{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,28]],"date-time":"2026-01-28T11:11:37Z","timestamp":1769598697693,"version":"3.49.0"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T00:00:00Z","timestamp":1741046400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T00:00:00Z","timestamp":1741046400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100018559","name":"Shenyang Young and Middle-aged Science and Technology Innovation Talent Support Program","doi-asserted-by":"publisher","award":["RC220452"],"award-info":[{"award-number":["RC220452"]}],"id":[{"id":"10.13039\/501100018559","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Complex Intell. Syst."],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Convolutional neural networks (CNNs) are constrained in their capacity to model geometric transformations due to their fixed geometric structure. To overcome this problem, researchers introduce deformable convolution, which allows the convolution kernel to be deformable on the feature map. However, deformable convolution may introduce irrelevant contextual information during the learning process and thus affect the model performance. DCNv2 introduces a modulation mechanism to control the diffusion of the sampling points to control the degree of contribution of offsets through weights, but we find that such problems still exist in practical use. Therefore, we propose a new limit deformable convolution to address this problem, which enhances the model ability by adding adaptive limiting units to constrain the offsets and adjusts the weight constraints on the offsets to enhance the image-focusing ability. In the subsequent work, we perform lightweight work on the limit deformable convolution and design three kinds of LDBottleneck to adapt to different scenarios. The limit deformable network, equipped with the optimal LDBottleneck, demonstrated an improvement in mAP75 of 1.4% compared to DCNv1 and 1.1% compared to DCNv2 on the VOC2012+2007 dataset. Furthermore, on the CoCo2017 dataset, different backbones equipped with our limit deformable module achieved satisfactory results. The source code for this work is publicly available at <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"https:\/\/github.com\/1977245719\/LDCN.\" ext-link-type=\"uri\">https:\/\/github.com\/1977245719\/LDCN.<\/jats:ext-link>\n          <\/jats:p>","DOI":"10.1007\/s40747-025-01799-8","type":"journal-article","created":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T03:32:07Z","timestamp":1741059127000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhancing geometric modeling in convolutional neural networks: limit deformable convolution"],"prefix":"10.1007","volume":"11","author":[{"given":"Wei","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0008-0512-8675","authenticated-orcid":false,"given":"Yuanze","family":"Meng","sequence":"additional","affiliation":[]},{"given":"Han","family":"Li","sequence":"additional","affiliation":[]},{"given":"Guiyong","family":"Chang","sequence":"additional","affiliation":[]},{"given":"Shun","family":"Li","sequence":"additional","affiliation":[]},{"given":"Chenghong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,4]]},"reference":[{"key":"1799_CR1","unstructured":"Chen H, Wang Y, Guo J, Tao D (2023a) Vanillanet: the power of minimalism in deep learning. arXiv:abs\/2305.12972"},{"key":"1799_CR2","doi-asserted-by":"crossref","unstructured":"Chen J, Hong Kao S, He H, Zhuo W, Wen S, Lee CH, Chan SHG (2023b) Run, don\u2019t walk: Chasing higher flops for faster neural networks. 