{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,20]],"date-time":"2026-06-20T16:32:31Z","timestamp":1781973151185,"version":"3.54.5"},"reference-count":34,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Xi'an Institute of Optics and Precision Mechanics of CAS","award":["No"],"award-info":[{"award-number":["No"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Object detection is a fundamental task in computer vision. Bounding box regression (BBR) losses are critical to detector performance. However, evaluation measures that rely on the Intersection over Union (IoU) between the predicted and ground truth boxes are highly sensitive to positional deviations, which can hinder optimization. To alleviate this issue, we propose ATDIoU, a novel arctangent-differential loss for bounding-box regression. ATDIoU computes distance similarity between a predicted and a ground truth box by modeling the distances between their corresponding vertices as a two-dimensional arctangent differential distribution (ATD). This arctangent differential-based design mitigates bounding box drift and reduces sensitivity to localization errors. As a result, it guides the model to learn target positions more effectively. We evaluate ATDIoU by integrating it into YOLOv6 and conducting experiments on PASCAL VOC and VisDrone2019. The results demonstrate that ATDIoU yields improvements of 1.4% and 0.7% in mean average precision (mAP) relative to MPDIoU.<\/jats:p>","DOI":"10.3390\/s26051545","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T08:51:57Z","timestamp":1772441517000},"page":"1545","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["ATDIOU: Arctangent Differential Loss Function for Bounding Box Regression"],"prefix":"10.3390","volume":"26","author":[{"given":"Qiang","family":"Tang","sequence":"first","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-5543-6241","authenticated-orcid":false,"given":"Hao","family":"Qiang","sequence":"additional","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuan","family":"Tian","sequence":"additional","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4348-7632","authenticated-orcid":false,"given":"Xubin","family":"Feng","sequence":"additional","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Hao","sequence":"additional","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meilin","family":"Xie","sequence":"additional","affiliation":[{"name":"Xi\u2019an Institute of Optics and Precision Mechanics of CAS, Xi\u2019an 710119, China"},{"name":"University of Chinese Academy of Sciences, Beijing 100049, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Han, B., Tang, Q., Song, J., Wang, Z., and Yang, Y. 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Proceedings of the 2020 39th Chinese Control Conference (CCC), IEEE.","DOI":"10.23919\/CCC50068.2020.9189594"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/5\/1545\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:32:54Z","timestamp":1772775174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/5\/1545"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,1]]},"references-count":34,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["s26051545"],"URL":"https:\/\/doi.org\/10.3390\/s26051545","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,1]]}}}