{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:06:34Z","timestamp":1792789594016,"version":"4.5.0"},"reference-count":38,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T00:00:00Z","timestamp":1676937600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20201100"],"award-info":[{"award-number":["BK20201100"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["42101433"],"award-info":[{"award-number":["42101433"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["AE202107"],"award-info":[{"award-number":["AE202107"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["BK20201100"],"award-info":[{"award-number":["BK20201100"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42101433"],"award-info":[{"award-number":["42101433"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["AE202107"],"award-info":[{"award-number":["AE202107"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Engineering Research Center for Agro-Ecological Big Data Analysis &amp; Application, Anhui University","award":["BK20201100"],"award-info":[{"award-number":["BK20201100"]}]},{"name":"National Engineering Research Center for Agro-Ecological Big Data Analysis &amp; Application, Anhui University","award":["42101433"],"award-info":[{"award-number":["42101433"]}]},{"name":"National Engineering Research Center for Agro-Ecological Big Data Analysis &amp; Application, Anhui University","award":["AE202107"],"award-info":[{"award-number":["AE202107"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>The existing digital watermarking schemes for vector maps focus mainly on the process of watermark embedding, while few works have been conducted on the topic of the self-optimization of watermark data in the process of watermark detection. There is thus still much room for accuracy improvement in watermark detection. In this paper, a model of mixed watermark data construction is built first. It constructs the error-correction codes and checking code of the original copyright watermark data and combines them to generate the final watermark data. Additionally, a lossless compression algorithm is designed for watermark data to constrain the total watermark length. Based on the constructed model, a self-error-correction-based reversible watermarking scheme is put forward for vector maps. In this scheme, map vertices are divided into non-intersecting groups first according to stability, and mixed watermark data are then embedded with respective vertex groups. Simulation results demonstrate that the watermark capacity of this scheme is 1.0000, the coordinate error caused by the watermark embedding process can be limited to no more than 0.00001 when the strength of watermark embedding is set to five, and several watermark bits can be effectively detected and corrected after watermark extraction. Experimental results and analysis show that it can strike a good balance among reversibility, invisibility, capacity and robustness. It can provide a novel solution to improve the watermark detection accuracy of digital watermarking schemes for vector maps.<\/jats:p>","DOI":"10.3390\/ijgi12030084","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T04:33:56Z","timestamp":1677040436000},"page":"84","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["A Self-Error-Correction-Based Reversible Watermarking Scheme for Vector Maps"],"prefix":"10.3390","volume":"12","author":[{"given":"Yinguo","family":"Qiu","sequence":"first","affiliation":[{"name":"Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiuyun","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaojue","family":"Zheng","sequence":"additional","affiliation":[{"name":"Nanjing Institute of Geography and Limnology, Chinese Academy of Sciences, Nanjing 210008, China"},{"name":"School of Environment Science and Spatial Informatics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1007\/s41651-021-00093-8","article-title":"Atmospheric Pollution Retrieval Using Path Radiance Derived from Remote Sensing Data","volume":"5","author":"Roy","year":"2021","journal-title":"J. Geovis. Spat. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/s41651-021-00094-7","article-title":"A GIS-based mathematical approach for generating 3D terrain model from high-resolution UAV imageries","volume":"5","author":"Ahmed","year":"2021","journal-title":"J. Geovis. Spat. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1007\/s11042-020-09776-8","article-title":"A novel multi-stage watermarking scheme of vector maps","volume":"80","author":"Qiu","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_4","first-page":"3475","article-title":"Storage feature-based watermarking algorithm with coordinate values preservation for vector line data","volume":"12","author":"Zhou","year":"2018","journal-title":"KSII Trans. Internet Inf. Syst."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1007\/s12145-017-0310-x","article-title":"A normalization-based watermarking scheme for 2D vector map data","volume":"10","author":"Yan","year":"2017","journal-title":"Earth Sci. Inform."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"30709","DOI":"10.1007\/s11042-020-08916-4","article-title":"A robust watermarking algorithm for vector geographic data based on qim and matching detection","volume":"79","author":"Yang","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Sahu, A.K., Hassaballah, M., Rao, R.S., and Suresh, G. (2022). Logistic-map based fragile image watermarking scheme for tamper detection and localization. Multimed. Tools Appl.","DOI":"10.1007\/s11042-022-13630-4"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1109\/TCSVT.2020.2969464","article-title":"A semi-fragile reversible watermarking for authenticating 2D engineering graphics based on improved region nesting","volume":"31","author":"Peng","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Guan, X., Feng, H., Zhang, W., Zhou, H., Zhang, J., and Yu, N. (2020, January 12\u201316). Reversible watermarking in deep convolutional neural networks for integrity authentication. Proceedings of the 28th ACM International Conference on Multimedia, Seattle, WA, USA.","DOI":"10.1145\/3394171.3413729"},{"key":"ref_10","first-page":"1","article-title":"Multilevel Digital Watermarking Algorithm for Vector Map Data","volume":"6","author":"Yang","year":"2021","journal-title":"Geomat. Spat. Inf. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, Y., Zhang, L., Wang, X., Zhang, X., and Zhang, Q. (2021). A novel invariant based commutative encryption and watermarking algorithm for vector maps. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10110718"},{"key":"ref_12","first-page":"684","article-title":"A blind watermarking algorithm for vector geo-spatial data based on coordinate mapping","volume":"15","author":"Yang","year":"2010","journal-title":"J. Image Graph."