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However, the accurate retention of the focused pixels to the fusion result remains a major challenge. This study proposes a multi-focus image fusion algorithm based on Hessian matrix decomposition and salient difference focus detection, which can effectively retain the sharp pixels in the focus region of a source image. First, the source image was decomposed using a Hessian matrix to obtain the feature map containing the structural information. A focus difference analysis scheme based on the improved sum of a modified Laplacian was designed to effectively determine the focusing information at the corresponding positions of the structural feature map and source image. In the process of the decision-map optimization, considering the variability of image size, an adaptive multiscale consistency verification algorithm was designed, which helped the final fused image to effectively retain the focusing information of the source image. Experimental results showed that our method performed better than some state-of-the-art methods in both subjective and quantitative evaluation.<\/jats:p>","DOI":"10.3390\/e24111527","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T22:00:27Z","timestamp":1666735227000},"page":"1527","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Multi-Focus Image Fusion Based on Hessian Matrix Decomposition and Salient Difference Focus Detection"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9859-8191","authenticated-orcid":false,"given":"Xilai","family":"Li","sequence":"first","affiliation":[{"name":"Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaopan","family":"Wang","sequence":"additional","affiliation":[{"name":"Guangdong Kegu Laboratory Technology Research Institute, Foshan 528225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqi","family":"Cheng","sequence":"additional","affiliation":[{"name":"Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8939-0452","authenticated-orcid":false,"given":"Haishu","family":"Tan","sequence":"additional","affiliation":[{"name":"Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528225, China"},{"name":"Ji Hua Laboratory, Foshan 528000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4672-1527","authenticated-orcid":false,"given":"Xiaosong","family":"Li","sequence":"additional","affiliation":[{"name":"Guangdong-Hong Kong-Macao Joint Laboratory for Intelligent Micro-Nano Optoelectronic Technology, School of Physics and Optoelectronic Engineering, Foshan University, Foshan 528225, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/j.inffus.2020.06.013","article-title":"Multi-focus image fusion: A Survey of the state of the art","volume":"64","author":"Liu","year":"2020","journal-title":"Inf. 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