{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,16]],"date-time":"2025-10-16T10:07:01Z","timestamp":1760609221930,"version":"build-2065373602"},"reference-count":53,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T00:00:00Z","timestamp":1583971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multi-level thresholding is one of the effective segmentation methods that have been applied in many applications. Traditional methods face challenges in determining the suitable threshold values; therefore, metaheuristic (MH) methods have been adopted to solve these challenges. In general, MH methods had been proposed by simulating natural behaviors of swarm ecosystems, such as birds, animals, and others. The current study proposes an alternative multi-level thresholding method based on a new MH method, a modified spherical search optimizer (SSO). This was performed by using the operators of the sine cosine algorithm (SCA) to enhance the exploitation ability of the SSO. Moreover, Fuzzy entropy is applied as the main fitness function to evaluate the quality of each solution inside the population of the proposed SSOSCA since Fuzzy entropy has established its performance in literature. Several images from the well-known Berkeley dataset were used to test and evaluate the proposed method. The evaluation outcomes approved that SSOSCA showed better performance than several existing methods according to different image segmentation measures.<\/jats:p>","DOI":"10.3390\/e22030328","type":"journal-article","created":{"date-parts":[[2020,3,12]],"date-time":"2020-03-12T12:22:51Z","timestamp":1584015771000},"page":"328","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Multi-Level Image Thresholding Based on Modified Spherical Search Optimizer and Fuzzy Entropy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6767-7540","authenticated-orcid":false,"given":"Husein","family":"Naji Alwerfali","sequence":"first","affiliation":[{"name":"School of Computer Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6956-7641","authenticated-orcid":false,"given":"Mohammed","family":"A. A. Al-qaness","sequence":"additional","affiliation":[{"name":"State Key Laboratory for Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7682-6269","authenticated-orcid":false,"given":"Mohamed","family":"Abd Elaziz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"Ewees","sequence":"additional","affiliation":[{"name":"Department of Computer, Damietta University, Damietta 34517, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8781-7993","authenticated-orcid":false,"given":"Diego","family":"Oliva","sequence":"additional","affiliation":[{"name":"Depto. de Ciencias Computacionales, Universidad de Guadalajara, CUCEI, Av. Revoluci\u00f3n 1500, Guadalajara C.P. 44100, Jalisco, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4489-2488","authenticated-orcid":false,"given":"Songfeng","family":"Lu","sequence":"additional","affiliation":[{"name":"Hubei Engineering Research Center on Big Data Security, School of Cyber Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China"},{"name":"Shenzhen Huazhong University of Science and Technology Research Institute, Shenzhen 518063, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8707","DOI":"10.1016\/j.eswa.2015.07.025","article-title":"Tsallis entropy based multilevel thresholding for colored satellite image segmentation using evolutionary algorithms","volume":"42","author":"Bhandari","year":"2015","journal-title":"Expert Syst. 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