{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:38:52Z","timestamp":1760150332601,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T00:00:00Z","timestamp":1699228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ningbo Science and Technology Innovation Project","award":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"],"award-info":[{"award-number":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"]}]},{"name":"Innovation Project of GUET Graduate Education","award":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"],"award-info":[{"award-number":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"]}]},{"name":"Innovation Project of Guangxi Graduate Education, China","award":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"],"award-info":[{"award-number":["2023Z016","2023Z013","2021YCXB07","YCBZ2022108"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Three-dimensional point cloud data generally contain complex scene information and diversified category structures. Existing point cloud semantic segmentation networks tend to learn feature information between sampled center points and their neighboring points, while ignoring the scale and structural information of the spatial context of the sampled center points. To address these issues, this paper introduces PointNAC (PointNet based on normal vector and attention copula feature enhancement), a network designed for point cloud semantic segmentation in large-scale complex scenes, which consists of the following two main modules: (1) The local stereoscopic feature-encoding module: this feature-encoding process incorporates distance, normal vectors, and angles calculated based on the cosine theorem, enabling the network to learn not only the spatial positional information of the point cloud but also the spatial scale and geometric structure; and (2) the copula-based similarity feature enhancement module. Based on the stereoscopic feature information, this module analyzes the correlation among points in the local neighborhood. It enhances the features of positively correlated points while leaving the features of negatively correlated points unchanged. By combining these enhancements, it effectively enhances the feature saliency within the same class and the feature distinctiveness between different classes. The experimental results show that PointNAC achieved an overall accuracy (OA) of 90.9% and a mean intersection over union (MIoU) of 67.4% on the S3DIS dataset. And on the Vaihingen dataset, PointNAC achieved an overall accuracy (OA) of 85.9% and an average F1 score of 70.6%. Compared to the segmentation results of other network models on public datasets, our algorithm demonstrates good generalization and segmentation capabilities.<\/jats:p>","DOI":"10.3390\/sym15112021","type":"journal-article","created":{"date-parts":[[2023,11,6]],"date-time":"2023-11-06T08:15:56Z","timestamp":1699258556000},"page":"2021","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["PointNAC: Copula-Based Point Cloud Semantic Segmentation Network"],"prefix":"10.3390","volume":"15","author":[{"given":"Chunyuan","family":"Deng","sequence":"first","affiliation":[{"name":"School of Electronic and Automation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3531-9276","authenticated-orcid":false,"given":"Ruixing","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Automation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wuyang","family":"Tang","sequence":"additional","affiliation":[{"name":"School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hexuan","family":"Chu","sequence":"additional","affiliation":[{"name":"School of Electronic and Automation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Xu","sequence":"additional","affiliation":[{"name":"Computer Vision Laboratory, Advanced Manufacturing Institute, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yue","family":"Cui","sequence":"additional","affiliation":[{"name":"Computer Vision Laboratory, Advanced Manufacturing Institute, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenyun","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Electronic and Automation, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ni, H., Lin, X.G., Ning, X., and Zhang, J. (2016). Edge detection and feature line tracing in 3D-point clouds by analyzing geometric properties of neighborhoods. Remote Sens., 8.","DOI":"10.3390\/rs8090710"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.isprsjprs.2015.01.011","article-title":"Octree-based region growing for point cloud segmentation","volume":"104","author":"Vo","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"11","DOI":"10.4316\/AECE.2013.03002","article-title":"Automatic building extraction from terrestrial laser scanning data","volume":"13","author":"Hao","year":"2013","journal-title":"Adv. Electr. Comput. Eng."},{"key":"ref_4","unstructured":"Wang, Y.M., and Shi, H.B. (2014). Geo-Informatics in Resource Management and Sustainable Ecosystem, Springer."