{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T21:43:31Z","timestamp":1762033411357,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2017,3,10]],"date-time":"2017-03-10T00:00:00Z","timestamp":1489104000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100007136","name":"Secretar\u00eda de Estado de Investigaci\u00f3n, Desarrollo e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2014-54710-P","MTM2014-54710-P"],"award-info":[{"award-number":["MTM2014-54710-P","MTM2014-54710-P"]}],"id":[{"id":"10.13039\/501100007136","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007136","name":"Secretar\u00eda de Estado de Investigaci\u00f3n, Desarrollo e Innovaci\u00f3n","doi-asserted-by":"publisher","award":["MTM2014-54710-P","MTM2014-54710-P"],"award-info":[{"award-number":["MTM2014-54710-P","MTM2014-54710-P"]}],"id":[{"id":"10.13039\/501100007136","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Centre for Mathematics of the University of Coimbra, Portuguese Government FCT\/MCTES and European Regional Development Fund, Partnership Agreement PT2020","award":["UID\/MAT\/00324\/2013"],"award-info":[{"award-number":["UID\/MAT\/00324\/2013"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1007\/s10851-017-0721-9","type":"journal-article","created":{"date-parts":[[2017,3,10]],"date-time":"2017-03-10T13:20:03Z","timestamp":1489152003000},"page":"427-446","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Cross-Diffusion Systems for Image Processing: II. The Nonlinear Case"],"prefix":"10.1007","volume":"58","author":[{"given":"A.","family":"Ara\u00fajo","sequence":"first","affiliation":[]},{"given":"S.","family":"Barbeiro","sequence":"additional","affiliation":[]},{"given":"E.","family":"Cuesta","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6001-3829","authenticated-orcid":false,"given":"A.","family":"Dur\u00e1n","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,3,10]]},"reference":[{"key":"721_CR1","volume-title":"Sobolev Spaces","author":"RA Adams","year":"1975","unstructured":"Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)"},{"key":"721_CR2","unstructured":"Ara\u00fajo, A., Barbeiro, S., Cuesta, E., Dur\u00e1n, A.: Cross-diffusion systems for image processing: I. The linear case. Preprint available at http:\/\/arxiv.org\/abs\/1605.02923"},{"key":"721_CR3","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF00375127","volume":"123","author":"L \u00c1lvarez","year":"1993","unstructured":"\u00c1lvarez, L., Guichard, F., Lions, P.-L., Morel, J.-M.: Axioms and fundamental equations for image processing. Arch. Ration. Mech. Anal. 123, 199\u2013257 (1993)","journal-title":"Arch. Ration. Mech. Anal."},{"issue":"1","key":"721_CR4","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1023\/A:1008170101536","volume":"39","author":"L \u00c1lvarez","year":"2000","unstructured":"\u00c1lvarez, L., Weickert, J., S\u00e1nchez, J.: Reliable estimation of dense optical flow fields with large displacements. Int. J. Comput. Vis. 39(1), 41\u201356 (2000)","journal-title":"Int. J. Comput. Vis."},{"key":"721_CR5","doi-asserted-by":"crossref","first-page":"1284","DOI":"10.1137\/110825789","volume":"50","author":"A Ara\u00fajo","year":"2012","unstructured":"Ara\u00fajo, A., Barbeiro, S., Serranho, P.: Stability of finite difference schemes for complex diffusion processes. SIAM J. Numer. Anal. 50, 1284\u20131296 (2012)","journal-title":"SIAM J. Numer. Anal."},{"key":"721_CR6","volume-title":"Mathematical Problems in Image Processing","author":"J Aubert","year":"2001","unstructured":"Aubert, J., Kornprobst, P.: Mathematical Problems in Image Processing. Springer, Berlin (2001)"},{"issue":"23","key":"721_CR7","doi-asserted-by":"crossref","first-page":"24048","DOI":"10.1364\/OE.18.024048","volume":"18","author":"R Bernardes","year":"2010","unstructured":"Bernardes, R., Maduro, C., Serranho, P., Ara\u00fajo, A., Barbeiro, S., Cunha-Vaz, J.: Improved adaptive complex diffusion despeckling filter. Opt. Express. 