{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T02:44:37Z","timestamp":1781059477768,"version":"3.54.1"},"reference-count":50,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T00:00:00Z","timestamp":1652486400000},"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>Buildings are important entity objects of cities, and the classification of building shapes plays an indispensable role in the cognition and planning of the urban structure. In recent years, some deep learning methods have been proposed for recognizing the shapes of building footprints in modern electronic maps. Furthermore, their performance depends on enough labeled samples for each class of building footprints. However, it is impractical to label enough samples for each type of building footprint shapes. Therefore, the deep learning methods using few labeled samples are more preferable to recognize and classify the building footprint shapes. In this paper, we propose a relation network based method for the recognization of building footprint shapes with few labeled samples. Relation network, composed of embedding module and relation module, is a metric based few-shot method which aims to learn a generalized metric function and predict the types of the new samples according to their relation with the prototypes of these few labeled samples. To better extract the shape features of the building footprints in the form of vector polygons, we have taken the TriangleConv embedding module to act as the embedding module of the relation network. We validate the effectiveness of our method based on a building footprint dataset with 10 typical shapes and compare it with three classical few-shot learning methods in accuracy. The results show that our method performs better for the classification of building footprint shapes with few labeled samples. For example, the accuracy reached 89.40% for the 2-way 5-shot classification task where there are only two classes of samples in the task and five labeled samples for each class.<\/jats:p>","DOI":"10.3390\/ijgi11050311","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T09:27:56Z","timestamp":1652520476000},"page":"311","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Few-Shot Building Footprint Shape Classification with Relation Network"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0887-9788","authenticated-orcid":false,"given":"Yaohui","family":"Hu","sequence":"first","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9055-8221","authenticated-orcid":false,"given":"Chun","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475000, China"},{"name":"Henan Industrial Technology Academy of Spatio-Temporal Big Data, Henan University, Zhengzhou 450046, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Computer and Information Engineering, Henan University, Kaifeng 475000, China"},{"name":"Henan Key Laboratory of Big Data Analysis and Processing, Henan University, Kaifeng 475000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]},{"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":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1111\/j.1467-9671.2008.01085.x","article-title":"An Approach for the Classification of Urban Building Structures Based on Discriminant Analysis Techniques","volume":"12","author":"Steiniger","year":"2008","journal-title":"Trans. GIS"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1109\/JSTARS.2015.2465131","article-title":"Building Types\u2019 Classification Using Shape-Based Features and Linear Discriminant Functions","volume":"9","author":"Wurm","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_3","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_4","first-page":"3","article-title":"Vision Science: Photons to Phenomenology","volume":"113","author":"Cambridge","year":"2000","journal-title":"Am. J. Psychol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.compenvurbsys.2013.07.002","article-title":"A shape analysis and template matching of building features by the Fourier transform method","volume":"41","author":"Ai","year":"2013","journal-title":"Comput. Environ. Urban Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/34.149591","article-title":"A theory of multiscale, curvature-based shape representation for planar curves","volume":"14","author":"Mokhtarian","year":"1992","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1227","DOI":"10.1080\/13658816.2012.752093","article-title":"An efficient measure of compactness for two-dimensional shapes and its application in regionalization problems","volume":"27","author":"Li","year":"2013","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_8","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_9","doi-asserted-by":"crossref","unstructured":"Fu, Z., Fan, L., Yu, Z., and Zhou, K. (2018). A Moment-Based Shape Similarity Measurement for Areal Entities in Geographical Vector Data. ISPRS Int. J. Geo-Inf., 7.","DOI":"10.3390\/ijgi7060208"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Fan, H., Zhao, Z., and Li, W. (2021). Towards Measuring Shape Similarity of Polygons Based on Multiscale Features and Grid Context Descriptors. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10050279"},{"key":"ref_11","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_12","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_13","doi-asserted-by":"crossref","unstructured":"Liu, C., Hu, Y., Li, Z., Xu, J., Han, Z., and Guo, J. (2021). TriangleConv: A Deep Point Convolutional Network for Recognizing Building Shapes in Map Space. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10100687"},{"key":"ref_14","unstructured":"Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., and Gelly, S. (2021). An Image is Worth 16 \u00d7 16 Words: Transformers for Image Recognition at Scale. arXiv."},{"key":"ref_15","unstructured":"Tolstikhin, I., Houlsby, N., Kolesnikov, A., Beyer, L., Zhai, X., Unterthiner, T., Yung, J., Steiner, A., Keysers, D., and Uszkoreit, J. (2021). MLP-Mixer: An all-MLP Architecture for Vision. arXiv."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, Z., Hu, H., Lin, Y., Yao, Z., Xie, Z., Wei, Y., Ning, J., Cao, Y., Zhang, Z., and Dong, L. (2021). Swin Transformer V2: Scaling Up Capacity and Resolution. arXiv.","DOI":"10.1109\/CVPR52688.2022.01170"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1038\/s41586-018-0438-y","article-title":"Deep learning of aftershock patterns following large earthquakes","volume":"560","author":"DeVries","year":"2018","journal-title":"Nature"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Feng, Y., Thiemann, F., and Sester, M. (2019). Learning Cartographic Building Generalization with Deep Convolutional Neural Networks. ISPRS Int. J. Geo-Inf., 8.","DOI":"10.3390\/ijgi8060258"},{"key":"ref_19","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_20","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1080\/13658816.2019.1599122","article-title":"Spatial interpolation using conditional generative adversarial neural networks","volume":"34","author":"Zhu","year":"2020","journal-title":"Int. J. Geogr. Inf. