{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T19:52:42Z","timestamp":1772221962208,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T00:00:00Z","timestamp":1514332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper describes a flexible camera calibration method using refined vanishing points without prior information. Vanishing points are estimated from human-made features like parallel lines and repeated patterns. With the vanishing points extracted from the three mutually orthogonal directions, the interior and exterior orientation parameters can be further calculated using collinearity condition equations. A vanishing point refinement process is proposed to reduce the uncertainty caused by vanishing point localization errors. The fine-tuning algorithm is based on the divergence of grouped feature points projected onto the reference plane, minimizing the standard deviation of each of the grouped collinear points with an O(1) computational complexity. This paper also presents an automated vanishing point estimation approach based on the cascade Hough transform. The experiment results indicate that the vanishing point refinement process can significantly improve camera calibration parameters and the root mean square error (RMSE) of the constructed 3D model can be reduced by about 30%.<\/jats:p>","DOI":"10.3390\/s18010063","type":"journal-article","created":{"date-parts":[[2017,12,27]],"date-time":"2017-12-27T11:16:00Z","timestamp":1514373360000},"page":"63","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Vanishing Point Extraction and Refinement for Robust Camera Calibration"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4252-9394","authenticated-orcid":false,"given":"Huan","family":"Chang","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, National Central University, Taoyuan City 32001, Taiwan"}]},{"given":"Fuan","family":"Tsai","sequence":"additional","affiliation":[{"name":"Center for Space and Remote Sensing Research, National Central University, Taoyuan City 32001, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhang, Z. 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