{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/radially-distorted-conjugate-translations","title":"Radially-Distorted Conjugate Translations","arxiv_id":"1711.11339","date":"2017-11-30","proceeding":"CVPR 2018 6","authors":["James Pritts","Zuzana Kukelova","Viktor Larsson","Ondrej Chum"],"abstract":"This paper introduces the first minimal solvers that jointly solve for\naffine-rectification and radial lens distortion from coplanar repeated\npatterns. Even with imagery from moderately distorted lenses, plane\nrectification using the pinhole camera model is inaccurate or invalid. The\nproposed solvers incorporate lens distortion into the camera model and extend\naccurate rectification to wide-angle imagery, which is now common from consumer\ncameras. The solvers are derived from constraints induced by the conjugate\ntranslations of an imaged scene plane, which are integrated with the division\nmodel for radial lens distortion. The hidden-variable trick with ideal\nsaturation is used to reformulate the constraints so that the solvers generated\nby the Grobner-basis method are stable, small and fast.\n  Rectification and lens distortion are recovered from either one conjugately\ntranslated affine-covariant feature or two independently translated\nsimilarity-covariant features. The proposed solvers are used in a \\RANSAC-based\nestimator, which gives accurate rectifications after few iterations. The\nproposed solvers are evaluated against the state-of-the-art and demonstrate\nsignificantly better rectifications on noisy measurements. Qualitative results\non diverse imagery demonstrate high-accuracy undistortions and rectifications.\nThe source code is publicly available at https://github.com/prittjam/repeats.","url_abs":"http://arxiv.org/abs/1711.11339v3","url_pdf":"http://arxiv.org/pdf/1711.11339v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"radially-distorted-conjugate-translations","repo_url":"https://github.com/prittjam/repeats","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.11339","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}