{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T10:05:18Z","timestamp":1778321118904,"version":"3.51.4"},"reference-count":41,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,27]],"date-time":"2022-07-27T00:00:00Z","timestamp":1658880000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2022R300"],"award-info":[{"award-number":["PNURSP2022R300"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Copyright protection of medical images is a vital goal in the era of smart healthcare systems. In recent telemedicine applications, medical images are sensed using medical imaging devices and transmitted to remote places for screening by physicians and specialists. During their transmission, the medical images could be tampered with by intruders. Traditional watermarking methods embed the information in the host images to protect the copyright of medical images. The embedding destroys the original image and cannot be applied efficiently to images used in medicine that require high integrity. Robust zero-watermarking methods are preferable over other watermarking algorithms in medical image security due to their outstanding performance. Most existing methods are presented based on moments and moment invariants, which have become a prominent method for zero-watermarking due to their favorable image description capabilities and geometric invariance. Although moment-based zero-watermarking can be an effective approach to image copyright protection, several present approaches cannot effectively resist geometric attacks, and others have a low resistance to large-scale attacks. Besides these issues, most of these algorithms rely on traditional moment computation, which suffers from numerical error accumulation, leading to numerical instabilities, and time consumption and affecting the performance of these moment-based zero-watermarking techniques. In this paper, we derived multi-channel Gaussian\u2013Hermite moments of fractional-order (MFrGHMs) to solve the problems. Then we used a kernel-based method for the highly accurate computation of MFrGHMs to solve the computation issue. Then, we constructed image features that are accurate and robust. Finally, we presented a new zero-watermarking scheme for color medical images using accurate MFrGHMs and 1D Chebyshev chaotic features to achieve lossless copyright protection of the color medical images. We performed experiments where their outcomes ensure the robustness of the proposed zero-watermarking algorithms against various attacks. The proposed zero-watermarking algorithm achieves a good balance between robustness and imperceptibility. Compared with similar existing algorithms, the proposed algorithm has superior robustness, security, and time computation.<\/jats:p>","DOI":"10.3390\/s22155612","type":"journal-article","created":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T03:21:16Z","timestamp":1658978476000},"page":"5612","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Robust Zero-Watermarking of Color Medical Images Using Multi-Channel Gaussian-Hermite Moments and 1D Chebyshev Chaotic Map"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9843-6392","authenticated-orcid":false,"given":"Doaa Sami","family":"Khafaga","sequence":"first","affiliation":[{"name":"Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Faten Khalid","family":"Karim","sequence":"additional","affiliation":[{"name":"Department of Computer Sciences, College of Computer and Information Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed M.","family":"Darwish","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Assiut University, Assiut 71516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8065-8977","authenticated-orcid":false,"given":"Khalid M.","family":"Hosny","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,27]]},"reference":[{"key":"ref_1","first-page":"1558","article-title":"A blind medical image watermarking for secure E-healthcare application using crypto-watermarking system","volume":"29","author":"Aparna","year":"2020","journal-title":"J. Intell. Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"38821","DOI":"10.1109\/ACCESS.2022.3165813","article-title":"Multiple Zero-Watermarking of Medical Images for Internet of Medical Things","volume":"10","author":"Magdy","year":"2022","journal-title":"IEEE Access"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2893474","article-title":"On-board format-independent security of functional magnetic resonance images","volume":"16","author":"Castiglione","year":"2017","journal-title":"ACM Trans. Embedded Comput. Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"77212","DOI":"10.1109\/ACCESS.2018.2879919","article-title":"Parallel Multi-core CPU and GPU for Fast and Robust Medical Image Watermarking","volume":"6","author":"Hosny","year":"2018","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2556","DOI":"10.1109\/TIFS.2020.2972159","article-title":"Joint Watermarking-Encryption-JPEG-LS for Medical Image Reliability Control in Encrypted and Compressed Domains","volume":"15","author":"Haddad","year":"2020","journal-title":"IEEE Trans. Inf. Forensic Secur."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Abdel-Aziz, M.M., Hosny, K.M., Lashin, N.A., and Fouda, M.M. (2021). Blind Watermarking of Color Medical Images Using Hadamard Transform and Fractional-Order Moments. Sensors, 21.","DOI":"10.3390\/s21237845"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Zhou, X., Ma, Y., Zhang, Q., Mohammed, M.A., and Dama\u0161evi\u010dius, R. (2021). A Reversible Watermarking System for Medical Color Images: Balancing Capacity, Imperceptibility, and Robustness. Electronics, 10.","DOI":"10.3390\/electronics10091024"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1016\/j.compeleceng.2017.05.015","article-title":"Invariant image watermarking using accurate polar harmonic transforms","volume":"62","author":"Hosny","year":"2017","journal-title":"Comput. Electr. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"101695","DOI":"10.1016\/j.bspc.2019.101695","article-title":"Improving the management of medical imaging by using robust and secure dual watermarking","volume":"56","year":"2020","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2997","DOI":"10.1007\/s10462-021-10070-8","article-title":"Secure video communication using firefly optimization and visual cryptography","volume":"55","author":"Kumar","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Juarez-Sandoval, O.U., Garcia-Ugalde, F.J., Cedillo-Hernandez, M., Ramirez-Hernandez, J., and Hernandez-Gonzalez, L. (2021). Imperceptible\u2013Visible Watermarking to Information Security Tasks in Color Imaging. Mathematics, 9.","DOI":"10.3390\/math9192374"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"25101","DOI":"10.1007\/s11042-022-11956-7","article-title":"Security of medical images for telemedicine: A systematic review","volume":"81","author":"Magdy","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_13","first-page":"214","article-title":"Concept and application of zero-watermark","volume":"31","author":"Wen","year":"2003","journal-title":"Acta Electron. Sin."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ren, N., Zhao, Y., Zhu, C., Zhou, Q., and Xu, D. (2021). Copyright Protection Based on Zero Watermarking and Blockchain for Vector Maps. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10050294"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhou, Q., Zhu, C., Ren, N., Chen, W., and Gong, W. (2021). Zero Watermarking Algorithm for Vector Geographic Data Based on the Number of Neighboring Features. Symmetry, 13.","DOI":"10.3390\/sym13020208"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.jss.2007.07.036","article-title":"Adaptive watermark mechanism for rightful ownership protection","volume":"81","author":"Chang","year":"2008","journal-title":"J. Syst. Softw."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"28685","DOI":"10.1007\/s11042-018-5995-4","article-title":"Distinguishable zero-watermarking scheme with similarity-based retrieval for digital rights Management of Fundus Image. Multimed","volume":"77","author":"Zou","year":"2018","journal-title":"Tools Appl."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1166\/jmihi.2019.2559","article-title":"Zero-watermarking algorithm for medical images based on dual-tree complex wavelet transform and discrete cosine transform","volume":"9","author":"Liu","year":"2019","journal-title":"J. Med. Imaging Health Inform."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8463","DOI":"10.1007\/s11042-018-6877-5","article-title":"Contourlet-DCT based multiple robust watermarking for medical images","volume":"78","author":"Wu","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1007\/s10851-020-01002-2","article-title":"Color image zero-watermarking using accurate quaternion generalized orthogonal Fourier\u2013Mellin moments","volume":"63","author":"Wang","year":"2021","journal-title":"J. Math. Imaging Vis."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.sigpro.2018.11.011","article-title":"Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms","volume":"157","author":"Xia","year":"2019","journal-title":"Signal Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.sigpro.2019.06.025","article-title":"Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments","volume":"164","author":"Xia","year":"2019","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"122544","DOI":"10.1109\/ACCESS.2019.2935174","article-title":"Geometrically invariant color medical image null-watermarking based on precise quaternion polar harmonic Fourier moments","volume":"7","author":"Xia","year":"2019","journal-title":"IEEE Access"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1007\/s10851-021-01048-w","article-title":"Double medical images zero-watermarking algorithm based on the chaotic system and ternary accurate polar complex exponential transform","volume":"63","author":"Ma","year":"2021","journal-title":"J. Math. Imaging Vis."