{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:31:22Z","timestamp":1726439482246},"reference-count":32,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Model. Simul. Sci. Comput."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p>Image super-resolution methods-based existing edge indicating operators \u2014 namely Gauss curvature, mean curvature and gradient \u2014 cannot effectively identify the edges, ramps and flat regions and suffer from the loss of fine textures. To address these issues, this paper presents a fractional anisotropic diffusion equation based on a new edge indicator, named fractional-order difference curvature, which can characterize the intensity variations in images. We introduce the frequency-domain definition for fractional-order derivative by the Fourier transform, which is easy to implement numerically. The new edge indicator is better than the existing edge indicating operators in distinguishing between ramps and edges and can better handle the fine textures. Comparative results for natural images validate that the proposed method can yield a visually pleasing result and better values of MSSIM and PSNR.<\/jats:p>","DOI":"10.1142\/s1793962319410125","type":"journal-article","created":{"date-parts":[[2018,12,27]],"date-time":"2018-12-27T09:47:43Z","timestamp":1545904063000},"page":"1941012","source":"Crossref","is-referenced-by-count":6,"title":["Fractional-order difference curvature-driven fractional anisotropic diffusion equation for image super-resolution"],"prefix":"10.1142","volume":"10","author":[{"given":"Xuehui","family":"Yin","sequence":"first","affiliation":[{"name":"School of Software and Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shunli","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software and Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liping","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, Chongqing University, Chongqing 400030, P. R. China"},{"name":"College of Computer Science, Chongqing University, Chongqing 400030, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shangbo","family":"Zhou","sequence":"additional","affiliation":[{"name":"Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, Chongqing University, Chongqing 400030, P. R. China"},{"name":"College of Computer Science, Chongqing University, Chongqing 400030, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,2,18]]},"reference":[{"key":"S1793962319410125BIB001","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2016.2542442"},{"key":"S1793962319410125BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2015.11.003"},{"issue":"15","key":"S1793962319410125BIB003","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.amc.2015.07.086","volume":"269","author":"Lee Y. J.","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"S1793962319410125BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.aeue.2014.10.022"},{"key":"S1793962319410125BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.procs.2016.05.258"},{"key":"S1793962319410125BIB006","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1007\/978-3-319-10593-2_13","volume-title":"Computer Vision: ECCV 2014","volume":"8692","author":"Dong C.","year":"2014"},{"key":"S1793962319410125BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2015.2462113"},{"key":"S1793962319410125BIB009","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2015.2439281"},{"key":"S1793962319410125BIB012","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2016.2542360"},{"key":"S1793962319410125BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2012.2231086"},{"key":"S1793962319410125BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-015-2910-0"},{"key":"S1793962319410125BIB015","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2049927"},{"key":"S1793962319410125BIB016","doi-asserted-by":"publisher","DOI":"10.1049\/iet-ipr.2016.0615"},{"key":"S1793962319410125BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.05.032"},{"key":"S1793962319410125BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2016.02.015"},{"key":"S1793962319410125BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90242-F"},{"key":"S1793962319410125BIB020","doi-asserted-by":"publisher","DOI":"10.1109\/34.56205"},{"volume-title":"Oscillating Patterns in Image Processing and Some Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures","year":"2001","author":"Meyer Y.","key":"S1793962319410125BIB021"},{"key":"S1793962319410125BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-010-0330-1"},{"key":"S1793962319410125BIB023","doi-asserted-by":"publisher","DOI":"10.1137\/090769521"},{"key":"S1793962319410125BIB024","doi-asserted-by":"publisher","DOI":"10.1137\/120901246"},{"key":"S1793962319410125BIB025","doi-asserted-by":"publisher","DOI":"10.1109\/83.568931"},{"key":"S1793962319410125BIB026","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1996.0011"},{"key":"S1793962319410125BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/s002220050344"},{"key":"S1793962319410125BIB028","doi-asserted-by":"publisher","DOI":"10.1006\/jvci.2001.0487"},{"key":"S1793962319410125BIB029","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2005.849294"},{"key":"S1793962319410125BIB030","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2007.904971"},{"key":"S1793962319410125BIB031","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2011.03.017"},{"key":"S1793962319410125BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/s11042-015-2488-6"},{"key":"S1793962319410125BIB033","doi-asserted-by":"publisher","DOI":"10.1155\/2015\/930984"},{"key":"S1793962319410125BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/j.imavis.2009.04.012"},{"key":"S1793962319410125BIB035","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2010.2050625"}],"container-title":["International Journal of Modeling, Simulation, and Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793962319410125","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,9]],"date-time":"2022-09-09T03:57:17Z","timestamp":1662695837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793962319410125"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2]]},"references-count":32,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,2,18]]},"published-print":{"date-parts":[[2019,2]]}},"alternative-id":["10.1142\/S1793962319410125"],"URL":"https:\/\/doi.org\/10.1142\/s1793962319410125","relation":{},"ISSN":["1793-9623","1793-9615"],"issn-type":[{"type":"print","value":"1793-9623"},{"type":"electronic","value":"1793-9615"}],"subject":[],"published":{"date-parts":[[2019,2]]}}}