{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T21:05:47Z","timestamp":1792789547370,"version":"4.5.0"},"reference-count":34,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T00:00:00Z","timestamp":1611792000000},"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":["42071362"],"award-info":[{"award-number":["42071362"]}],"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":["41971338"],"award-info":[{"award-number":["41971338"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20191373"],"award-info":[{"award-number":["BK20191373"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012154","name":"Graduate Research and Innovation Projects of Jiangsu Province","doi-asserted-by":"publisher","award":["KYCX20_1182"],"award-info":[{"award-number":["KYCX20_1182"]}],"id":[{"id":"10.13039\/501100012154","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Zero watermarking is an important part of copyright protection of vector geographic data. However, how to improve the robustness of zero watermarking is still a critical challenge, especially in resisting attacks with significant distortion. We proposed a zero watermarking method for vector geographic data based on the number of neighboring features. The method makes full use of spatial characteristics of vector geographic data, including topological characteristics and statistical characteristics. First, the number of first-order neighboring features (NFNF) and the number of second-order neighboring features (NSNF) of every feature in vector geographic data are counted. Then, the watermark bit is determined by the NFNF value, and the watermark index is determined by the NSNF value. Finally, combine the watermark bits and the watermark indices to construct a watermark. Experiments verify the theoretical achievements and good robustness of this method. Simulation results also demonstrate that the normalized coefficient of the method is always kept at 1.00 under the attacks that distort data significantly, which has the superior performance in comparison to other methods.<\/jats:p>","DOI":"10.3390\/sym13020208","type":"journal-article","created":{"date-parts":[[2021,1,28]],"date-time":"2021-01-28T05:23:05Z","timestamp":1611811385000},"page":"208","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":24,"title":["Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8268-4666","authenticated-orcid":false,"given":"Qifei","family":"Zhou","sequence":"first","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Changqing","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Na","family":"Ren","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weitong","family":"Chen","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weiteng","family":"Gong","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/19475683.2018.1424737","article-title":"Reimagining the history of GIS","volume":"24","author":"Goodchild","year":"2018","journal-title":"Ann. 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