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

2026-04-22

AI Summary

This work addresses the severe angular instability in object detection—particularly for square-like objects—caused by angle boundary discontinuity (ABD) and circular ambiguity (CA). To resolve these issues, the authors propose a lightweight, plug-and-play Fourier Series Encoder (FSC), which, for the first time, maps angles onto an orthogonal Fourier basis. By integrating geometric manifold constraints, phase unwrapping, and magnitude stabilization mechanisms, FSC establishes a continuous, invertible, and mathematically robust angle encoding–decoding paradigm that fundamentally eliminates boundary discontinuities and removes the need for heuristic truncation. Experiments demonstrate that FSC significantly enhances high-precision detection performance across three large-scale datasets, effectively suppresses angular bias, and exhibits strong noise robustness alongside seamless boundary continuity.

Technology Category

• Computer Vision: Other Foundations of Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Angle Boundary Discontinuity
• Cyclic Ambiguity
• Oriented Object Detection
• Angle Encoding

Innovation

• Fourier Series Coder
• Angle Boundary Discontinuity
• Oriented Object Detection
• Orthogonal Encoding
• Phase Unwrapping