# Detection as Regression: Certified Object Detection by Median Smoothing

arXiv: https://arxiv.org/abs/2007.03730 · HTML: https://mlsanity.com/paper/2007.03730/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2020.

## Built on by (most cited first, 30 of 47)

- [Segment and Complete: Defending Object Detectors against Adversarial Patch Attacks with Robust Patch Detection](https://mlsanity.com/paper/2112.04532/) (2021)
- [Planting Undetectable Backdoors in Machine Learning Models](https://mlsanity.com/paper/2204.06974/) (2022)
- [Boosting Randomized Smoothing with Variance Reduced Classifiers](https://mlsanity.com/paper/2106.06946/) (2021)
- [CROP: Certifying Robust Policies for Reinforcement Learning through Functional Smoothing](https://mlsanity.com/paper/2106.09292/) (2021)
- [Certified Neural Network Watermarks with Randomized Smoothing](https://mlsanity.com/paper/2207.07972/) (2022)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [PatchZero: Defending against Adversarial Patch Attacks by Detecting and Zeroing the Patch](https://mlsanity.com/paper/2207.01795/) (2022)
- [DetectorGuard: Provably Securing Object Detectors against Localized Patch Hiding Attacks](https://mlsanity.com/paper/2102.02956/) (2021)
- [Double Sampling Randomized Smoothing](https://mlsanity.com/paper/2206.07912/) (2022)
- [Center Smoothing: Certified Robustness for Networks with Structured Outputs](https://mlsanity.com/paper/2102.09701/) (2021)
- [Provably Unlearnable Data Examples](https://mlsanity.com/paper/2405.03316/) (2024)
- [Collective Robustness Certificates: Exploiting Interdependence in Graph Neural Networks](https://mlsanity.com/paper/2302.02829/) (2023)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [Incremental Randomized Smoothing Certification](https://mlsanity.com/paper/2305.19521/) (2023)
- [Private and Reliable Neural Network Inference](https://mlsanity.com/paper/2210.15614/) (2022)
- [Invariance-Aware Randomized Smoothing Certificates](https://mlsanity.com/paper/2211.14207/) (2022)
- [Backdoor Attacks against Image-to-Image Networks](https://mlsanity.com/paper/2407.10445/) (2024)
- [A Survey and Evaluation of Adversarial Attacks for Object Detection](https://mlsanity.com/paper/2408.01934/) (2024)
- [Certified Human Trajectory Prediction](https://mlsanity.com/paper/2403.13778/) (2024)
- [(De-)Randomized Smoothing for Decision Stump Ensembles](https://mlsanity.com/paper/2205.13909/) (2022)
- [A Certified Radius-Guided Attack Framework to Image Segmentation Models](https://mlsanity.com/paper/2304.02693/) (2023)
- [Guardians of Image Quality: Benchmarking Defenses Against Adversarial Attacks on Image Quality Metrics](https://mlsanity.com/paper/2408.01541/) (2024)
- [RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothing](https://mlsanity.com/paper/2405.08892/) (2024)
- [Breaking the Barrier: Enhanced Utility and Robustness in Smoothed DRL Agents](https://mlsanity.com/paper/2406.18062/) (2024)
- [Towards Formal Verification of Deep Neural Networks for Object Detection](https://mlsanity.com/paper/2407.01295/) (2024)
- [Certifiably Robust Image Watermark](https://mlsanity.com/paper/2407.04086/) (2024)
- [Adaptive Hierarchical Certification for Segmentation using Randomized Smoothing](https://mlsanity.com/paper/2402.08400/) (2024)
- [PBCAT: Patch-based composite adversarial training against physically realizable attacks on object detection](https://mlsanity.com/paper/2506.23581/) (2025)
- [Multi-head Ensemble of Smoothed Classifiers for Certified Robustness](https://mlsanity.com/paper/2211.10882/) (2022)
- [COMMIT: Certifying Robustness of Multi-Sensor Fusion Systems against Semantic Attacks](https://mlsanity.com/paper/2403.02329/) (2024)

## Abstract (arXiv)

Despite the vulnerability of object detectors to adversarial attacks, very few defenses are known to date. While adversarial training can improve the empirical robustness of image classifiers, a direct extension to object detection is very expensive. This work is motivated by recent progress on certified classification by randomized smoothing. We start by presenting a reduction from object detection to a regression problem. Then, to enable certified regression, where standard mean smoothing fails, we propose median smoothing, which is of independent interest. We obtain the first model-agnostic, training-free, and certified defense for object detection against ℓ2-bounded attacks. The code for all experiments in the paper is available at http://github.com/Ping-C/CertifiedObjectDetection .