{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T04:30:56Z","timestamp":1776745856295,"version":"3.51.2"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T00:00:00Z","timestamp":1634083200000},"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":["41871316"],"award-info":[{"award-number":["41871316"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The classification and recognition of the shapes of buildings in map space play an important role in spatial cognition, cartographic generalization, and map updating. As buildings in map space are often represented as the vector data, research was conducted to learn the feature representations of the buildings and recognize their shapes based on graph neural networks. Due to the principles of graph neural networks, it is necessary to construct a graph to represent the adjacency relationships between the points (i.e., the vertices of the polygons shaping the buildings), and extract a list of geometric features for each point. This paper proposes a deep point convolutional network to recognize building shapes, which executes the convolution directly on the points of the buildings without constructing the graphs and extracting the geometric features of the points. A new convolution operator named TriangleConv was designed to learn the feature representations of each point by aggregating the features of the point and the local triangle constructed by the point and its two adjacency points. The proposed method was evaluated and compared with related methods based on a dataset consisting of 5010 vector buildings. In terms of accuracy, macro-precision, macro-recall, and macro-F1, the results show that the proposed method has comparable performance with typical graph neural networks of GCN, GAT, and GraphSAGE, and point cloud neural networks of PointNet, PointNet++, and DGCNN in the task of recognizing and classifying building shapes in map space.<\/jats:p>","DOI":"10.3390\/ijgi10100687","type":"journal-article","created":{"date-parts":[[2021,10,13]],"date-time":"2021-10-13T21:36:15Z","timestamp":1634160975000},"page":"687","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["TriangleConv: A Deep Point Convolutional Network for Recognizing Building Shapes in Map Space"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9055-8221","authenticated-orcid":false,"given":"Chun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"},{"name":"Henan Industrial Technology Academy of Spatio-Temporal Big Data, Henan University, Zhengzhou 450046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0887-9788","authenticated-orcid":false,"given":"Yaohui","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2971-4803","authenticated-orcid":false,"given":"Junkui","family":"Xu","sequence":"additional","affiliation":[{"name":"Henan Industrial Technology Academy of Spatio-Temporal Big Data, Henan University, Zhengzhou 450046, China"},{"name":"College of Geography and Environmental Science, Henan University, Kaifeng 475000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9993-3382","authenticated-orcid":false,"given":"Zhigang","family":"Han","sequence":"additional","affiliation":[{"name":"Henan Industrial Technology Academy of Spatio-Temporal Big Data, Henan University, Zhengzhou 450046, China"},{"name":"College of Geography and Environmental Science, Henan University, Kaifeng 475000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianzhong","family":"Guo","sequence":"additional","affiliation":[{"name":"Henan Industrial Technology Academy of Spatio-Temporal Big Data, Henan University, Zhengzhou 450046, China"},{"name":"College of Geography and Environmental Science, Henan University, Kaifeng 475000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.isprsjprs.2015.03.011","article-title":"Semantic classification of urban buildings combining VHR image and GIS data: An improved random forest approach","volume":"105","author":"Du","year":"2015","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Zhou, X., Chen, Z., Zhang, X., and Ai, T. (2018). Change Detection for Building Footprints with Different Levels of Detail Using Combined Shape and Pattern Analysis. ISPRS Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7100406"},{"key":"ref_3","first-page":"56","article-title":"Cartographic Generalization in a Digital Environment: When and How to Generalize","volume":"1","author":"Shea","year":"1989","journal-title":"J. Fluid Mech."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1080\/136588199241003","article-title":"Cognitive models of geographical space","volume":"13","author":"Mark","year":"1999","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1217","DOI":"10.3390\/rs2051217","article-title":"Automatic Detection of Buildings and Changes in Buildings for Updating of Maps","volume":"2","author":"Matikainen","year":"2010","journal-title":"Remote Sens."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1080\/23729333.2019.1613071","article-title":"Is deep learning the new agent for map generalization?","volume":"5","author":"Touya","year":"2019","journal-title":"Int. J. Cartogr."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Richardson, D.E., and van Oosterom, P. (2002). Template Matching in Support of Generalisation of Rural Buildings. Advances in Spatial Data Handling, Springer.","DOI":"10.1007\/978-3-642-56094-1"},{"key":"ref_8","first-page":"269","article-title":"The application of mathematical morphology and pattern recognition to building polygon simplification","volume":"34","author":"Wang","year":"2005","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1952","DOI":"10.1080\/13658816.2017.1346257","article-title":"Performance of shape indices and classification schemes for characterising perceptual shape complexity of building footprints in GIS","volume":"31","author":"Basaraner","year":"2017","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1016\/j.neucom.2017.09.067","article-title":"A novel method for 2D nonrigid partial shape matching","volume":"275","author":"Yang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1016\/j.patcog.2011.09.021","article-title":"A novel hybrid CNN-SVM classifier for recognizing handwritten digits","volume":"45","author":"Niu","year":"2012","journal-title":"Pattern Recognit."