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Before embedding watermark, the color watermark image <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>W<\/mml:mi><\/mml:mrow><\/mml:math> with size of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>M<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>M<\/mml:mi><\/mml:math> is scrambled by Arnold transformation to obtain a meaningless image <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>W<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><\/mml:math>. Then, the color host image <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math> with size of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mi>N<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>N<\/mml:mi><\/mml:math> is divided into nonoverlapping <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:mrow><mml:mo>\u00d7<\/mml:mo><mml:mrow><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><mml:mo>\/<\/mml:mo><mml:mrow><mml:mi>M<\/mml:mi><\/mml:mrow><\/mml:mrow><\/mml:math> pixel blocks. In each <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> pixel block <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, we form a real matrix <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> with the red, green, and blue components of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> and perform the SVD of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. We then replace the three smallest singular values of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> by the red, green, and blue values of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>W<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> with scaling factor, to form a new watermarked host image <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M14\"><mml:mrow><mml:msub><mml:mrow><mml:mover accent=\"true\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><mml:mo>~<\/mml:mo><\/mml:mover><\/mml:mrow><mml:mrow><mml:mi>i<\/mml:mi><mml:mi>j<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. With the reserve procedure, we can extract the watermark from the watermarked host image. In the process of the algorithm, we only need to perform real number algebra operations, which have very low computational complexity and are more effective than the one using the quaternion SVD of color image.<\/jats:p>","DOI":"10.1155\/2016\/2497379","type":"journal-article","created":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T16:03:12Z","timestamp":1480003392000},"page":"1-9","source":"Crossref","is-referenced-by-count":8,"title":["A New Double Color Image Watermarking Algorithm Based on the SVD and Arnold Scrambling"],"prefix":"10.1155","volume":"2016","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1829-7327","authenticated-orcid":true,"given":"Ying","family":"Li","sequence":"first","affiliation":[{"name":"College of Mathematical Sciences, Liaocheng University, Shandong 252000, China"}]},{"given":"Musheng","family":"Wei","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Liaocheng University, Shandong 252000, China"},{"name":"College of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China"}]},{"given":"Fengxia","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Liaocheng University, Shandong 252000, China"}]},{"given":"Jianli","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematical Sciences, Liaocheng University, Shandong 252000, China"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-006-0008-4"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2009.08.010"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1109\/79.879337"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2009.02.005"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2010.05.032"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2010.11.030"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2013.06.025"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1155\/s1110865703211227"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.aeue.2010.09.008"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-013-1653-z"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2015.02.130"},{"key":"10","year":"2013"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1109\/tassp.1976.1162766"},{"key":"2","year":"1968"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1049\/el:19961331"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.02.068"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2016.03.031"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2013.08.026"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1109\/tip.2003.819861"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/2497379.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/2497379.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2016\/2497379.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,5,18]],"date-time":"2018-05-18T10:55:22Z","timestamp":1526640922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/jam\/2016\/2497379\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":19,"alternative-id":["2497379","2497379"],"URL":"https:\/\/doi.org\/10.1155\/2016\/2497379","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}