{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T02:13:01Z","timestamp":1777601581368,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,28]],"date-time":"2018-10-28T00:00:00Z","timestamp":1540684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang province public welfare project","award":["2017C31126"],"award-info":[{"award-number":["2017C31126"]}]},{"name":"Quzhou science and technology projects","award":["2016Y015; H2018007"],"award-info":[{"award-number":["2016Y015; H2018007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Spatial correlation information between pixels is considered to be very important in thresholding methods. However, it is often ignored and thus unsatisfied segmentation results maybe obtained. To overcome this shortcoming, we propose a new image segmentation approach by taking not only pixels\u2019 spatial information but also pixels\u2019s gray level into account. First, a non-local mean filter is imposed on the image. Then the filtered image and the original image together are adopted to build a two dimensional histogram, it is called non-local mean two dimensional histogram. Finally, a minimum relative entropy criteria is used to select the ideal thresholding vector. Since the non-local mean filter process is performed in a neighborhood of current pixel, it carries out the spatial information of current pixel. Segmentation results on several images illustrate the effectiveness of the proposed thresholding method, whose segmentation accuracy are greatly improved compared to most existing thresholding methods.<\/jats:p>","DOI":"10.3390\/e20110827","type":"journal-article","created":{"date-parts":[[2018,10,29]],"date-time":"2018-10-29T11:10:41Z","timestamp":1540811441000},"page":"827","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Nonlocal Means Two Dimensional Histogram-Based Image Segmentation via Minimizing Relative Entropy"],"prefix":"10.3390","volume":"20","author":[{"given":"Chundi","family":"Jiang","sequence":"first","affiliation":[{"name":"College of Electrical and Information Engineering, Quzhou University, Quzhou 324000, China"},{"name":"Logistic Engineering College, Shanghai Maritime University, Shanghai 200135, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei","family":"Yang","sequence":"additional","affiliation":[{"name":"State GRID Quzhou Power Supply Company, No.6, XinHe Road, Quzhou 324000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Guo","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Wu","sequence":"additional","affiliation":[{"name":"College of Electrical and Information Engineering, Quzhou University, Quzhou 324000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7440-1742","authenticated-orcid":false,"given":"Yinggan","family":"Tang","sequence":"additional","affiliation":[{"name":"Institute of Electrical Engineering, Yanshan University, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/s00521-016-2391-8","article-title":"A novel segmentation algorithm for nucleus in white blood cells based on low-rank representation","volume":"28","author":"Cao","year":"2017","journal-title":"Neural Comput. 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