# Rethinking Boundary Discontinuity Problem for Oriented Object Detection

arXiv: https://arxiv.org/abs/2305.10061 · HTML: https://mlsanity.com/paper/2305.10061/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 30 of 35)

- [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)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Objects as Points](https://mlsanity.com/paper/1904.07850/) (2019)
- [DOTA: A Large-scale Dataset for Object Detection in Aerial Images](https://mlsanity.com/paper/1711.10398/) (2017)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [UnitBox: An Advanced Object Detection Network](https://mlsanity.com/paper/1608.01471/) (2016)
- [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)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [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)
- [IoU Loss for 2D/3D Object Detection](https://mlsanity.com/paper/1908.03851/) (2019)
- [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)
- [Dynamic Refinement Network for Oriented and Densely Packed Object Detection](https://mlsanity.com/paper/2005.09973/) (2020)
- [Dynamic Anchor Learning for Arbitrary-Oriented Object Detection](https://mlsanity.com/paper/2012.04150/) (2020)
- [Oriented Object Detection in Aerial Images with Box Boundary-Aware Vectors](https://mlsanity.com/paper/2008.07043/) (2020)
- [SCRDet++: Detecting Small, Cluttered and Rotated Objects via Instance-Level Feature Denoising and Rotation Loss Smoothing](https://mlsanity.com/paper/2004.13316/) (2020)
- [PIoU Loss: Towards Accurate Oriented Object Detection in Complex Environments](https://mlsanity.com/paper/2007.09584/) (2020)
- [R2CNN: Rotational Region CNN for Orientation Robust Scene Text Detection](https://mlsanity.com/paper/1706.09579/) (2017)
- [Oriented Objects as pairs of Middle Lines](https://mlsanity.com/paper/1912.10694/) (2019)
- [Phase-Shifting Coder: Predicting Accurate Orientation in Oriented Object Detection](https://mlsanity.com/paper/2211.06368/) (2022)

## Built on by (most cited first, 15 of 15)

- [RSAR: Restricted State Angle Resolver and Rotated SAR Benchmark](https://mlsanity.com/paper/2501.04440/) (2025)
- [Theoretically Achieving Continuous Representation of Oriented Bounding Boxes](https://mlsanity.com/paper/2402.18975/) (2024)
- [OpenRSD: Towards Open-prompts for Object Detection in Remote Sensing Images](https://mlsanity.com/paper/2503.06146/) (2025)
- [GauCho: Gaussian Distributions with Cholesky Decomposition for Oriented Object Detection](https://mlsanity.com/paper/2502.01565/) (2025)
- [Open-Text Aerial Detection: A Unified Framework For Aerial Visual Grounding And Detection](https://mlsanity.com/paper/2602.07827/) (2026)
- [Real-Time Oriented Object Detection Transformer in Remote Sensing Images](https://mlsanity.com/paper/2603.15497/) (2026)
- [Active-SAOOD: Active Sparsely Annotated Oriented Object Detection in Remote Sensing Images](https://mlsanity.com/paper/2605.10162/) (2026)
- [Structure Tensor Representation for Robust Oriented Object Detection](https://mlsanity.com/paper/2411.10497/) (2024)
- [S2Teacher: Step-by-step Teacher for Sparsely Annotated Oriented Object Detection](https://mlsanity.com/paper/2504.11111/) (2025)
- [Semantic-decoupled Spatial Partition Guided Point-supervised Oriented Object Detection](https://mlsanity.com/paper/2506.10601/) (2025)
- [ABBSPO: Adaptive Bounding Box Scaling and Symmetric Prior based Orientation Prediction for Detecting Aerial Image Objects](https://mlsanity.com/paper/2512.10031/) (2025)
- [Image Rotation Angle Estimation: Comparing Circular-Aware Methods](https://mlsanity.com/paper/2603.25351/) (2026)
- [Fourier Series Coder: A Novel Perspective on Angle Boundary Discontinuity Problem for Oriented Object Detection](https://mlsanity.com/paper/2604.20281/) (2026)
- [From Full Boards to Tiny Defects: Scale-Aware Tile Inference with Topology-Aware Merging for High-Resolution PCB Defect Detection](https://mlsanity.com/paper/2605.24726/) (2026)
- [Geometry Meets Semantics: Fractional Gradient Stabilization for Semantic-Driven Bounding Box Optimization in Visual Detection Tasks](https://mlsanity.com/paper/2607.23530/) (2026)

## Abstract (arXiv)

Oriented object detection has been developed rapidly in the past few years, where rotation equivariance is crucial for detectors to predict rotated boxes. It is expected that the prediction can maintain the corresponding rotation when objects rotate, but severe mutation in angular prediction is sometimes observed when objects rotate near the boundary angle, which is well-known boundary discontinuity problem. The problem has been long believed to be caused by the sharp loss increase at the angular boundary, and widely used joint-optim IoU-like methods deal with this problem by loss-smoothing. However, we experimentally find that even state-of-the-art IoU-like methods actually fail to solve the problem. On further analysis, we find that the key to solution lies in encoding mode of the smoothing function rather than in joint or independent optimization. In existing IoU-like methods, the model essentially attempts to fit the angular relationship between box and object, where the break point at angular boundary makes the predictions highly unstable.To deal with this issue, we propose a dual-optimization paradigm for angles. We decouple reversibility and joint-optim from single smoothing function into two distinct entities, which for the first time achieves the objectives of both correcting angular boundary and blending angle with other parameters.Extensive experiments on multiple datasets show that boundary discontinuity problem is well-addressed. Moreover, typical IoU-like methods are improved to the same level without obvious performance gap. The code is available at https://github.com/hangxu-cv/cvpr24acm.