{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:50:15Z","timestamp":1760233815078,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T00:00:00Z","timestamp":1614038400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, we explore the advantages of a fractional calculus based watermarking system for detecting Gaussian watermarks. To reach this goal, we selected a typical watermarking scheme and replaced the detection equation set by another set of equations derived from fractional calculus principles; then, we carried out a statistical assessment of the performance of both schemes by analyzing the Receiver Operating Characteristic (ROC) curve and the False Positive Percentage (FPP) when they are used to detect Gaussian watermarks. The results show that the ROC of a fractional equation based scheme has 48.3% more Area Under the Curve (AUC) and a False Positives Percentage median of 0.2% whilst the selected typical watermarking scheme has 3%. In addition, the experimental results suggest that the target applications of fractional schemes for detecting Gaussian watermarks are as a semi-fragile image watermarking systems robust to Gaussian noise.<\/jats:p>","DOI":"10.3390\/e23020255","type":"journal-article","created":{"date-parts":[[2021,2,23]],"date-time":"2021-02-23T12:40:16Z","timestamp":1614084016000},"page":"255","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Statistical Assessment of Discrimination Capabilities of a Fractional Calculus Based Image Watermarking System for Gaussian Watermarks"],"prefix":"10.3390","volume":"23","author":[{"given":"Mario","family":"Gonzalez-Lee","sequence":"first","affiliation":[{"name":"Facultad de Ingenier\u00eda en Electr\u00f3nica y Comunicaciones, Universidad Veracruzana, Av. Venustiano Carranza S\/N, Poza Rica Veracruz C.P. 93390, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7785-5272","authenticated-orcid":false,"given":"Hector","family":"Vazquez-Leal","sequence":"additional","affiliation":[{"name":"Facultad de Instrumentaci\u00f3n Electr\u00f3nica, Universidad Veracruzana Lomas del Estadio S\/N, Xalapa Veracruz C.P. 91090, Mexico"},{"name":"Consejo Veracruzano de Investigaci\u00f3n Cient\u00edfica y Desarrollo Tecnol\u00f3gico (COVEICYDET), Av. Rafael Murillo Vidal No. 1735, Cuauhtemoc, Xalapa Veracruz C.P. 91069, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis J.","family":"Morales-Mendoza","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda en Electr\u00f3nica y Comunicaciones, Universidad Veracruzana, Av. Venustiano Carranza S\/N, Poza Rica Veracruz C.P. 93390, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1346-7825","authenticated-orcid":false,"given":"Mariko","family":"Nakano-Miyatake","sequence":"additional","affiliation":[{"name":"Seccion de Estudios de Posgrado e Investigacion, Instituto Polit\u00e9cnico Nacional, Av. Santa Ana No. 1000, Del. Coyacan, Ciudad de Mexico C.P. 04440, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7786-2050","authenticated-orcid":false,"given":"Hector","family":"Perez-Meana","sequence":"additional","affiliation":[{"name":"Seccion de Estudios de Posgrado e Investigacion, Instituto Polit\u00e9cnico Nacional, Av. Santa Ana No. 1000, Del. Coyacan, Ciudad de Mexico C.P. 04440, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan R.","family":"Laguna-Camacho","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda en Mec\u00e1nica Electrica, Universidad Veracruzana, Av. Venustiano Carranza S\/N, Poza Rica Veracruz C.P. 93390, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1109\/79.879337","article-title":"Watermarking digital image and video data. A state-of-the-art overview","volume":"17","author":"Langelaar","year":"2000","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_2","unstructured":"Gonzalez-Lee, M., Morales-Mendoza, L.J., and Gonzalez-Lee, E. (2012). Detecci\u00f3n \u00f3ptima de marcas de agua digitales. 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