Gaussian Combined Distance: A Generic Metric for Object Detection

2025-10-31

AI Summary

Existing metrics for small-object detection suffer from several limitations: IoU is highly sensitive to localization errors; Wasserstein distance lacks scale invariance; and independent optimization of center coordinates and dimensions leads to slow convergence and suboptimal accuracy. To address these issues, this paper proposes the Gaussian Coupled Distance (GCD), a novel metric grounded in Gaussian distribution modeling of bounding boxes. GCD jointly integrates Wasserstein distance and KL divergence, thereby achieving both scale invariance and coupled gradient optimization between center location and size attributes. It serves flexibly as either a regression loss or a label assignment criterion. Extensive experiments demonstrate that GCD achieves state-of-the-art performance on AI-TOD-v2, and significantly outperforms Wasserstein-based baselines on MS-COCO-2017 and Visdrone-2019—validating its strong cross-scale generalization capability and training stability.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Computer Vision: Object Detection & Categorization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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.

Problem

• Improving small object detection by addressing IoU sensitivity to positional deviations
• Overcoming Wasserstein Distance's lack of scale invariance in object detection
• Enhancing model convergence and precision through joint optimization of bounding boxes

Innovation

• GCD metric replaces IoU for small object detection
• GCD enables joint optimization and scale invariance
• GCD achieves state-of-the-art performance across datasets