{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:13:38Z","timestamp":1760238818975,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,8]],"date-time":"2020-09-08T00:00:00Z","timestamp":1599523200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Istituto Nazionale di Alta Matematica, Gruppo Nazionale per il Calcolo Scientifico (INdAM-GNCS)","award":["N.A."],"award-info":[{"award-number":["N.A."]}]},{"name":"Italian Ministry of University and Research","award":["PON03PE_00060_5"],"award-info":[{"award-number":["PON03PE_00060_5"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We present a total-variation-regularized image segmentation model that uses local regularization parameters to take into account spatial image information. We propose some techniques for defining those parameters, based on the cartoon-texture decomposition of the given image, on the mean and median filters, and on a thresholding technique, with the aim of preventing excessive regularization in piecewise-constant or smooth regions and preserving spatial features in nonsmooth regions. Our model is obtained by modifying a well-known image segmentation model that was developed by T. Chan, S. Esedo\u1e21lu, and M. Nikolova. We solve the modified model by an alternating minimization method using split Bregman iterations. Numerical experiments show the effectiveness of our approach.<\/jats:p>","DOI":"10.3390\/a13090226","type":"journal-article","created":{"date-parts":[[2020,9,8]],"date-time":"2020-09-08T09:03:48Z","timestamp":1599555828000},"page":"226","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Spatially Adaptive Regularization in Image Segmentation"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4031-099X","authenticated-orcid":false,"given":"Laura","family":"Antonelli","sequence":"first","affiliation":[{"name":"Institute for High Performance Computing and Networking (ICAR), Italian National Research Council\r\n(CNR), via P. Castellino 111, I-80131 Naples, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3357-5252","authenticated-orcid":false,"given":"Valentina","family":"De Simone","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, viale A. Lincoln 5, I-81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8215-0771","authenticated-orcid":false,"given":"Daniela","family":"di Serafino","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cLuigi Vanvitelli\u201d, viale A. Lincoln 5, I-81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1002\/cpa.3160420503","article-title":"Optimal approximations by piecewise smooth functions and associated variational problems","volume":"42","author":"Mumford","year":"1989","journal-title":"Comm. Pure Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"266","DOI":"10.1109\/83.902291","article-title":"Active contours without edges","volume":"10","author":"Chan","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1632","DOI":"10.1137\/040615286","article-title":"Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models","volume":"66","author":"Chan","year":"2006","journal-title":"SIAM J. Appl. 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