{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T19:50:19Z","timestamp":1774900219563,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T00:00:00Z","timestamp":1609372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61875074"],"award-info":[{"award-number":["61875074"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61971201"],"award-info":[{"award-number":["61971201"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2018A030313912"],"award-info":[{"award-number":["2018A030313912"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The existing lens correction methods deal with the distortion correction by one or more specific image distortion models. However, distortion determination may fail when an unsuitable model is used. So, methods based on the distortion model would have some drawbacks. A model-free lens distortion correction based on the phase analysis of fringe-patterns is proposed in this paper. Firstly, the mathematical relationship of the distortion displacement and the modulated phase of the sinusoidal fringe-pattern are established in theory. By the phase demodulation analysis of the fringe-pattern, the distortion displacement map can be determined point by point for the whole distorted image. So, the image correction is achieved according to the distortion displacement map by a model-free approach. Furthermore, the distortion center, which is important in obtaining an optimal result, is measured by the instantaneous frequency distribution according to the character of distortion automatically. Numerical simulation and experiments performed by a wide-angle lens are carried out to validate the method.<\/jats:p>","DOI":"10.3390\/s21010209","type":"journal-article","created":{"date-parts":[[2020,12,31]],"date-time":"2020-12-31T14:31:49Z","timestamp":1609425109000},"page":"209","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Model-Free Lens Distortion Correction Based on Phase Analysis of Fringe-Patterns"],"prefix":"10.3390","volume":"21","author":[{"given":"Jiawen","family":"Weng","sequence":"first","affiliation":[{"name":"Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China"}]},{"given":"Weishuai","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China"}]},{"given":"Simin","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, South China Agricultural University, Guangzhou 510642, China"}]},{"given":"Pan","family":"Qi","sequence":"additional","affiliation":[{"name":"Department of Electronics Engineering, Guangdong Communication Polytechnic, Guangzhou 510650, China"}]},{"given":"Jingang","family":"Zhong","sequence":"additional","affiliation":[{"name":"Department of Optoelectronic Engineering, Jinan University, Guangzhou 510632, China"},{"name":"Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Guangzhou 510650, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1109\/TPAMI.2016.2578333","article-title":"Planar structure-from-motion with affine camera models: Closed-form solutions, ambiguities and degeneracy analysis","volume":"39","author":"Collins","year":"2017","journal-title":"IEEE Trans. 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