},{"key":"ref_12","unstructured":"Simonyan, K., and Zisserman, A. (2015). Very Deep Convolutional Networks for Large-Scale Image Recognition. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11263-015-0816-y","article-title":"Imagenet large scale visual recognition challenge","volume":"115","author":"Russakovsky","year":"2015","journal-title":"Int. J. Comput. Vis."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Szegedy, C., Liu, W., Jia, Y., Sermanet, P., Reed, S., Anguelov, D., Erhan, D., Vanhoucke, V., and Rabinovich, A. (2015, January 7\u201312). Going deeper with convolutions. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Boston, MA, USA.","DOI":"10.1109\/CVPR.2015.7298594"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kalchbrenner, N., Grefenstette, E., and Blunsom, P. (2014). A Convolutional Neural Network for Modelling Sentences. arXiv.","DOI":"10.3115\/v1\/P14-1062"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kim, Y., Jernite, Y., Sontag, D., and Rush, A.M. (2016, January 12\u201317). Character-Aware neural language models. Proceedings of the 30th AAAI Conference on Artificial Intelligence, AAAI 2016, Phoenix, AZ, USA.","DOI":"10.1609\/aaai.v30i1.10362"},{"key":"ref_17","first-page":"1995","article-title":"Convolutional networks for images, speech, and time series","volume":"3361","author":"LeCun","year":"1995","journal-title":"Handb. Brain Theory Neural Netw."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Li, X., Zheng, H., Han, C., Zheng, W., Chen, H., Jing, Y., and Dong, K. (2021). SFRS-Net: A Cloud-Detection Method Based on Deep Convolutional Neural Networks for GF-1 Remote-Sensing Images. Remote Sens., 13.","DOI":"10.3390\/rs13152910"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1126\/science.1167742","article-title":"Life in the network: The coming age of computational social science","volume":"323","author":"Lazer","year":"2009","journal-title":"Science"},{"key":"ref_20","first-page":"755","article-title":"A survey on graph convolutional neural network","volume":"43","author":"Xu","year":"2020","journal-title":"Chin. J. Comput."},{"key":"ref_21","unstructured":"Bruna, J., Zaremba, W., Szlam, A., and LeCun, Y. (2014). Spectral Networks and Locally Connected Networks on Graphs. arXiv."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1533","DOI":"10.1109\/TASLP.2014.2339736","article-title":"Convolutional Neural Networks for Speech Recognition","volume":"22","author":"Mohamed","year":"2014","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"ref_23","unstructured":"Kipf, T.N., and Welling, M. (2017). Semi-Supervised Classification with Graph Convolutional Networks. arXiv."},{"key":"ref_24","unstructured":"Veli\u010dkovi\u0107, P., Cucurull, G., Casanova, A., Romero, A., Li\u00f2, P., and Bengio, Y. (2018). Graph Attention Networks. arXiv."},{"key":"ref_25","unstructured":"Hamilton, W.L., Ying, R., and Leskovec, J. (2018). Inductive Representation Learning on Large Graphs. arXiv."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhang, C., Wang, J., and Yao, K. (2021). Global Random Graph Convolution Network for Hyperspectral Image Classification. Remote Sens., 13.","DOI":"10.3390\/rs13122285"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/j.isprsjprs.2019.02.010","article-title":"A graph convolutional neural network for classification of building patterns using spatial vector data","volume":"150","author":"Yan","year":"2019","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"490","DOI":"10.1080\/13658816.2020.1768260","article-title":"Graph convolutional autoencoder model for the shape coding and cognition of buildings in maps","volume":"35","author":"Yan","year":"2021","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_29","unstructured":"Qi, C.R., Su, H., Mo, K., and Guibas, L.J. (2017, January 21\u201326). PointNet: Deep learning on point sets for 3D classification and segmentation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA."},{"key":"ref_30","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_31","doi-asserted-by":"crossref","unstructured":"Wang, Y., Sun, Y., Liu, Z., Sarma, S.E., Bronstein, M.M., and Solomon, J.M. (2019). Dynamic Graph CNN for Learning on Point Clouds. ACM Trans. Graph., 38.","DOI":"10.1145\/3326362"},{"key":"ref_32","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., and Antiga, L. (2019). PyTorch: An Imperative Style, High-Performance Deep Learning Library. arXiv."},{"key":"ref_33","unstructured":"Kingma, D.P., and Ba, J. (2017). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Yan, X., Ai, T., and Zhang, X. (2017). Template Matching and Simplification Method for Building Features Based on Shape Cognition. ISPRS Int. J. Geo-Inf., 6.","DOI":"10.3390\/ijgi6080250"},{"key":"ref_35","first-page":"112","article-title":"Algorithms for the reduction of the number of points required to represent a digitized line or its caricature","volume":"10","author":"Douglas","year":"1973","journal-title":"Cartogr. Int. J. Geogr. Inf. Geovis."},{"key":"ref_36","unstructured":"DGL Development Team (2021, February 03). Deep Graph Library. Available online: https:\/\/docs.dgl.ai\/en\/0.5.x\/index.html."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/10\/687\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:12:25Z","timestamp":1760166745000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/10\/10\/687"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,13]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["ijgi10100687"],"URL":"https:\/\/doi.org\/10.3390\/ijgi10100687","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,13]]}}}