Perdigoto, LuisAraujo, Helder2025-07-152025-07-152016-10Luis Perdigoto, Helder Araujo, Estimation of mirror shape and extrinsic parameters in axial non-central catadioptric systems, Image and Vision Computing, Volume 54, 2016, Pages 45-59, ISSN 0262-8856, https://doi.org/10.1016/j.imavis.2016.06.0090262-8856http://hdl.handle.net/10400.8/13655We propose a method to estimate the mirror shape and position, and the extrinsic parameters in axial noncentral catadioptric systems (i.e. systems with an axial symmetrical mirror and a pinhole camera with its optical center located at the mirror axis). Our method requires one or more images of a planar calibration pattern consisting of points and lines with known position (e.g. a checkerboard), and that the camera be internally calibrated. We also present an alternative algorithm for the particular case of catadioptric systems with spherical mirror, were the estimation is achieved by fitting quartic curves to the images of lines of the calibration pattern. An analytical solution is presented for every method. Each analytical solution is then refined by a non-linear optimization procedure. We present experimental results, on simulated and real images, that demonstrate the validity of our work.engNon-central catadioptric vision systemsCalibrationMirror shape estimationjournal article10.1016/j.imavis.2016.06.009