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"106568","DOI":"10.1016\/j.knosys.2020.106568","article-title":"Local quaternion polar harmonic Fourier moments-based multiple zero-watermarking scheme for color medical images","volume":"216","author":"Xia","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s10851-022-01084-0","article-title":"Fast Quaternion Log-Polar Radial Harmonic Fourier Moments for Color Image Zero-Watermarking","volume":"64","author":"Niu","year":"2022","journal-title":"J. Math. Imaging Vis."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"107324","DOI":"10.1016\/j.patcog.2020.107324","article-title":"New Fractional-order Legendre-Fourier Moments for Pattern Recognition Applications","volume":"103","author":"Hosny","year":"2020","journal-title":"Pattern Recognit."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107545","DOI":"10.1016\/j.sigpro.2020.107545","article-title":"Novel Fractional-Order Generic Jacobi-Fourier Moments for Image Analysis","volume":"172","author":"Hosny","year":"2020","journal-title":"Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2533","DOI":"10.1016\/j.jfranklin.2020.01.025","article-title":"Novel Fractional-Order Polar Harmonic Transforms for Gray-scale and Color Image Analysis","volume":"357","author":"Hosny","year":"2020","journal-title":"J. Frankl. Inst."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"103007","DOI":"10.1016\/j.bspc.2021.103007","article-title":"New geometrically invariant multiple zero-watermarking algorithm for color medical images","volume":"70","author":"Hosny","year":"2021","journal-title":"Biomed. Signal Process. Control"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s10489-021-02476-2","article-title":"A robust zero-watermarking algorithm for lossless copyright protection of medical images","volume":"52","author":"Xia","year":"2021","journal-title":"Appl. Intell."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wang, X., Zhang, Y., Tian, J., Niu, P., and Yang, H. (2022). Accurate quaternion fractional-order pseudo-Jacobi\u2013Fourier moments. Pattern Anal. Appl., 1\u201325.","DOI":"10.1007\/s10044-022-01071-6"},{"key":"ref_33","unstructured":"Abramowitz, M., and Stegun, I.A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Reprinted by Dover Publications: New York, NY, USA, 1965."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2290","DOI":"10.1016\/j.sigpro.2011.04.012","article-title":"Image analysis by Gaussian\u2013Hermite moments","volume":"91","author":"Yang","year":"2011","journal-title":"Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2488","DOI":"10.1109\/TIP.2022.3156380","article-title":"Image Analysis by Fractional-Order Gaussian-Hermite Moments","volume":"31","author":"Yang","year":"2022","journal-title":"IEEE Trans. Image Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.dsp.2018.04.001","article-title":"Multi-channel versus quaternion orthogonal rotation invariant moments for color image representation","volume":"78","author":"Chandan","year":"2018","journal-title":"Digit. Signal Prog."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.patcog.2018.11.014","article-title":"New set of multi-channel orthogonal moments for color image representation and recognition","volume":"88","author":"Hosny","year":"2019","journal-title":"Pattern Recognit."},{"key":"ref_38","unstructured":"Faires, J.D., and Burden, R.L. (2002). Numerical Methods, Brooks Cole Publication. [3rd ed.]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3740","DOI":"10.1016\/j.patcog.2007.05.004","article-title":"Circularly orthogonal moments for geometrically robust image watermarking","volume":"40","author":"Xin","year":"2007","journal-title":"Pattern Recognit."},{"key":"ref_40","unstructured":"Johnson, K.A., and Becker, J.A. (2022, April 19). The Whole Brain Atlas. Available online: http:\/\/www.med.harvard.edu\/AANLIB\/home.html."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.ins.2021.12.126","article-title":"2D e\u03c0-map for image encryption","volume":"589","author":"Erkan","year":"2022","journal-title":"Inf. Sci."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5612\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:57:38Z","timestamp":1760140658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/15\/5612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,27]]},"references-count":41,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["s22155612"],"URL":"https:\/\/doi.org\/10.3390\/s22155612","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,27]]}}}