18(23), 24048\u201324059 (2010)","journal-title":"Opt. Express."},{"key":"721_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-70914-7","volume-title":"Functional Analysis. Sobolev Spaces and Partial Differential Equations","author":"H Brezis","year":"2011","unstructured":"Brezis, H.: Functional Analysis. Sobolev Spaces and Partial Differential Equations. Springer, New York (2011)"},{"issue":"1","key":"721_CR9","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1137\/0729012","volume":"29","author":"F Catt\u00e9","year":"1992","unstructured":"Catt\u00e9, F., Lions, P.-L., Morel, J.-M., Coll, B.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182\u2013193 (1992)","journal-title":"SIAM J. Numer. Anal."},{"key":"721_CR10","doi-asserted-by":"crossref","unstructured":"Cr\u00e9t\u00e9-Roffet, F., Dolmiere, T., Ladret, P., Nicolas, M.: The blur effect: perception and estimation with a new no-reference perceptual blur metric. In: Proc. SPIE on Human Vision and Electronic Imaging XII, San Jos\u00e9, California, USA, 11 pages (2007)","DOI":"10.1117\/12.702790"},{"issue":"2","key":"721_CR11","first-page":"281","volume":"95","author":"G Galiano","year":"2001","unstructured":"Galiano, G., Garz\u00f3n, M.J., J\u00fcngel, A.: Analysis and numerical solution of a nonlinear cross-diffusion system arising in population dynamics. Rev. R. Acad. Cie. Ser. A Mat. 95(2), 281\u2013295 (2001)","journal-title":"Rev. R. Acad. Cie. Ser. A Mat."},{"key":"721_CR12","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/s002110200406","volume":"93","author":"G Galiano","year":"2003","unstructured":"Galiano, G., Garz\u00f3n, M.J., J\u00fcngel, A.: Semi-discretization in time and numerical convergence of solutions of a nonlinear cross-diffusion population model. Numer. Math. 93, 655\u2013673 (2003)","journal-title":"Numer. Math."},{"key":"721_CR13","doi-asserted-by":"crossref","unstructured":"Gilboa, G., Zeevi, Y. Y., Sochen, N. A.: Complex diffusion processes for image filtering. In: Scale-Space and Morphology in Computer Vision, pp. 299-307, Springer, Berlin (2001)","DOI":"10.1007\/3-540-47778-0_27"},{"key":"721_CR14","doi-asserted-by":"crossref","unstructured":"Gilboa, G., Sochen, N. A., Zeevi, Y. Y.: Generalized shock filters and complex diffusion. In: Computer Vision-ECCV, pp. 399-413, Springer, Berlin (2002)","DOI":"10.1007\/3-540-47969-4_27"},{"issue":"8","key":"721_CR15","doi-asserted-by":"crossref","first-page":"1020","DOI":"10.1109\/TPAMI.2004.47","volume":"26","author":"G Gilboa","year":"2004","unstructured":"Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020\u20131036 (2004)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"721_CR16","doi-asserted-by":"crossref","unstructured":"ter Haar Romeny, B. (Ed.).: Geometry-Driven Diffusion in Computer Vision, Springer, New York (1994)","DOI":"10.1007\/978-94-017-1699-4"},{"key":"721_CR17","doi-asserted-by":"crossref","first-page":"1328","DOI":"10.1137\/S003613999529558X","volume":"57","author":"S Kinchenassamy","year":"1997","unstructured":"Kinchenassamy, S.: The Perona\u2013Malik paradox. SIAM J. Appl. Math. 57, 1328\u20131342 (1997)","journal-title":"SIAM J. Appl. Math."},{"key":"721_CR18","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/023","volume-title":"Linear and Quasilinear Equations of Parabolic Type","author":"OA Ladyzenskaya","year":"1968","unstructured":"Ladyzenskaya, O.A., Solonnikov, V.A., Ural\u2019ceva, N.N.: Linear and Quasilinear Equations of Parabolic Type. Amer. Math. Soc, Providence (1968)"},{"key":"721_CR19","doi-asserted-by":"crossref","unstructured":"Wah, B. (ed.): Scale space. Encyclopedia of Computer Science and Engineering, vol. IV, pp. 2495\u20132509. Willey, Hoboken (2009)","DOI":"10.1002\/9780470050118.ecse609"},{"key":"721_CR20","unstructured":"Lorenz, D.A., Bredies, K., Zeevi, Y.Y.: Nonlinear complex and cross diffusion. Unpublished report, University of Bremen (2006). Freely available in: https:\/\/www.researchgate.net"},{"key":"721_CR21","doi-asserted-by":"crossref","first-page":"565","DOI":"10.1109\/TPAMI.1986.4767833","volume":"8","author":"H-H Nagel","year":"1986","unstructured":"Nagel, H.