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To this aim, Chan et al. (SIAM J Appl Math 66(5):1632\u20131648, 2006) designed a model well suited for smooth images. One drawback of this model is that it may produce a bad segmentation when the image contains oscillatory components. Based on a cartoon-texture decomposition of the image to be segmented, we propose a new model that is able to produce an accurate segmentation of images also containing noise or oscillatory information like texture. The novel model leads to a non-smooth constrained optimization problem which we solve by means of the ADMM method. The convergence of the numerical scheme is also proved. Several experiments on smooth, noisy, and textural images show the effectiveness of the proposed model.<\/jats:p>","DOI":"10.1007\/s10589-022-00387-7","type":"journal-article","created":{"date-parts":[[2022,7,12]],"date-time":"2022-07-12T12:05:56Z","timestamp":1657627556000},"page":"5-26","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Cartoon-texture evolution for two-region image segmentation"],"prefix":"10.1007","volume":"84","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4031-099X","authenticated-orcid":false,"given":"Laura","family":"Antonelli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valentina","family":"De Simone","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Viola","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,11]]},"reference":[{"key":"387_CR1","doi-asserted-by":"publisher","first-page":"293","DOI":"10.3934\/ipi.2014.8.293","volume":"8","author":"J Zhang","year":"2014","unstructured":"Zhang, J., Chen, K., Yu, B., Gould, D.A.: A local information based variational model for selective image segmentation. 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