# Gaussian Combined Distance: A Generic Metric for Object Detection

arXiv: https://arxiv.org/abs/2510.27649 · HTML: https://mlsanity.com/paper/2510.27649/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 31 Oct 2025.

## 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)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [MMDetection: Open MMLab Detection Toolbox and Benchmark](https://mlsanity.com/paper/1906.07155/) (2019)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [UnitBox: An Advanced Object Detection Network](https://mlsanity.com/paper/1608.01471/) (2016)
- [Rethinking Rotated Object Detection with Gaussian Wasserstein Distance Loss](https://mlsanity.com/paper/2101.11952/) (2021)
- [Learning High-Precision Bounding Box for Rotated Object Detection via Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.01883/) (2021)
- [An Analysis of Scale Invariance in Object Detection - SNIP](https://mlsanity.com/paper/1711.08189/) (2017)
- [SNIPER: Efficient Multi-Scale Training](https://mlsanity.com/paper/1805.09300/) (2018)
- [Inside-Outside Net: Detecting Objects in Context with Skip Pooling and Recurrent Neural Networks](https://mlsanity.com/paper/1512.04143/) (2015)
- [Perceptual Generative Adversarial Networks for Small Object Detection](https://mlsanity.com/paper/1706.05274/) (2017)
- [M2Det: A Single-Shot Object Detector based on Multi-Level Feature Pyramid Network](https://mlsanity.com/paper/1811.04533/) (2018)
- [Scale Match for Tiny Person Detection](https://mlsanity.com/paper/1912.10664/) (2019)
- [Focal and Efficient IOU Loss for Accurate Bounding Box Regression](https://mlsanity.com/paper/2101.08158/) (2021)
- [Detecting tiny objects in aerial images: A normalized Wasserstein distance and a new benchmark](https://mlsanity.com/paper/2206.13996/) (2022)

## Built on by (most cited first, 1 of 1)

- [RFAssigner: A Generic Label Assignment Strategy for Dense Object Detection](https://mlsanity.com/paper/2601.01240/) (2026)

## Abstract (arXiv)

In object detection, a well-defined similarity metric can significantly enhance model performance. Currently, the IoU-based similarity metric is the most commonly preferred choice for detectors. However, detectors using IoU as a similarity metric often perform poorly when detecting small objects because of their sensitivity to minor positional deviations. To address this issue, recent studies have proposed the Wasserstein Distance as an alternative to IoU for measuring the similarity of Gaussian-distributed bounding boxes. However, we have observed that the Wasserstein Distance lacks scale invariance, which negatively impacts the model's generalization capability. Additionally, when used as a loss function, its independent optimization of the center attributes leads to slow model convergence and unsatisfactory detection precision. To address these challenges, we introduce the Gaussian Combined Distance (GCD). Through analytical examination of GCD and its gradient, we demonstrate that GCD not only possesses scale invariance but also facilitates joint optimization, which enhances model localization performance. Extensive experiments on the AI-TOD-v2 dataset for tiny object detection show that GCD, as a bounding box regression loss function and label assignment metric, achieves state-of-the-art performance across various detectors. We further validated the generalizability of GCD on the MS-COCO-2017 and Visdrone-2019 datasets, where it outperforms the Wasserstein Distance across diverse scales of datasets. Code is available at https://github.com/MArKkwanGuan/mmdet-GCD.