{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:07:01Z","timestamp":1760242021987,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2018,11,24]],"date-time":"2018-11-24T00:00:00Z","timestamp":1543017600000},"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":["41401518","41801303"],"award-info":[{"award-number":["41401518","41801303"]}],"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":["BK20140066"],"award-info":[{"award-number":["BK20140066"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Vector geographic data play an important role in location information services. Digital watermarking has been widely used in protecting vector geographic data from being easily duplicated by digital forensics. Because the production and application of vector geographic data refer to many units and departments, the demand for multiple watermarking technology is increasing. However, multiple watermarking algorithm for vector geographic data draw less attention, and there are many urgent problems to be solved. Therefore, an efficient robust multiple watermark algorithm for vector geographic data is proposed in this paper. The coordinates in vector geographic data are first randomly divided into non-repetitive sets. The multiple watermarks are then embedded into the different sets. In watermark detection correlation, the Lindeberg theory is used to build a detection model and to confirm the detection threshold. Finally, experiments are made in order to demonstrate the detection algorithm, and to test its robustness against common attacks, especially against cropping attacks. The experimental results show that the proposed algorithm is robust against the deletion of vertices, addition of vertices, compression, and cropping attacks. Moreover, the proposed detection algorithm is compatible with single watermarking detection algorithms, and it has good performance in terms of detection efficiency.<\/jats:p>","DOI":"10.3390\/info9120296","type":"journal-article","created":{"date-parts":[[2018,11,26]],"date-time":"2018-11-26T03:24:27Z","timestamp":1543202667000},"page":"296","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["An Efficient Robust Multiple Watermarking Algorithm for Vector Geographic Data"],"prefix":"10.3390","volume":"9","author":[{"given":"Yingying","family":"Wang","sequence":"first","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution, Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6408-9962","authenticated-orcid":false,"given":"Chengsong","family":"Yang","sequence":"additional","affiliation":[{"name":"Field Engineering College, Army Engineering University of PLA, Nanjing 210007, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changqing","family":"Zhu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Virtual Geographic Environment, Ministry of Education, Nanjing Normal University, Nanjing 210023, China"},{"name":"State Key Laboratory Cultivation Base of Geographical Environment Evolution, Nanjing 210023, China"},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1339-813X","authenticated-orcid":false,"given":"Kaimeng","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Networks and Tele-Communications Engineering, Jinling Institute of Technology, Nanjing 211169, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Voigt, M., Yang, B., and Busch, C. 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