{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:03:22Z","timestamp":1760238202773,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,7,26]],"date-time":"2020-07-26T00:00:00Z","timestamp":1595721600000},"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":["61272432"],"award-info":[{"award-number":["61272432"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Innovation and Entrepreneurship Training Program of University of  Science and Technology Liaoning","award":["202010146561"],"award-info":[{"award-number":["202010146561"]}]},{"DOI":"10.13039\/501100007129","name":"Shandong Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["ZR2014JL044"],"award-info":[{"award-number":["ZR2014JL044"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"name":"MOE (Ministry of Education in China) Project of Humanities and Social Sciences","award":["18YJAZH110"],"award-info":[{"award-number":["18YJAZH110"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Creative digital artwork is usually the outcome of a long period of intellectual creation and labor of an artist. Similarly, computer-created digital artwork is an outcome of a large amount of machine time and computational resources. However, such intellectual properties can be easily copied by illegal users. Copyright protection of digital art is increasingly more important than before. Recently, using a computational approach to generate string art tends to be popular and attractive. To protect the illegal usage of the digital form of string art, we propose a data hiding algorithm specifically designed for string art. A digital string art image consists of a sequence of string lines, each specified by two nails fixed at the two ends of that line. The encrypted secret data (the watermark) is embedded into the list of line segments by odd\u2013even modulation, where a bit \u20181\u2019 is embedded by forcing the next node to be an odd node, and a bit \u20180\u2019 is embedded by forcing the next node to be an even node. To minimize the impact of data embedding on the quality of the original string art image, a local optimization algorithm is developed to select the nodes that produce minimal distortion. To quantify the embedding distortion, we introduce a smoothing filter model for the human vision system (HVS) specifically tailored to string art image. Experimental results show that using the proposed algorithm, the distortion between the original string art image and the watermarked string art image is unnoticeable. The modified string art image is statistically indistinguishable from the original string art, and hence is secure under steganalysis. To our best knowledge, this is the first work towards data hiding and copyright protection of digital string art.<\/jats:p>","DOI":"10.3390\/sym12081227","type":"journal-article","created":{"date-parts":[[2020,7,27]],"date-time":"2020-07-27T09:24:49Z","timestamp":1595841889000},"page":"1227","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Data Hiding in Symmetric Circular String Art"],"prefix":"10.3390","volume":"12","author":[{"given":"Yu-Song","family":"Yan","sequence":"first","affiliation":[{"name":"School of Architecture and Art Design, University of Science and Technology LiaoNing, Anshan 114051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui-Li","family":"Cai","sequence":"additional","affiliation":[{"name":"College of Internet of Things Engineering, Hohai University, Changzhou 213022, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2929-464X","authenticated-orcid":false,"given":"Bin","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Electronic and Information Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1111\/cgf.13609","article-title":"LinesLab: A Flexible Low-Cost Approach for the Generation of Physical Monochrome Art","volume":"38","author":"Stoppel","year":"2019","journal-title":"Comput. 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