{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T11:37:59Z","timestamp":1778067479647,"version":"3.51.4"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T00:00:00Z","timestamp":1636156800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T00:00:00Z","timestamp":1636156800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100009051","name":"Universidad T\u00e9cnica Federico Santa Mar\u00eda","doi-asserted-by":"publisher","award":["PI_LI_19_11"],"award-info":[{"award-number":["PI_LI_19_11"]}],"id":[{"id":"10.13039\/100009051","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100009051","name":"Universidad T\u00e9cnica Federico Santa Mar\u00eda","doi-asserted-by":"publisher","award":["PI_LIR_2020_20"],"award-info":[{"award-number":["PI_LIR_2020_20"]}],"id":[{"id":"10.13039\/100009051","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"crossref","award":["MATH-AMSUD 20-MATH-03"],"award-info":[{"award-number":["MATH-AMSUD 20-MATH-03"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100020884","name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","doi-asserted-by":"crossref","award":["MATH-AMSUD 20-MATH-03"],"award-info":[{"award-number":["MATH-AMSUD 20-MATH-03"]}],"id":[{"id":"10.13039\/501100020884","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Advanced Center for Electrical and Electronic Engineering","award":["FB-0008"],"award-info":[{"award-number":["FB-0008"]}]},{"name":"Secretar\u00eda de Ciencia y Tecnolog\u00eda","award":["PID 33620180100055CB"],"award-info":[{"award-number":["PID 33620180100055CB"]}]},{"name":"Secretar\u00eda de Ciencia y Tecnolog\u00eda","award":["PID 33620180100055CB"],"award-info":[{"award-number":["PID 33620180100055CB"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["SIViP"],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s11760-021-02051-9","type":"journal-article","created":{"date-parts":[[2021,11,6]],"date-time":"2021-11-06T20:02:31Z","timestamp":1636228951000},"page":"1035-1042","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Statistical estimation of the structural similarity index for image quality assessment"],"prefix":"10.1007","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4675-5201","authenticated-orcid":false,"given":"Felipe","family":"Osorio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronny","family":"Vallejos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wilson","family":"Barraza","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Silvia Mar\u00eda","family":"Ojeda","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcos Alejandro","family":"Landi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,6]]},"reference":[{"key":"2051_CR1","doi-asserted-by":"publisher","first-page":"4695","DOI":"10.1109\/TIP.2012.2214050","volume":"21","author":"A Mittal","year":"2012","unstructured":"Mittal, A., Moorthy, A.K., Bovik, A.C.: No-reference image quality assessment in the spatial domain. IEEE Trans. Image Process. 21, 4695\u20134708 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"2051_CR2","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1109\/LGRS.2014.2329183","volume":"12","author":"K Wang","year":"2015","unstructured":"Wang, K., Yong, B., Gu, X., Xiao, P., Zhang, X.: Spectral similarity measure using frequency spectrum for hyperspectral image classification. IEEE Geosci. Remote Sens. 12, 130\u2013134 (2015)","journal-title":"IEEE Geosci. Remote Sens."},{"key":"2051_CR3","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1109\/97.995823","volume":"9","author":"Z Wang","year":"2002","unstructured":"Wang, Z., Bovik, A.C.: A universal image quality index. IEEE Signal Proc. Lett. 9, 81\u201384 (2002)","journal-title":"IEEE Signal Proc. Lett."},{"key":"2051_CR4","doi-asserted-by":"crossref","unstructured":"Zhang, L., Zhang, L., Mou, X., ZHang, D.: FSIM: A feature similarity index for image quality assessment. IEEE Trans. Image Process. 20, 2378\u20132386 (2011)","DOI":"10.1109\/TIP.2011.2109730"},{"key":"2051_CR5","doi-asserted-by":"publisher","first-page":"1488","DOI":"10.1109\/TIP.2011.2173206","volume":"21","author":"D Brunet","year":"2012","unstructured":"Brunet, D., Vrscay, E.R., Wang, Z.: On the mathematical properties of the structural similarity index. IEEE Trans. Image Process. 21, 1488\u20131499 (2012)","journal-title":"IEEE Trans. Image Process."},{"key":"2051_CR6","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s10851-016-0635-y","volume":"56","author":"R Vallejos","year":"2016","unstructured":"Vallejos, R., Mancilla, D., Acosta, J.: Image similarity assessment based on coefficients of spatial association. J. Math. Imaging Vis. 56, 77\u201398 (2016)","journal-title":"J. Math. Imaging Vis."