon representation methods, achieving 30.6 mAP on the MS COCO 2017 benchmark. At lower image resolutions, it runs at 26.6 FPS with 24.3 mAP. It reaches 23.3 mAP using just eight parameters to represent the mask (note that at least four parameters are needed for bounding box prediction only). Qualitative analysis shows that suppressing a reasonable proportion of higher frequencies of Fourier series, still generates meaningful masks. These results validate our understanding that lower frequency components hold higher information for the segmentation task, and therefore, we can achieve a compressed representation. Code is available at: github.com/cogsys-tuebingen/FourierNet.