# FourierMask: Instance Segmentation using Fourier Mapping in Implicit Neural Networks

arXiv: https://arxiv.org/abs/2112.12535 · HTML: https://mlsanity.com/paper/2112.12535/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 28 references that are in the map.
- First posted on arXiv 23 Dec 2021.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [YOLACT: Real-time Instance Segmentation](https://mlsanity.com/paper/1904.02689/) (2019)
- [PointRend: Image Segmentation as Rendering](https://mlsanity.com/paper/1912.08193/) (2019)
- [Mask Scoring R-CNN](https://mlsanity.com/paper/1903.00241/) (2019)
- [CenterMask : Real-Time Anchor-Free Instance Segmentation](https://mlsanity.com/paper/1911.06667/) (2019)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [Boundary IoU: Improving Object-Centric Image Segmentation Evaluation](https://mlsanity.com/paper/2103.16562/) (2021)
- [Bottom-up Object Detection by Grouping Extreme and Center Points](https://mlsanity.com/paper/1901.08043/) (2019)
- [PolyTransform: Deep Polygon Transformer for Instance Segmentation](https://mlsanity.com/paper/1912.02801/) (2019)
- [ShapeMask: Learning to Segment Novel Objects by Refining Shape Priors](https://mlsanity.com/paper/1904.03239/) (2019)
- [Explicit Shape Encoding for Real-Time Instance Segmentation](https://mlsanity.com/paper/1908.04067/) (2019)
- [Dense RepPoints: Representing Visual Objects with Dense Point Sets](https://mlsanity.com/paper/1912.11473/) (2019)
- [EmbedMask: Embedding Coupling for One-stage Instance Segmentation](https://mlsanity.com/paper/1912.01954/) (2019)
- [FourierNet: Compact mask representation for instance segmentation using differentiable shape decoders](https://mlsanity.com/paper/2002.02709/) (2020)

## Abstract (arXiv)

We present FourierMask, which employs Fourier series combined with implicit neural representations to generate instance segmentation masks. We apply a Fourier mapping (FM) to the coordinate locations and utilize the mapped features as inputs to an implicit representation (coordinate-based multi-layer perceptron (MLP)). FourierMask learns to predict the coefficients of the FM for a particular instance, and therefore adapts the FM to a specific object. This allows FourierMask to be generalized to predict instance segmentation masks from natural images. Since implicit functions are continuous in the domain of input coordinates, we illustrate that by sub-sampling the input pixel coordinates, we can generate higher resolution masks during inference. Furthermore, we train a renderer MLP (FourierRend) on the uncertain predictions of FourierMask and illustrate that it significantly improves the quality of the masks. FourierMask shows competitive results on the MS COCO dataset compared to the baseline Mask R-CNN at the same output resolution and surpasses it on higher resolution.