},{"key":"2051_CR7","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","volume":"13","author":"Z Wang","year":"2004","unstructured":"Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600\u2013612 (2004)","journal-title":"IEEE Trans. Image Process."},{"key":"2051_CR8","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1109\/TIP.2005.859378","volume":"15","author":"HR Sheikh","year":"2006","unstructured":"Sheikh, H.R., Bovik, C.: Image information and visual quality. IEEE Trans. Image Process. 15, 430\u2013444 (2006)","journal-title":"IEEE Trans. Image Process."},{"key":"2051_CR9","doi-asserted-by":"publisher","first-page":"2284","DOI":"10.1109\/TIP.2007.901820","volume":"16","author":"DM Chandler","year":"2007","unstructured":"Chandler, D.M., Hemami, S.S.: VSNR: A wavelet-based visual signal-to-noise-ratio for natural images. IEEE T. Image Process. 16, 2284\u20132298 (2007)","journal-title":"IEEE T. Image Process."},{"key":"2051_CR10","doi-asserted-by":"publisher","first-page":"3345","DOI":"10.1109\/TIP.2015.2442920","volume":"24","author":"K Ma","year":"2015","unstructured":"Ma, K., Zeng, K., Wang, Z.: Perceptual quality assessment for multi-exposure image fusion. IEEE Trans. Image Process. 24, 3345\u20133356 (2015)","journal-title":"IEEE Trans. Image Process."},{"key":"2051_CR11","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1109\/LGRS.2016.2515621","volume":"13","author":"YK Wang","year":"2016","unstructured":"Wang, Y.K., Li, L., Zhou, X.Y., Cui, T.J.: Supervised automatic detection of UWB ground-penetrating radar targets using the regression SSIM measure. IEEE Geosci. Remote Sens. 13, 621\u2013625 (2016)","journal-title":"IEEE Geosci. Remote Sens."},{"key":"2051_CR12","doi-asserted-by":"crossref","unstructured":"Ojeda, S., Vallejos, R., Lamberti, P.: Measure of similarity between images based on the codispersion coefficient. J. Electron. Imaging 21, 023019 (2012)","DOI":"10.1117\/1.JEI.21.2.023019"},{"key":"2051_CR13","doi-asserted-by":"publisher","first-page":"2925","DOI":"10.1016\/j.csda.2011.04.021","volume":"55","author":"H Wang","year":"2011","unstructured":"Wang, H., Maldonado, D., Silwal, S.: A nonparametric-test-based structural similarity measure for digital images. Comput. Stat. Data Anal. 55, 2925\u20132936 (2011)","journal-title":"Comput. Stat. Data Anal."},{"key":"2051_CR14","doi-asserted-by":"crossref","unstructured":"Rehuman, A., Wang, Z.: Reduced-reference SSIM estimation. In: Proceedings of 2010 IEEE 17th International Conference on Image Processing. Hong Kong, pp. 26\u201329 (2010)","DOI":"10.1109\/ICIP.2010.5653508"},{"key":"2051_CR15","first-page":"221","volume":"8","author":"Z Wang","year":"2015","unstructured":"Wang, Z., Li, L., Wu, S., Xia, Y., Wan, Z., Cai, C.: A new image quality assessment algorithm based on SSIM and multiple regressions. Int. J. Signal Process. 8, 221\u2013230 (2015)","journal-title":"Int. J. Signal Process."},{"key":"2051_CR16","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/s11760-009-0144-1","volume":"5","author":"R Dosselmann","year":"2011","unstructured":"Dosselmann, R., Yang, X.D.: A comprehensive assessment of the structural similarity index. SIViP 5, 81\u201391 (2011)","journal-title":"SIViP"},{"key":"2051_CR17","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1109\/TCSVT.2013.2240918","volume":"23","author":"C Yeo","year":"2013","unstructured":"Yeo, C., Tan, H.L., Tan, Y.H.: On rate distortion optimization using SSIM. IEEE Trans. Circuits Syst. Video 23, 1170\u20131181 (2013)","journal-title":"IEEE Trans. Circuits Syst. Video"},{"key":"2051_CR18","doi-asserted-by":"publisher","first-page":"489","DOI":"10.1007\/s11760-017-1184-6","volume":"12","author":"S Kim","year":"2018","unstructured":"Kim, S., Pak, D., Lee, S.: SSIM-based distortion metric for film grain noise in HEVC. SIViP 12, 489\u2013496 (2018)","journal-title":"SIViP"},{"key":"2051_CR19","doi-asserted-by":"publisher","first-page":"1079","DOI":"10.1080\/01621459.1987.10478543","volume":"82","author":"M Davidian","year":"1987","unstructured":"Davidian, M., Carroll, R.J.: Variance function estimation. J. Am. Stat. Assoc. 82, 1079\u20131091 (1987)","journal-title":"J. Am. Stat. Assoc."