2023 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 12021\u201312031. https:\/\/api.semanticscholar.org\/CorpusID:257378655","DOI":"10.1109\/CVPR52729.2023.01157"},{"key":"1799_CR3","doi-asserted-by":"crossref","unstructured":"Chollet F (2016) Xception: Deep learning with depthwise separable convolutions. 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp 1800\u20131807. https:\/\/api.semanticscholar.org\/CorpusID:2375110","DOI":"10.1109\/CVPR.2017.195"},{"key":"1799_CR4","doi-asserted-by":"crossref","unstructured":"Dai J, Qi H, Xiong Y, Li Y, Zhang G, Hu H, Wei Y (2017) Deformable convolutional networks. 2017 IEEE International Conference on Computer Vision (ICCV), pp 764\u2013773. https:\/\/api.semanticscholar.org\/CorpusID:4028864","DOI":"10.1109\/ICCV.2017.89"},{"key":"1799_CR5","unstructured":"El-Nouby A, Touvron H, Caron M, Bojanowski P, Douze M, Joulin A, Laptev I, Neverova N, Synnaeve G, Verbeek J, J\u00e9gou H (2021). Xcit: Cross-covariance image transformers, in: Neural Information Processing Systems. https:\/\/api.semanticscholar.org\/CorpusID:235458262"},{"key":"1799_CR6","unstructured":"Everingham M, Van\u00a0Gool L, Williams C.K.I, Winn J, Zisserman A (2012). The PASCAL visual object classes challenge 2012 (VOC2012) results. http:\/\/www.pascal-network.org\/challenges\/VOC\/voc2012\/workshop\/index.html"},{"key":"1799_CR7","doi-asserted-by":"crossref","unstructured":"Han K, Wang Y, Tian Q, Guo J, Xu C, Xu C (2019). Ghostnet: More features from cheap operations. 2020 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 1577\u20131586 https:\/\/api.semanticscholar.org\/CorpusID:208310058","DOI":"10.1109\/CVPR42600.2020.00165"},{"key":"1799_CR8","doi-asserted-by":"crossref","unstructured":"He K, Zhang X, Ren S, Sun J (2015). Deep residual learning for image recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 770\u2013778 https:\/\/api.semanticscholar.org\/CorpusID:206594692","DOI":"10.1109\/CVPR.2016.90"},{"key":"1799_CR9","doi-asserted-by":"crossref","unstructured":"Howard A.G, Sandler M, Chu G, Chen L.C, Chen B, Tan M, Wang W, Zhu Y, Pang R, Vasudevan V, Le Q.V, Adam H (2019). Searching for mobilenetv3. 2019 IEEE\/CVF International Conference on Computer Vision (ICCV) , 1314\u20131324 https:\/\/api.semanticscholar.org\/CorpusID:146808333","DOI":"10.1109\/ICCV.2019.00140"},{"key":"1799_CR10","unstructured":"Howard A.G, Zhu M, Chen B, Kalenichenko D, Wang W, Weyand T, Andreetto M, Adam H (2017). Mobilenets: Efficient convolutional neural networks for mobile vision applications. ArXiv preprint abs\/1704.04861. arXiv:abs\/1704.04861"},{"key":"1799_CR11","unstructured":"Huang T, Huang L, You S, Wang F, Qian C, Xu C (2022). Lightvit: Towards light-weight convolution-free vision transformers. ArXiv abs\/2207.05557. https:\/\/api.semanticscholar.org\/CorpusID:250451295"},{"key":"1799_CR12","unstructured":"Li C, Zhou A, Yao A (2022a). Omni-dimensional dynamic convolution. ArXiv abs\/2209.07947. https:\/\/api.semanticscholar.org\/CorpusID:251647798"},{"key":"1799_CR13","doi-asserted-by":"crossref","unstructured":"Li D, Hu J, Wang C, Li X, She Q, Zhu L, Zhang T, Chen Q (2021). Involution: Inverting the inherence of convolution for visual recognition. 