# Fourier Series Coder: A Novel Perspective on Angle Boundary Discontinuity Problem for Oriented Object Detection

arXiv: https://arxiv.org/abs/2604.20281 · HTML: https://mlsanity.com/paper/2604.20281/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 55 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [FCOS: Fully Convolutional One-Stage Object Detection](https://mlsanity.com/paper/1904.01355/) (2019)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Object Detection in Optical Remote Sensing Images: A Survey and A New Benchmark](https://mlsanity.com/paper/1909.00133/) (2019)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [R3Det: Refined Single-Stage Detector with Feature Refinement for Rotating Object](https://mlsanity.com/paper/1908.05612/) (2019)
- [Align Deep Features for Oriented Object Detection](https://mlsanity.com/paper/2008.09397/) (2020)
- [Arbitrary-Oriented Scene Text Detection via Rotation Proposals](https://mlsanity.com/paper/1703.01086/) (2017)
- [Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss](https://mlsanity.com/paper/2101.11952/) (2021)
- [Gliding vertex on the horizontal bounding box for multi-oriented object detection](https://mlsanity.com/paper/1911.09358/) (2019)
- [Learning High-Precision Bounding Box for Rotated Object Detection via Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.01883/) (2021)
- [MMRotate: A Rotated Object Detection Benchmark using PyTorch](https://mlsanity.com/paper/2204.13317/) (2022)
- [Anchor-free Oriented Proposal Generator for Object Detection](https://mlsanity.com/paper/2110.01931/) (2021)
- [Rotation-Sensitive Regression for Oriented Scene Text Detection](https://mlsanity.com/paper/1803.05265/) (2018)
- [Dense Label Encoding for Boundary Discontinuity Free Rotation Detection](https://mlsanity.com/paper/2011.09670/) (2020)
- [Learning Modulated Loss for Rotated Object Detection](https://mlsanity.com/paper/1911.08299/) (2019)
- [The KFIoU Loss for Rotated Object Detection](https://mlsanity.com/paper/2201.12558/) (2022)
- [SCRDet++: Detecting Small, Cluttered and Rotated Objects via Instance-Level Feature Denoising and Rotation Loss Smoothing](https://mlsanity.com/paper/2004.13316/) (2020)
- [Antipodal Robotic Grasping using Generative Residual Convolutional Neural Network](https://mlsanity.com/paper/1909.04810/) (2019)
- [PIoU Loss: Towards Accurate Oriented Object Detection in Complex Environments](https://mlsanity.com/paper/2007.09584/) (2020)
- [Phase-Shifting Coder: Predicting Accurate Orientation in Oriented Object Detection](https://mlsanity.com/paper/2211.06368/) (2022)
- [CFC-Net: A Critical Feature Capturing Network for Arbitrary-Oriented Object Detection in Remote Sensing Images](https://mlsanity.com/paper/2101.06849/) (2021)
- [Gaussian Bounding Boxes and Probabilistic Intersection-over-Union for Object Detection](https://mlsanity.com/paper/2106.06072/) (2021)
- [Rethinking Boundary Discontinuity Problem for Oriented Object Detection](https://mlsanity.com/paper/2305.10061/) (2023)
- [Adaptive Period Embedding for Representing Oriented Objects in Aerial Images](https://mlsanity.com/paper/1906.09447/) (2019)
- [Theoretically Achieving Continuous Representation of Oriented Bounding Boxes](https://mlsanity.com/paper/2402.18975/) (2024)
- [Multi-Grained Angle Representation for Remote Sensing Object Detection](https://mlsanity.com/paper/2209.02884/) (2022)
- [GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection](https://mlsanity.com/paper/2502.01565/) (2025)
- [Wholly-WOOD: Wholly Leveraging Diversified-quality Labels for Weakly-supervised Oriented Object Detection](https://mlsanity.com/paper/2502.09471/) (2025)
- [Fourier Angle Alignment for Oriented Object Detection in Remote Sensing](https://mlsanity.com/paper/2602.23790/) (2026)

## Abstract (arXiv)

With the rapid advancement of intelligent driving and remote sensing, oriented object detection has gained widespread attention. However, achieving high-precision performance is fundamentally constrained by the Angle Boundary Discontinuity (ABD) and Cyclic Ambiguity (CA) problems, which typically cause significant angle fluctuations near periodic boundaries. Although recent studies propose continuous angle coders to alleviate these issues, our theoretical and empirical analyses reveal that state-of-the-art methods still suffer from substantial cyclic errors. We attribute this instability to the structural noise amplification within their non-orthogonal decoding mechanisms. This mathematical vulnerability significantly exacerbates angular deviations, particularly for square-like objects. To resolve this fundamentally, we propose the Fourier Series Coder (FSC), a lightweight plug-and-play component that establishes a continuous, reversible, and mathematically robust angle encoding-decoding paradigm. By rigorously mapping angles onto a minimal orthogonal Fourier basis and explicitly enforcing a geometric manifold constraint, FSC effectively prevents feature modulus collapse. This structurally stabilized representation ensures highly robust phase unwrapping, intrinsically eliminating the need for heuristic truncations while achieving strict boundary continuity and superior noise immunity. Extensive experiments across three large-scale datasets demonstrate that FSC achieves highly competitive overall performance, yielding substantial improvements in high-precision detection. The code will be available at https://github.com/weiminghong/FSC.