},{"key":"2051_CR20","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1109\/36.581981","volume":"35","author":"AC Frery","year":"1997","unstructured":"Frery, A.C., M\u00fcller, H.J., Yanasse, C.C.F., Sant\u2019Anna, S.J.S.: A model for extremely heterogeneous clutter. IEEE Trans. Geosci. Remote 35, 648\u2013659 (1997)","journal-title":"IEEE Trans. Geosci. Remote"},{"key":"2051_CR21","volume-title":"Nonlinear Methods in Econometrics","author":"SM Goldfeld","year":"1972","unstructured":"Goldfeld, S.M., Quandt, R.E.: Nonlinear Methods in Econometrics. North-Holland, Amsterdam (1972)"},{"key":"2051_CR22","volume-title":"Nonlinear Regression","author":"GAF Seber","year":"1988","unstructured":"Seber, G.A.F., Wild, C.J.: Nonlinear Regression. Wiley, New York (1988)"},{"key":"2051_CR23","doi-asserted-by":"publisher","first-page":"801","DOI":"10.1016\/S0167-9473(02)00102-0","volume":"40","author":"F Cribari-Neto","year":"2002","unstructured":"Cribari-Neto, F., Frery, A.C., Silva, M.F.: Improved estimation of clutter properties in speckled imagery. Comput. Stat. Data Anal. 40, 801\u2013824 (2002)","journal-title":"Comput. Stat. Data Anal."},{"key":"2051_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-2873-3","volume-title":"Transformation and Weighting in Regression","author":"RJ Carroll","year":"1988","unstructured":"Carroll, R.J., Ruppert, D.: Transformation and Weighting in Regression. Chapman and Hall, New York (1988)"},{"key":"2051_CR25","volume-title":"Algorithms for Minimization without Derivatives","author":"RP Brent","year":"1973","unstructured":"Brent, R.P.: Algorithms for Minimization without Derivatives. Dover, New York (1973)"},{"key":"2051_CR26","volume-title":"Compact Numerical Methods for Computers. Linear Algebra and Function Minimization","author":"JC Nash","year":"1990","unstructured":"Nash, J.C.: Compact Numerical Methods for Computers. Linear Algebra and Function Minimization. Adam Hilger, Bristol (1990)"},{"key":"2051_CR27","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511751950","volume-title":"Statistics and Econometrics Models: General Concepts, Estimation, Prediction, and Algortihms","author":"C Gorieroux","year":"1995","unstructured":"Gorieroux, C., Monfort, A.: Statistics and Econometrics Models: General Concepts, Estimation, Prediction, and Algortihms. Cambridge University Press, Cambridge (1995)"},{"key":"2051_CR28","first-page":"206","volume":"34","author":"GR Terrell","year":"2002","unstructured":"Terrell, G.R.: The gradient statistic. Comput. Sci. Stat. 34, 206\u2013215 (2002)","journal-title":"Comput. Sci. Stat."},{"key":"2051_CR29","unstructured":"Osorio, F., Vallejos, R.: SpatialPack: Tools for assessment the association between two spatial processes. R package version 0.3-8196. CRAN.R-project.org\/package=SpatialPack (2020)"},{"key":"2051_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-56681-4","volume-title":"Spatial Relationships Between Two Georeferenced Variables: With Applications in R","author":"R Vallejos","year":"2020","unstructured":"Vallejos, R., Osorio, F., Bevilacqua, M.: Spatial Relationships Between Two Georeferenced Variables: With Applications in R. Springer, Cham (2020)"},{"key":"2051_CR31","doi-asserted-by":"publisher","first-page":"925","DOI":"10.1198\/106186007X238828","volume":"16","author":"C Loader","year":"2007","unstructured":"Loader, C., Pilla, R.S.: Iteratively reweighted generalized least squares for estimation and testing with correlated data: an inference function framework. J. Computat. Graph. Stat. 16, 925\u2013945 (2007)","journal-title":"J. Computat. Graph. Stat."},{"key":"2051_CR32","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1080\/01621459.1996.10476932","volume":"91","author":"JP Buonaccorsi","year":"1996","unstructured":"Buonaccorsi, J.P.: Measurement error in the response in the general linear model. J. Am. Stat. Assoc. 91, 633\u2013642 (1996)","journal-title":"J. Am. Stat. Assoc."}],"container-title":["Signal, Image and Video Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-021-02051-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11760-021-02051-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11760-021-02051-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,16]],"date-time":"2022-04-16T14:15:08Z","timestamp":1650118508000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11760-021-02051-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,6]]},"references-count":32,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["2051"],"URL":"https:\/\/doi.org\/10.1007\/s11760-021-02051-9","relation":{},"ISSN":["1863-1703","1863-1711"],"issn-type":[{"value":"1863-1703","type":"print"},{"value":"1863-1711","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,6]]},"assertion":[{"value":"11 February 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 July 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 October 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 November 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}