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sung, F., Yang, Y., Zhang, L., Xiang, T., Torr, P.H., and Hospedales, T.M. (2018, January 18\u201322). Learning to Compare: Relation Network for Few-Shot Learning. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00131"},{"key":"ref_22","unstructured":"Bendre, N., Mar\u00edn, H.T., and Najafirad, P. (2020). Learning from Few Samples: A Survey. arXiv."},{"key":"ref_23","first-page":"1","article-title":"Generalizing from a Few Examples: A Survey on Few-Shot Learning","volume":"53","author":"Wang","year":"2020","journal-title":"ACM Comput. Surv."},{"key":"ref_24","unstructured":"Koch, G., Zemel, R., and Salakhutdinov, R. (2015, January 6\u201311). Siamese neural networks for one-shot image recognition. Proceedings of the 32nd International Conference on Machine Learning (ICML), Lille, France."},{"key":"ref_25","unstructured":"Snell, J., Swersky, K., and Zemel, R.S. (2017). Prototypical Networks for Few-shot Learning. arXiv."},{"key":"ref_26","unstructured":"Ravi, S., and Larochelle, H. (2017, January 24\u201326). Optimization as a model for few-shot learning. Proceedings of the 5th International Conference on Learning Representations (ICLR), Toulon, France."},{"key":"ref_27","unstructured":"Finn, C., Abbeel, P., and Levine, S. (2017, January 6\u201311). Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks. Proceedings of the 34th International Conference on Machine Learning, Sydney, Australia."},{"key":"ref_28","unstructured":"Zhou, F., Wu, B., and Li, Z. (2018). Deep Meta-Learning: Learning to Learn in the Concept Space. arXiv."},{"key":"ref_29","unstructured":"Lee, D., Sugiyama, M., Luxburg, U., Guyon, I., and Garnett, R. (2016). Matching Networks for One Shot Learning. Advances in Neural Information Processing Systems, Curran Associates, Inc."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhang, C., Cai, Y., Lin, G., and Shen, C. (2020, January 13\u201319). DeepEMD: Few-Shot Image Classification With Differentiable Earth Mover\u2019s Distance and Structured Classifiers. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Seattle, WA, USA.","DOI":"10.1109\/CVPR42600.2020.01222"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"10398","DOI":"10.1109\/TGRS.2019.2934218","article-title":"Hyperspectral Image Classification Based on Two-Phase Relation Learning Network","volume":"57","author":"Ma","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","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_33","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_34","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1080\/04353684.1985.11879515","article-title":"Compactness of Geographic Shape: Comparison and Evaluation of Measures","volume":"67","author":"Maceachren","year":"1985","journal-title":"Geogr. Ann. Ser. B Hum. Geogr."},{"key":"ref_35","unstructured":"Wentz, E.A. (1997, January 7\u201310). Shape analysis in GIS. Proceedings of the Auto-Carto, Seattle, WA, USA."},{"key":"ref_36","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_37","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/34.993558","article-title":"Shape matching and object recognition using shape contexts","volume":"24","author":"Belongie","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.1016\/j.patcog.2006.12.005","article-title":"Shape retrieval using triangle-area representation and dynamic space warping","volume":"40","author":"Alajlan","year":"2007","journal-title":"Pattern Recognit."},{"key":"ref_39","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 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Szegedy, C., Ioffe, S., Vanhoucke, V., and Alemi, A.A. (2017, January 4\u20139). Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning. Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, AAAI\u201917, San Francisco, CA, USA.","DOI":"10.1609\/aaai.v31i1.11231"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1038\/nature24270","article-title":"Mastering the game of go without human knowledge","volume":"550","author":"Silver","year":"2017","journal-title":"Nature"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1109\/TPAMI.2006.79","article-title":"One-shot learning of object categories","volume":"28","author":"Fergus","year":"2006","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_43","unstructured":"Lake, B., Salakhutdinov, R., Gross, J., and Tenenbaum, J. (2011, January 20\u201323). One shot learning of simple visual concepts. Proceedings of the Annual Meeting of the Cognitive Science Society(CogSci), Boston, MA, USA."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhang, H., Zhang, J., and Koniusz, P. (2019, January 15\u201320). Few-Shot Learning via Saliency-Guided Hallucination of Samples. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00288"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Chen, Z., Fu, Y., Wang, Y.X., Ma, L., Liu, W., and Hebert, M. (2019, January 15\u201320). Image Deformation Meta-Networks for One-Shot Learning. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00888"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Schonfeld, E., Ebrahimi, S., Sinha, S., Darrell, T., and Akata, Z. (2019, January 15\u201320). Generalized Zero- and Few-Shot Learning via Aligned Variational Autoencoders. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00844"},{"key":"ref_47","unstructured":"Schwartz, E., Karlinsky, L., Feris, R., Giryes, R., and Bronstein, A.M. (2020). Baby steps towards few-shot learning with multiple semantics. arXiv."},{"key":"ref_48","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. Geovisualization"},{"key":"ref_49","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_50","first-page":"2579","article-title":"Visualizing data using t-SNE","volume":"9","author":"Hinton","year":"2008","journal-title":"J. Mach. Learn. Res."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/5\/311\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:10:49Z","timestamp":1760137849000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/11\/5\/311"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,14]]},"references-count":50,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["ijgi11050311"],"URL":"https:\/\/doi.org\/10.3390\/ijgi11050311","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,14]]}}}