{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:11:41Z","timestamp":1760058701421,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42261068","20242BAB25112"],"award-info":[{"award-number":["42261068","20242BAB25112"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004479","name":"Natural Science Foundation of Jiangxi Province","doi-asserted-by":"publisher","award":["42261068","20242BAB25112"],"award-info":[{"award-number":["42261068","20242BAB25112"]}],"id":[{"id":"10.13039\/501100004479","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the actual industrial production environment, the surface defects of products are subtle, and the number of different types of defect data samples is also quite small. Most deep learning models rely on a large number of training samples and parameters to achieve high-precision defect detection. At the same time, the edge computing layer in the actual industrial environment may also encounter transmission delays and insufficient resources. Training a proper model for a specific type of surface defect while simultaneously satisfying the real-time accuracy of defect detection is still a challenging task. To effectively deal with the above challenges, we propose an edge-cloud computing defect detection model based on the intrinsic mean feature detector in the Lie Group space. The modules in the model adopt a symmetrical structure, which can extract related features more effectively. Different from existing models, this model utilizes the Lie Group space intrinsic mean feature as a metric to characterize the essential attributes of different types of surface defects. In addition, we propose an intrinsic mean attention mechanism in the Lie Group manifold space that is easy to implement at the edge service layer without increasing the number of model parameters, thereby enhancing the detection performance of tiny surface defects. Extensive experiments on three publicly available and challenging datasets reveal the superiority of our model in terms of detection accuracy, real-time detection, number of parameters, and computational performance. In addition, our proposed model also shows competitiveness and advantages compared with state-of-the-art models.<\/jats:p>","DOI":"10.3390\/sym17040612","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T05:11:16Z","timestamp":1744953076000},"page":"612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Lie Group Intrinsic Mean Feature Detectors for Real-Time Industrial Surface Defect Detection"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2052-7419","authenticated-orcid":false,"given":"Chengjun","family":"Xu","sequence":"first","affiliation":[{"name":"School of Software, Jiangxi Normal University, Nanchang 330022, China"},{"name":"School of Remote Sensing and Information Engineering, Wuhan University, Wuhan 430072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingqian","family":"Shu","sequence":"additional","affiliation":[{"name":"School of Software, Jiangxi Normal University, Nanchang 330022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenghan","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Jiangxi Normal University, Nanchang 330022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jialin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Software, Jiangxi Normal University, Nanchang 330022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"18387","DOI":"10.1109\/JIOT.2023.3280162","article-title":"A Multimodel Edge Computing Offloading Framework for Deep-Learning Application Based on Bayesian Optimization","volume":"10","author":"Zhao","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Al-Sarawi, S., Anbar, M., Abdullah, R., and Al Hawari, A.B. 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