A minimal solution using two affine correspondences is presented to estimate the common focal length and the fundamental matrix between two semi-calibrated cameras - known intrinsic parameters except a common focal length. To the best of our knowledge, this problem is unsolved. The proposed approach extends point correspondence-based techniques with linear constraints derived from local affine transformations. The obtained multivariate polynomial system is efficiently solved by the hidden-variable technique. Observing the geometry of local affinities, we introduce novel conditions eliminating invalid roots. To select the best one out of the remaining candidates, a root selection technique is proposed outperforming the recent ones especially in case of high-level noise. The proposed 2-point algorithm is validated on both synthetic data and 104 publicly available real image pairs. A Matlab implementation of the proposed solution is included in the paper.
A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences
School of Aerospace Science and Engineering, National University of Defense Technology（航天科学与工程学院，国防科技大学）；Hunan Provincial Key Laboratory of Image Measurement and Vision Navigation（图像测量与视觉导航省级重点实验室）；Global Navigation Satellite System Research Center（全球导航卫星系统研究中心）；School of Geodesy and Geomatics, Wuhan University（测绘学院，武汉大学）；School of Remote Sensing Information Engineering, Wuhan University（遥感信息工程学院，武汉大学）；School of Software, Henan University（软件学院，河南大学）
GP2C: Geometric Projection Parameter Consensus for Joint 3D Pose and Focal Length Estimation in the Wild
Institute of Computer Graphics and Vision, Graz University of Technology, Austria（奥地利格拉茨工业大学计算机图形与视觉研究所）；Laboratoire Bordelais de Recherche en Informatique, University of Bordeaux, France（法国波尔多大学波尔多信息学实验室）
Learning Affine Correspondences by Integrating Geometric Constraints
College of Aerospace Science and Engineering, National University of Defense Technology（国防科技大学航天科学与工程学院）；ETH Zurich（苏黎世联邦理工学院）；HUN-REN SZTAKI（匈牙利科学院核子研究所）
Globally Optimal Solution to the Generalized Relative Pose Estimation Problem using Affine Correspondences
College of Aerospace Science and Engineering, National University of Defense Technology（航空科学与工程学院，国防科技大学）；Global Navigation Satellite System Research Center, Wuhan University（导航卫星系统研究所，武汉大学）
Practical solutions to the relative pose of three calibrated cameras
Visual Recognition Group, Faculty of Electrical Engineering, Czech Technical University in Prague（视觉识别组，电气工程系，布拉格捷克技术大学）；Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava（数学、物理和信息学系，布拉迪斯拉发康门尼乌斯大学）；ETH Zürich (Zurich), HUN-REN SZTAKI (Budapest)（苏黎世ETH，匈牙利-中国SZTAKI（布达佩斯））；Czech Institute of Informatics, Robotics and Cybernetics, Czech Technical University in Prague（捷克信息学、机器人学与自动控制研究所，布拉格捷克技术大学）