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Su, H., Maji, S., Kalogerakis, E., and Learned-Miller, E. (2015, January 7\u201313). Multi-view convolutional neural networks for 3d shape recognition. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Santiago, Chile.","DOI":"10.1109\/ICCV.2015.114"},{"key":"ref_6","unstructured":"Maturana, D., and Scherer, S. (October, January 28). VoxNet: A 3D Convolutional Neural Network for real-time object recognition. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Hamburg, Germany."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Landrieu, L., and Simonovsky, M. (2018, January 18\u201323). Large-scale point cloud semantic segmentation with superpoint graphs. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00479"},{"key":"ref_8","first-page":"1","article-title":"Dynamic graph cnn for learning on point clouds","volume":"38","author":"Wang","year":"2019","journal-title":"ACM Trans. Graph. (tog)"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lin, Z.H., Huang, S.Y., and Wang, Y.C.F. (2020, January 13\u201319). Convolution in the cloud: Learning deformable kernels in 3d graph convolution networks for point cloud analysis. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00187"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Charles, R.Q., Su, H., Kaichun, M., and Guibas, L.J. (2017, January 21\u201326). PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.16"},{"key":"ref_11","unstructured":"Qi, C.R., Yi, L., Su, H., and Guibas, L.J. (2017). PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space. arXiv."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Jiang, M., Wu, Y., Zhao, T., Zhao, Z., and Lu, C. (2018). Pointsift: A sift-like network module for 3d point cloud semantic segmentation. arXiv.","DOI":"10.1109\/IGARSS.2019.8900102"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhao, H., Jiang, L., Fu, C.W., and Jia, J. (2019, January 15\u201320). Pointweb: Enhancing local neighborhood features for point cloud processing. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00571"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hu, Q., Yang, B., Xie, L., Rosa, S., Guo, Y., Wang, Z., Trigoni, N., and Markham, A. (2020, January 13\u201319). Randla-net: Efficient semantic segmentation of large-scale point clouds. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.01112"},{"key":"ref_15","unstructured":"Li, Y., Bu, R., Sun, M., Wu, W., Di, X., and Chen, B. (2018). Pointcnn: Convolution on x-transformed points. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Xu, M., Ding, R., Zhao, H., and Qi, X. (2021, January 20\u201325). Paconv: Position adaptive convolution with dynamic kernel assembling on point clouds. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA.","DOI":"10.1109\/CVPR46437.2021.00319"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.isprsjprs.2020.05.023","article-title":"DANCE-NET: Density-aware convolution networks with context encoding for airborne LiDAR point cloud classification","volume":"166","author":"Li","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_18","first-page":"1","article-title":"DenseKPNET: Dense Kernel Point Convolutional Neural Networks for Point Cloud Semantic Segmentation","volume":"60","author":"Li","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.isprsjprs.2021.05.009","article-title":"Semantic segmentation of 3D indoor LiDAR point clouds through feature pyramid architecture search","volume":"177","author":"Lin","year":"2021","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"104757","DOI":"10.1016\/j.autcon.2023.104757","article-title":"Label-efficient semantic segmentation of large-scale industrial point clouds using weakly supervised learning","volume":"148","author":"Yin","year":"2023","journal-title":"Autom. Constr."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zhang, T., Ma, M., Yan, F., Li, H., and Chen, Y. (2023, January 2\u20137). PIDS: Joint point interaction-dimension search for 3D point cloud. Proceedings of the IEEE\/CVF Winter Conference on Applications of Computer Vision, Waikoloa, HI, USA.","DOI":"10.1109\/WACV56688.2023.00135"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016, January 27\u201330). Deep Residual Learning for Image Recognition. Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Deng, C., Peng, Z., Chen, Z., and Chen, R. (2023). Point Cloud Deep Learning Network Based on Balanced Sampling and Hybrid Pooling. Sensors, 23.","DOI":"10.3390\/s23020981"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Deng, H., Birdal, T., and Ilic, S. (2018, January 8\u201314). PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors. Proceedings of the 15th European Conference, Munich, Germany.","DOI":"10.1007\/978-3-030-01228-1_37"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1016\/j.ins.2021.02.076","article-title":"Correlation-oriented Complex System Structural Risk Assessment using Copula and Belief Rule Base","volume":"564","author":"Chang","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1145\/142920.134011","article-title":"Surface reconstruction from unorganized points","volume":"Volume 26","author":"Hoppe","year":"1992","journal-title":"SIGGRAPH \u203292: Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques"},{"key":"ref_27","unstructured":"Oh, D.H. (2014). Copulas for High Dimensions: Models, Estimation, Inference, and Applications. [Ph.D. Thesis, Duke University]."