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Most semi\u2010supervised semantic segmentation methods primarily focus on sample augmentation in spatial dimensions to reduce the shortage of labeled samples. These methods tend to ignore the structural information of objects. In addition, frequency\u2010domain information also supplies another perspective to evaluate information from images, which includes different properties compared to the spatial\u00a0domain.<\/jats:p><\/jats:sec><jats:sec><jats:title>Purpose<\/jats:title><jats:p>In this study, we attempt to answer these two questions: (1) is it helpful to provide structural information of objects in semi\u2010supervised semantic segmentation tasks for medical images? (2) is it more effective to evaluate the segmentation performance in the frequency domain compared to the spatial domain for semi\u2010supervised medical image segmentation? Therefore, we seek to introduce structural and frequency information to improve the performance of semi\u2010supervised semantic segmentation for medical\u00a0images.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>We present a novel structural tensor loss (<jats:bold>STL<\/jats:bold>) to guide feature learning on the spatial domain for semi\u2010supervised semantic segmentation. Specifically, STL utilizes the structural information encoded in the tensors to enforce the consistency of objects across spatial regions, thereby promoting more robust and accurate feature extraction. Additionally, we proposed a frequency\u2010domain alignment loss (<jats:bold>FAL<\/jats:bold>) to enable the neural networks to learn frequency\u2010domain information across different augmented samples. It leverages the inherent patterns present in frequency\u2010domain representations to guide the network in capturing and aligning features across diverse augmentation variations, thereby enhancing the model's robustness for the inputting variations.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>We conduct our experiments on three benchmark datasets, which include MRI (ACDC) for cardiac, CT (Synapse) for abdomen organs, and ultrasound image (BUSI) for breast lesion segmentation. The experimental results demonstrate that our method outperforms state\u2010of\u2010the\u2010art semi\u2010supervised approaches regarding the Dice similarity\u00a0coefficient.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>We find the proposed approach could improve the final performance of the semi\u2010supervised medical image segmentation task. It will help reduce the need for medical image labels. Our code will are available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/apple1986\/STLFAL\">https:\/\/github.com\/apple1986\/STLFAL<\/jats:ext-link>.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.17399","type":"journal-article","created":{"date-parts":[[2024,9,17]],"date-time":"2024-09-17T18:55:37Z","timestamp":1726599337000},"page":"8929-8942","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Structural tensor and frequency guided semi\u2010supervised segmentation for medical images"],"prefix":"10.1002","volume":"51","author":[{"given":"Xuesong","family":"Leng","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Hubei Key Laboratory of Intelligent Robot Wuhan Institute of Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaxia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Hubei Key Laboratory of Intelligent Robot Wuhan Institute of Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenbo","family":"Yue","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Hubei Key Laboratory of Intelligent Robot Wuhan Institute of Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianxiu","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering South China University of Technology Guangzhou China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guoping","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Hubei Key Laboratory of Intelligent Robot Wuhan Institute of Technology Wuhan Hubei China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,9,16]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2017.2699184"},{"key":"e_1_2_8_3_1","doi-asserted-by":"crossref","unstructured":"LongJ ShelhamerE DarrellT.Fully convolutional networks for semantic segmentation. 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