{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T05:06:32Z","timestamp":1762059992909,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,30]],"date-time":"2022-07-30T00:00:00Z","timestamp":1659139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["1601268","61803237","61901246","ZR2019BF035","ZR2020MF042","ZR2020QF034"],"award-info":[{"award-number":["1601268","61803237","61901246","ZR2019BF035","ZR2020MF042","ZR2020QF034"]}]},{"name":"Natural Science Foundation of Shandong Province","award":["1601268","61803237","61901246","ZR2019BF035","ZR2020MF042","ZR2020QF034"],"award-info":[{"award-number":["1601268","61803237","61901246","ZR2019BF035","ZR2020MF042","ZR2020QF034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Robust quantization watermarking with perceptual JND model has made a great success for image copyright protection. Generally, either restores each color channel separately or processes the vector representation from three color channels with the traditional monochromatic model. And it cannot make full use of the high correlation among RGB channels. In this paper, we proposed a robust quaternion JND Model for color image watermarking (QuatJND). In contrast to the existing perceptual JND models, the advantage of QuatJND is that it can integrate quaternion representation domain and colorfulness simultaneously, and QuatJND incorporates the pattern guided contrast masking effect in quaternion domain. On the other hand, in order to efficiently utilize the color information, we further develop a robust quantization watermarking framework using the color properties of the quaternion DCT coefficients in QuatJND. And the quantization steps of each quaternion DCT block in the scheme are optimal. Experimental results show that our method has a good performance in term of robustness with better visual quality.<\/jats:p>","DOI":"10.3390\/e24081051","type":"journal-article","created":{"date-parts":[[2022,7,31]],"date-time":"2022-07-31T23:37:29Z","timestamp":1659310649000},"page":"1051","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["QuatJND: A Robust Quaternion JND Model for Color Image Watermarking"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1447-0524","authenticated-orcid":false,"given":"Wenbo","family":"Wan","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenqing","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenxiu","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zihan","family":"Diao","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yantong","family":"Zhan","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Shandong Normal University, Jinan 250358, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00500-017-2489-7","article-title":"Robust color image watermarking technique in the spatial domain","volume":"22","author":"Su","year":"2018","journal-title":"Soft Comput."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1109\/TIFS.2007.916275","article-title":"Color image watermarking using multidimensional Fourier transforms","volume":"3","author":"Tsui","year":"2008","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Thongkor, K., and Amornraksa, T. (2014, January 9\u201312). Digital image watermarking with partial embedding on blue color component. In Proceedings of Asia-Pacific Signal and Information Processing Association Annual Summit and Conference 2014 (APSIPA), Chiang Mai, Thailand.","DOI":"10.1109\/APSIPA.2014.7041667"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Watson, A.B. (1993, January 1\u20134). DCT quantization matrices visually optimized for individual images. Proceedings of the Human Vision, Visual Processing, and Digital Display IV, San Jose, CA, USA.","DOI":"10.1117\/12.152694"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1587\/transinf.E93.D.843","article-title":"Adaptive spread-transform dither modulation using a new perceptual model for color image watermarking","volume":"93","author":"Ma","year":"2010","journal-title":"IEICE Trans. Inf. Syst."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1109\/LSP.2013.2272193","article-title":"A novel DCT-based JND model for luminance adaptation effect in DCT frequency","volume":"20","author":"Bae","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1016\/j.sigpro.2004.12.002","article-title":"Improved estimation for just-noticeable visual distortion","volume":"85","author":"Zhang","year":"2005","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"13481","DOI":"10.1007\/s11042-015-2853-5","article-title":"Improved logarithmic spread transform dither modulation using a robust perceptual model","volume":"75","author":"Wan","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.patrec.2018.08.009","article-title":"Pattern complexity-based JND estimation for quantization watermarking","volume":"130","author":"Wan","year":"2020","journal-title":"Pattern Recognit. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"112868.1","DOI":"10.1016\/j.eswa.2019.112868","article-title":"Color image watermarking based on orientation diversity and color complexity","volume":"140","author":"Wang","year":"2020","journal-title":"Expert Syst. Appl."},{"key":"ref_11","first-page":"1080","article-title":"Robust image watermarking via perceptual structural regularity-based JND model","volume":"13","author":"Wang","year":"2019","journal-title":"Ksii Trans. Internet Inf. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Tsui, T.K., Zhang, X.P., and Androutsos, D. (2006, January 23\u201327). Quaternion image watermarking using the spatio-chromatic fourier coefficients analysis. Proceedings of the 14th ACM International Conference on Multimedia, Santa Barbara, CA, USA.","DOI":"10.1145\/1180639.1180682"},{"key":"ref_13","unstructured":"Bas, P., Le Bihan, N., and Chassery, J.M. (2003, January 6\u201310). Color image watermarking using quaternion Fourier transform. Proceedings of the 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, China."