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1109\/TIFS.2007.902677","article-title":"Reversible data-hiding scheme for 2-D vector maps based on difference expansion","volume":"2","author":"Wang","year":"2007","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.cad.2013.10.005","article-title":"A high capacity reversible data hiding method for 2D vector maps based on virtual coordinates","volume":"47","author":"Wang","year":"2014","journal-title":"Comput.-Aided Des."},{"key":"ref_15","first-page":"114","article-title":"Discussion on the application of digital watermarking technology in vector map","volume":"20","author":"Yang","year":"2022","journal-title":"Geospat. Inf."},{"key":"ref_16","first-page":"1017","article-title":"Geo-information security technology: Progress and prospects","volume":"51","author":"Zhu","year":"2022","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_17","first-page":"136","article-title":"A blind watermarking algorithm for vector data against geometric transformation attack","volume":"39","author":"Wang","year":"2013","journal-title":"Comput. Eng."},{"key":"ref_18","first-page":"256","article-title":"Robust watermarking algorithm for geometrical transform for vector geo-spatial data based on invariant function","volume":"40","author":"Yang","year":"2011","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"11721","DOI":"10.1007\/s11042-014-2259-9","article-title":"Blind watermarking scheme for polylines in vector geo-spatial data","volume":"74","author":"Peng","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhou, Q., Ren, N., Zhu, C., and Zhu, A. (2020). Blind Digital Watermarking Algorithm against Projection Transformation for Vector Geographic Data. ISPRS Int. J. Geo-Inf., 9.","DOI":"10.3390\/ijgi9110692"},{"key":"ref_21","first-page":"175","article-title":"A blind watermarking algorithm robust to projection attacks for vector data","volume":"32","author":"Zhang","year":"2017","journal-title":"Remote Sens. Inf."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1109\/TVCG.2007.1050","article-title":"An optimal detector structure for the fourier descriptors domain watermarking of 2D vector graphics","volume":"13","author":"Doncel","year":"2007","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"367","DOI":"10.12928\/telkomnika.v12i2.49","article-title":"A new copyright protection for vector map using FFT-based watermarking","volume":"12","author":"Neyman","year":"2014","journal-title":"Telkomnika"},{"key":"ref_24","first-page":"190","article-title":"Watermarking algorithm for vector maps based on improved DFT and QR code","volume":"47","author":"Xi","year":"2022","journal-title":"Sci. Surv. Mapp."},{"key":"ref_25","first-page":"990","article-title":"A blind watermarking algorithm for copyright protection of vector geospatial data under controllable errors based on DFT","volume":"40","author":"Zhang","year":"2015","journal-title":"Geomat. Inf. Sci. Wuhan Univ."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhou, Q., Zhu, C., Ren, N., Chen, W., and Gong, W. (2021). Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features. Symmetry, 13.","DOI":"10.3390\/sym13020208"},{"key":"ref_27","first-page":"146","article-title":"A digital map watermarking algorithm based on discrete cosine transform","volume":"24","author":"Min","year":"2007","journal-title":"Comput. Appl. Softw."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wang, C., Li, Z., Liang, B., Zheng, H., Du, W., and Peng, Y. (2011, January 18\u201320). Watermarking vector maps based on minimum encasing rectangle. Proceedings of the 2011 IEEE International Conference on Intelligent Computation Technology and Automation, Shenzhen, China.","DOI":"10.1109\/ICICTA.2011.589"},{"key":"ref_29","first-page":"342","article-title":"A perception-based reversible watermarking algorithm for 2D-vector maps","volume":"20","author":"Men","year":"2010","journal-title":"Chin. High Technol. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1109\/LSP.2008.2006338","article-title":"Vector watermarking robust to both global and local geometrical distortions","volume":"15","author":"Im","year":"2008","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_31","first-page":"110","article-title":"Complementary watermarking algorithm of vector map based on discrete wavelet transform","volume":"30","author":"Zhang","year":"2010","journal-title":"J. Comput. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ren, N., Zhao, Y., Zhu, C., Zhou, Q., and Xu, D. (2021). Copyright Protection Based on Zero Watermarking and Blockchain for Vector Maps. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10050294"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/BF02962205","article-title":"Digital image watermarking based on discrete wavelet transform","volume":"17","author":"Ding","year":"2000","journal-title":"J. Comput. Sci. Technol."},{"key":"ref_34","first-page":"2379","article-title":"Reversible watermarking for vector maps based on interval mapping and maximum perturbation region","volume":"51","author":"Xi","year":"2022","journal-title":"Acta Geod. Cartogr. Sin."},{"key":"ref_35","first-page":"202","article-title":"Watermark embedded in polygonal line for copyright protection of contour map","volume":"6","author":"Zhou","year":"2006","journal-title":"Int. J. Comput. Sci. Netw. Secur."},{"key":"ref_36","first-page":"24","article-title":"Authentication-based double images fractal watermarking model of vector maps","volume":"30","author":"Sun","year":"2009","journal-title":"J. Commun."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"103183","DOI":"10.1016\/j.jnca.2021.103183","article-title":"A provably secure ECC-based access and handover authentication protocol for space information networks","volume":"193","author":"Guo","year":"2021","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2021131","DOI":"10.6703\/IJASE.202109_18(5).010","article-title":"Efficient and secure multiple digital signature to prevent forgery based on ECC","volume":"18","author":"Tanwar","year":"2021","journal-title":"Int. J. Appl. Sci. Eng."}],"container-title":["ISPRS International Journal of Geo-Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/3\/84\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:38:15Z","timestamp":1760121495000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2220-9964\/12\/3\/84"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,21]]},"references-count":38,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["ijgi12030084"],"URL":"https:\/\/doi.org\/10.3390\/ijgi12030084","relation":{},"ISSN":["2220-9964"],"issn-type":[{"value":"2220-9964","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,21]]}}}