{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T18:27:56Z","timestamp":1772821676567,"version":"3.50.1"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T00:00:00Z","timestamp":1767657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shaanxi Natural Science Basic Research Program","award":["S2024-JC-YB-2227"],"award-info":[{"award-number":["S2024-JC-YB-2227"]}]},{"name":"Shaanxi Natural Science Basic Research Program","award":["2024JC-YBQN-0575"],"award-info":[{"award-number":["2024JC-YBQN-0575"]}]},{"name":"Xi\u2019an Shiyou University, School of Electronic Engineering"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Bounding box regression (BBR) loss plays a critical role in object detection within computer vision. Existing BBR loss functions are typically based on the Intersection over Union (IoU) between predicted and ground truth boxes. However, these methods neither account for the effect of predicted box scale on regression nor effectively address the drift problem inherent in BBR. To overcome these limitations, this paper introduces a novel BBR loss function, termed Gaussian Adaptive Ochiai BBR loss (GAOC), which combines the Ochiai Coefficient (OC) with a Gaussian Adaptive (GA) distribution. The OC component normalizes by the square root of the product of bounding box dimensions, ensuring scale invariance. Meanwhile, the GA distribution models the distance between the top-left and bottom-right corners (TL\/BR) coordinates of predicted and ground truth boxes, enabling a similarity measure that reduces sensitivity to positional deviations. This design enhances detection robustness and accuracy. GAOC was integrated into YOLOv5 and RT-DETR and evaluated on the PASCAL VOC and MS COCO 2017 benchmarks. Experimental results demonstrate that GAOC consistently outperforms existing BBR loss functions, offering a more effective solution.<\/jats:p>","DOI":"10.3390\/s26020368","type":"journal-article","created":{"date-parts":[[2026,1,6]],"date-time":"2026-01-06T13:49:46Z","timestamp":1767707386000},"page":"368","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["GAOC: A Gaussian Adaptive Ochiai Loss for Bounding Box Regression"],"prefix":"10.3390","volume":"26","author":[{"given":"Binbin","family":"Han","sequence":"first","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710312, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Tang","sequence":"additional","affiliation":[{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"},{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiuxu","family":"Song","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710312, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710312, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8360-2709","authenticated-orcid":false,"given":"Yi","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Electronic Engineering, Xi\u2019an Shiyou University, Xi\u2019an 710312, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/s11227-024-06765-8","article-title":"YOLO-SS: Optimizing YOLO for enhanced small object detection in remote sensing imagery","volume":"81","author":"Tang","year":"2025","journal-title":"J. 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