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ma, X., Xu, Y., Song, L., Yang, X., and Burkhardt, H. (April, January 23). Color image watermarking using local quaternion Fourier spectral analysis. Proceedings of the 2008 IEEE International Conference on Multimedia and Expo, Hannover, Germany.","DOI":"10.1109\/ICME.2008.4607414"},{"key":"ref_15","first-page":"2242","article-title":"Content based image watermarking algorithm in hypercomplex frequency domain","volume":"31","author":"Jiang","year":"2009","journal-title":"Syst. Eng. Electron."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.dsp.2014.02.010","article-title":"Full 4-D quaternion discrete Fourier transform based watermarking for color images","volume":"28","author":"Chen","year":"2014","journal-title":"Digit. Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Yanshan, L. (2010, January 24\u201328). A new color image blind watermarking algorithm based on quaternion. Proceedings of the IEEE 10th International Conference on Signal Processing Proceedings, Beijing, China.","DOI":"10.1109\/ICOSP.2010.5656141"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"23483","DOI":"10.1007\/s11042-018-5652-y","article-title":"Optimal blind watermarking for color images based on the U matrix of quaternion singular value decomposition","volume":"77","author":"Liu","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00500-016-2320-x","article-title":"A QDCT and SVD-based color image watermarking scheme using an optimized encrypted binary computer-generated hologram","volume":"22","author":"Li","year":"2018","journal-title":"Soft Comput."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Feng, W., and Hu, B. (2008, January 27\u201330). Quaternion discrete cosine transform and its application in color template matching. Proceedings of the 2008 Congress on Image and Signal Processing, Washington, DC, USA.","DOI":"10.1109\/CISP.2008.61"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2783","DOI":"10.1109\/78.960426","article-title":"Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT","volume":"49","author":"Pei","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1474","DOI":"10.1109\/TCSVT.2018.2841642","article-title":"High-quality color image compression by quantization crossing color spaces","volume":"29","author":"Zhu","year":"2019","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"133","DOI":"10.3126\/njst.v15i2.12130","article-title":"Comparative analysis of color image watermarking technique in RGB, YUV, and YCbCr color channels","volume":"15","author":"Koju","year":"2014","journal-title":"Nepal J. Sci. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1850015","DOI":"10.1142\/S0219467818500158","article-title":"An HVS inspired robust non-blind watermarking scheme in YCbCr Color Space","volume":"18","author":"Roy","year":"2018","journal-title":"Int. J. Image Graph."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4907","DOI":"10.1007\/s11042-018-6860-1","article-title":"Hybrid JND model-guided watermarking method for screen content images","volume":"79","author":"Wan","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"24057","DOI":"10.1007\/s11042-020-09102-2","article-title":"A novel attention-guided JND Model for improving robust image watermarking","volume":"79","author":"Wang","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"996","DOI":"10.1109\/LSP.2013.2277884","article-title":"Salient motion detection in compressed domain","volume":"20","author":"Muthuswamy","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Hasler, D., and Suesstrunk, S.E. (2003, January 20\u201324). Measuring colorfulness in natural images. In Proceedings of Human Vision and Electronic Imaging VIII, Santa Clara, CA, USA.","DOI":"10.1117\/12.477378"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1109\/TCE.2013.6626251","article-title":"No reference color image contrast and quality measures","volume":"59","author":"Panetta","year":"2013","journal-title":"IEEE Trans. Consum. Electron."},{"key":"ref_30","first-page":"30","article-title":"TID2008\u2014A Database for Evaluation of Full-Reference Visual Quality Assessment Metrics","volume":"10","author":"Ponomarenko","year":"2009","journal-title":"Adv. Mod. Radioelectron."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1526","DOI":"10.1109\/TIP.2011.2181522","article-title":"Quaternion Structural Similarity: A New Quality Index for Color Images","volume":"21","author":"Kolaman","year":"2011","journal-title":"IEEE Trans. Image Process."},{"key":"ref_32","first-page":"203","article-title":"Blind watermarking scheme based on U matrix through QSVD transformation","volume":"9","author":"Liu","year":"2015","journal-title":"Int. J. Secur. Its Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s00500-019-03924-5","article-title":"An improved watermarking algorithm for color image using Schur decomposition","volume":"24","author":"Su","year":"2020","journal-title":"Soft Comput."},{"key":"ref_34","unstructured":"Ell, T.A., and Sangwine, S.J. (2000, January 4\u20138). Decomposition of 2D hypercomplex Fourier transforms into pairs of complex Fourier transforms. In Proceeding of the 10th European Signal Processing Conference, Tampere, Finland."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1051\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:59:57Z","timestamp":1760140797000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/8\/1051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,30]]},"references-count":34,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["e24081051"],"URL":"https:\/\/doi.org\/10.3390\/e24081051","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2022,7,30]]}}}