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Although much progress has been made for tracking multiple objects, it remains a challenging task to track individuals due to factors such as occlusion and target appearance variation. In this paper, we first introduce a NACA airfoil model as a deformable appearance model of fish. For occluded fish, we estimate their positions, angles, and postures with template matching and simulated annealing algorithms to effectively optimize their parameters. To improve performance of tracking, we repeatedly track fish with the parameter estimation algorithm forwards and backwards. We prepared two real fish scenes in which the average number of fish is over 25 in each frame and multiple fish superimpose over 50 times. Experimental results for the scenes show that fish are practically tracked with our method compared to a tracking method based on a mixture particle filter. Over 75 % of fish in each scene have been tracked throughout the scene, and the average difference is less than 4 % of the mean body length of the school.<\/jats:p>","DOI":"10.1186\/s41074-016-0004-1","type":"journal-article","created":{"date-parts":[[2016,8,3]],"date-time":"2016-08-03T16:54:14Z","timestamp":1470243254000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Multiple fish tracking with an NACA airfoil model for collective behavior analysis"],"prefix":"10.1186","volume":"8","author":[{"given":"Kei","family":"Terayama","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hitoshi","family":"Habe","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masa-aki","family":"Sakagami","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,8,2]]},"reference":[{"issue":"3","key":"4_CR1","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.physrep.2012.03.004","volume":"517","author":"T Vicsek","year":"2012","unstructured":"Vicsek T, Zafeiris A (2012) Collective motion. 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