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"307","DOI":"10.1038\/nature16948","article-title":"Universal resilience patterns in complex networks","volume":"530","author":"Gao","year":"2016","journal-title":"Nature"},{"key":"ref_29","unstructured":"Sklar, M. (1959). Fonctions de Repartition an Dimensions et Leurs Marges, Publications de l\u2019Institut de Statistique de l\u2019Universit\u00e9 de Paris."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Armeni, I., Sener, O., Zamir, A.R., Jiang, H., Brilakis, I., Fischer, M., and Savarese, S. (2016, January 27\u201330). 3D Semantic Parsing of Large-Scale Indoor Spaces. Proceedings of the Computer Vision & Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.170"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Cramer, M. (2010). The DGPF-test on digital airborne camera evaluation overview and test design. Photogramm.-Fernerkund.-Geoinf., 73\u201382.","DOI":"10.1127\/1432-8364\/2010\/0041"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ye, X., Li, J., Huang, H., Du, L., and Zhang, X. (2018, January 8\u201314). 3D Recurrent Neural Networks with Context Fusion for Point Cloud Semantic Segmentation. Proceedings of the European Conference on Computer Vision, Munich, Germany.","DOI":"10.1007\/978-3-030-01234-2_25"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1729881419857532","DOI":"10.1177\/1729881419857532","article-title":"NormNet: Point-wise normal estimation network for three-dimensional point cloud data","volume":"16","author":"Hyeon","year":"2019","journal-title":"Int. J. Adv. Robot. Syst."},{"key":"ref_34","unstructured":"Chen, L.Z., Li, X.Y., Fan, D.P., Wang, K., Lu, S.P., and Cheng, M.M. (2019). LSANet: Feature Learning on Point Sets by Local Spatial Attention. arXiv."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Lin, Y., Yan, Z., Huang, H., Du, D., Liu, L., Cui, S., and Han, X. (2020, January 13\u201319). Fpconv: Learning local flattening for point convolution. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.00435"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"6069","DOI":"10.1007\/s11042-021-11825-9","article-title":"Dilated Multi-scale Fusion for Point Cloud Classification and Segmentation","volume":"81","author":"Guo","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1016\/j.isprsjprs.2020.02.020","article-title":"Deep point embedding for urban classification using ALS point clouds: A new perspective from local to global","volume":"163","author":"Huang","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Yang, Z., Tan, B., Pei, H., and Jiang, W. (2018). Segmentation and Multi-Scale Convolutional Neural Network-Based Classification of Airborne Laser Scanner Data. Sensors, 18.","DOI":"10.3390\/s18103347"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1080\/13658816.2018.1431840","article-title":"Classifying airborne LiDAR point clouds via deep features learned by a multi-scale convolutional neural network","volume":"32","author":"Zhao","year":"2018","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.isprsjprs.2020.02.004","article-title":"Directionally Constrained Fully Convolutional Neural Network For Airborne Lidar Point Cloud Classification","volume":"162","author":"Wen","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.isprsjprs.2020.03.016","article-title":"A geometry-attentional network for ALS point cloud classification","volume":"164","author":"Li","year":"2020","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.isprsjprs.2021.04.017","article-title":"GraNet: Global relation-aware attentional network for semantic segmentation of ALS point clouds","volume":"177","author":"Huang","year":"2021","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.isprsjprs.2021.01.007","article-title":"Airborne LiDAR point cloud classification with global-local graph attention convolution neural network","volume":"173","author":"Wen","year":"2021","journal-title":"ISPRS J. Photogramm. Remote Sens."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2021\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:18:09Z","timestamp":1760131089000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/2021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,11,6]]},"references-count":43,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["sym15112021"],"URL":"https:\/\/doi.org\/10.3390\/sym15112021","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,11,6]]}}}