2021 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 12316\u201312325 https:\/\/api.semanticscholar.org\/CorpusID:232170607","DOI":"10.1109\/CVPR46437.2021.01214"},{"key":"1799_CR14","unstructured":"Li H, Li J, Wei H, Liu Z, Zhan Z, Ren Q (2022b). Slim-neck by gsconv: A better design paradigm of detector architectures for autonomous vehicles. ArXiv preprint abs\/2206.02424. arXiv:abs\/2206.02424"},{"key":"1799_CR15","doi-asserted-by":"crossref","unstructured":"Lin T.Y, Maire M, Belongie S.J, Hays J, Perona P, Ramanan D, Doll\u00e1r P, Zitnick,C.L, (2014). Microsoft coco: Common objects in context, in: European Conference on Computer Vision. https:\/\/api.semanticscholar.org\/CorpusID:14113767","DOI":"10.1007\/978-3-319-10602-1_48"},{"key":"1799_CR16","doi-asserted-by":"crossref","unstructured":"Liu Z, Lin Y, Cao Y, Hu H, Wei Y, Zhang Z, Lin S, Guo B (2021). Swin transformer: Hierarchical vision transformer using shifted windows. 2021 IEEE\/CVF International Conference on Computer Vision (ICCV) , 9992\u201310002 https:\/\/api.semanticscholar.org\/CorpusID:232352874","DOI":"10.1109\/ICCV48922.2021.00986"},{"key":"1799_CR17","unstructured":"Lu J, Yao J, Zhang J, Zhu X, Xu H, Gao W, Xu C, Xiang T, Zhang L (2021). Soft: Softmax-free transformer with linear complexity, in: Neural Information Processing Systems. https:\/\/api.semanticscholar.org\/CorpusID:239616022"},{"key":"1799_CR18","doi-asserted-by":"crossref","unstructured":"Ma N, Zhang X, Zheng H, Sun J, (2018) Shufflenet v2: Practical guidelines for efficient cnn architecture design. ArXiv preprint abs\/1807.11164. arXiv:abs\/1807.11164","DOI":"10.1007\/978-3-030-01264-9_8"},{"key":"1799_CR19","doi-asserted-by":"crossref","unstructured":"Qi Y, He Y, Qi X, Zhang Y, Yang G (2023). Dynamic snake convolution based on topological geometric constraints for tubular structure segmentation. 2023 IEEE\/CVF International Conference on Computer Vision (ICCV) , 6047\u20136056 https:\/\/api.semanticscholar.org\/CorpusID:259937654","DOI":"10.1109\/ICCV51070.2023.00558"},{"key":"1799_CR20","unstructured":"Rao Y, Zhao W, Tang Y, Zhou J, Lim S.N, Lu J (2022). Hornet: Efficient high-order spatial interactions with recursive gated convolutions. ArXiv preprint abs\/2207.14284. arXiv:abs\/2207.14284"},{"key":"1799_CR21","doi-asserted-by":"crossref","unstructured":"Sandler M, Howard A.G, Zhu M, Zhmoginov A, Chen L.C (2018). Mobilenetv2: Inverted residuals and linear bottlenecks. 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition , 4510\u20134520 https:\/\/api.semanticscholar.org\/CorpusID:4555207","DOI":"10.1109\/CVPR.2018.00474"},{"key":"1799_CR22","unstructured":"Simonyan K, Zisserman A (2014). Very deep convolutional networks for large-scale image recognition. CoRR abs\/1409.1556. https:\/\/api.semanticscholar.org\/CorpusID:14124313"},{"key":"1799_CR23","doi-asserted-by":"crossref","unstructured":"Szegedy C, Ioffe S, Vanhoucke V, Alemi A.A (2016). Inception-v4, inception-resnet and the impact of residual connections on learning. ArXiv abs\/1602.07261. https:\/\/api.semanticscholar.org\/CorpusID:1023605","DOI":"10.1609\/aaai.v31i1.11231"},{"key":"1799_CR24","doi-asserted-by":"publisher","unstructured":"Szegedy C, Liu W, Jia Y, Sermanet P, Reed S, Anguelov D, Erhan D, Vanhoucke V, Rabinovich , (2015a). Going deeper with convolutions, in: 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1\u20139. https:\/\/doi.org\/10.1109\/CVPR.2015.7298594","DOI":"10.1109\/CVPR.2015.7298594"},{"key":"1799_CR25","doi-asserted-by":"crossref","unstructured":"Szegedy C, Vanhoucke V, Ioffe S, Shlens J, Wojna Z (2015b). Rethinking the inception architecture for computer vision. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) , 2818\u20132826 https:\/\/api.semanticscholar.org\/CorpusID:206593880","DOI":"10.1109\/CVPR.2016.308"},{"key":"1799_CR26","unstructured":"Tan M, Le Q.V (2019). Efficientnet: Rethinking model scaling for convolutional neural networks. ArXiv abs\/1905.11946. https:\/\/api.semanticscholar.org\/CorpusID:167217261"},{"key":"1799_CR27","unstructured":"Tan M, Le,Q.V (2021). Efficientnetv2: Smaller models and faster training, in: International Conference on Machine Learning. https:\/\/api.semanticscholar.org\/CorpusID:232478903"},{"key":"1799_CR28","unstructured":"Wang A, Chen H, Lin Z, Pu H, Ding G (2023). Repvit: Revisiting mobile cnn from vit perspective. ArXiv preprint abs\/2307.09283. arXiv:abs\/2307.09283"},{"key":"1799_CR29","doi-asserted-by":"publisher","unstructured":"Wang J, Chen K, Xu R, Liu Z, Loy C.C, Lin D (2019). Carafe: Content-aware reassembly of features, in: 2019 IEEE\/CVF International Conference on Computer Vision (ICCV), pp. 3007\u20133016. https:\/\/doi.org\/10.1109\/ICCV.2019.00310","DOI":"10.1109\/ICCV.2019.00310"},{"key":"1799_CR30","doi-asserted-by":"crossref","unstructured":"Wang W, Dai J, Chen Z, Huang Z, Li Z, Zhu X, hua Hu X, Lu T, Lu L, Li H, Wang X, Qiao Y (2022). Internimage: Exploring large-scale vision foundation models with deformable convolutions. 2023 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 14408\u201314419 https:\/\/api.semanticscholar.org\/CorpusID:253446956","DOI":"10.1109\/CVPR52729.2023.01385"},{"key":"1799_CR31","doi-asserted-by":"crossref","unstructured":"Woo S, Park J, Lee J.Y, Kweon I.S (2018). Cbam: Convolutional block attention module. ArXiv preprint abs\/1807.06521. arXiv:abs\/1807.06521","DOI":"10.1007\/978-3-030-01234-2_1"},{"key":"1799_CR32","doi-asserted-by":"crossref","unstructured":"Yang Z, Liu S, Hu H, Wang L, Lin S (2019). Reppoints: Point set representation for object detection. 2019 IEEE\/CVF International Conference on Computer Vision (ICCV) , 9656\u20139665 https:\/\/api.semanticscholar.org\/CorpusID:131775182","DOI":"10.1109\/ICCV.2019.00975"},{"key":"1799_CR33","doi-asserted-by":"crossref","unstructured":"Zhang X, Zhou X, Lin M, Sun J (2017). Shufflenet: An extremely efficient convolutional neural network for mobile devices. 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition , 6848\u20136856 https:\/\/api.semanticscholar.org\/CorpusID:24982157","DOI":"10.1109\/CVPR.2018.00716"},{"key":"1799_CR34","doi-asserted-by":"publisher","first-page":"3838","DOI":"10.1109\/TIP.2022.3176537","volume":"31","author":"C Zhao","year":"2022","unstructured":"Zhao C, Zhu W, Feng S (2022) Superpixel guided deformable convolution network for hyperspectral image classification. IEEE Transactions on Image Processing 31:3838\u20133851. https:\/\/doi.org\/10.1109\/TIP.2022.3176537","journal-title":"IEEE Transactions on Image Processing"},{"key":"1799_CR35","doi-asserted-by":"crossref","unstructured":"Zhu X, Hu H, Lin S, Dai J (2018). Deformable convnets v2: More deformable, better results. 2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , 9300\u20139308 https:\/\/api.semanticscholar.org\/CorpusID:53745820","DOI":"10.1109\/CVPR.2019.00953"}],"container-title":["Complex &amp; Intelligent Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-01799-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40747-025-01799-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40747-025-01799-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T21:20:32Z","timestamp":1743369632000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40747-025-01799-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,4]]},"references-count":35,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["1799"],"URL":"https:\/\/doi.org\/10.1007\/s40747-025-01799-8","relation":{},"ISSN":["2199-4536","2198-6053"],"issn-type":[{"value":"2199-4536","type":"print"},{"value":"2198-6053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,4]]},"assertion":[{"value":"3 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"202"}}