-H., Enkelmann, W.: An investigation of smoothness constraints for the estimation of displacement vector fields from images sequences. IEEE Trans. Pattern Anal. Mach. Intell. 8, 565\u2013593 (1986)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"issue":"1","key":"721_CR22","first-page":"9","volume":"45","author":"W-M Ni","year":"1998","unstructured":"Ni, W.-M.: Diffusion, cross-diffusion and their spike-layer steady states. Notices AMS. 45(1), 9\u201318 (1998)","journal-title":"Notices AMS."},{"issue":"7","key":"721_CR23","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1109\/34.391411","volume":"17","author":"EJ Pauwels","year":"1995","unstructured":"Pauwels, E.J., Van Gool, L.J., Fiddelaers, P., Moons, T.: An extended class of scale-invariant and recursive scale space filters. Pattern Anal. Mach. Intell. 17(7), 691\u2013701 (1995)","journal-title":"Pattern Anal. Mach. Intell."},{"key":"721_CR24","doi-asserted-by":"crossref","unstructured":"Peter, P., Weickert, J., Munk, A., Krivobokova, T., Li, H.: Justifying tensor-driven diffusion from structure-adaptive statistics of natural images. In: Energy Minimization Methods in Computer Vision and Pattern Recognition, Volume 8932 of the series Lecture Notes in Computer Science, pp. 263\u2013277 (2015)","DOI":"10.1007\/978-3-319-14612-6_20"},{"key":"721_CR25","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1109\/34.56205","volume":"12","author":"P Perona","year":"1990","unstructured":"Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629\u2013639 (1990)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"721_CR26","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/978-94-017-1699-4_9","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"M Proesmans","year":"1994","unstructured":"Proesmans, M., Pauwels, E., Van Gool, L.: Coupled geometry-driven diffusion equations for low-level vision. In: ter Haar-Romeny, B. (ed.) Geometry-Driven Diffusion in Computer Vision, pp. 191\u2013228. Springer, New York (1994)"},{"key":"721_CR27","volume-title":"Anisotropic Diffusion in Image Processing","author":"J Weickert","year":"1998","unstructured":"Weickert, J.: Anisotropic Diffusion in Image Processing. B.G. Teubner, Stuttgart (1998)"},{"key":"721_CR28","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/978-94-017-1699-4_4","volume-title":"Geometry-Driven Diffusion in Computer Vision","author":"R Whitaker","year":"1994","unstructured":"Whitaker, R., Gerig, G.: Vector-valued diffusion. In: ter Haar-Romeny, B. (ed.) Geometry-Driven Diffusion in Computer Vision, pp. 93\u2013124. Springer, New York (1994)"},{"key":"721_CR29","doi-asserted-by":"crossref","unstructured":"Zabandan, G., Kiliman, A.: A new version of Jensen\u2019s inequality and related results. J. Inequal. Appl. 238 (2012)","DOI":"10.1186\/1029-242X-2012-238"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10851-017-0721-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-017-0721-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-017-0721-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T15:42:39Z","timestamp":1692718959000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10851-017-0721-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,10]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["721"],"URL":"https:\/\/doi.org\/10.1007\/s10851-017-0721-9","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"type":"print","value":"0924-9907"},{"type":"electronic","value":"1573-7683"}],"subject":[],"published":{"date-parts":[[2017,3,10]]}}}