A EUCLIDEAN FORMULATION OF INTERIOR ORIENTATION COSTRAINTS IMPOSED BY THE FUNDAMENTAL MATRIX
- 1Laboratory of Photogrammetry, Department of Civil Engineering and Surveying & Geoinformatics Engineering, Technological Educational Institute of Athens, 12210 Athens, Greece
- 2Laboratory of Photogrammetry, Department of Surveying, National Technical University of Athens, 15780 Athens, Greece
Keywords: epipolar geometry, camera calibration, fundamental matrix
Abstract. Epipolar geometry of a stereopair can be expressed either in 3D, as the relative orientation (i.e. translation and rotation) of two bundles of optical rays in case of calibrated cameras or, in case of unclalibrated cameras, in 2D as the position of the epipoles on the image planes and a projective transformation that maps points in one image to corresponding epipolar lines on the other. The typical coplanarity equation describes the first case; the Fundamental matrix describes the second. It has also been proven in the Computer Vision literature that 2D epipolar geometry imposes two independent constraints on the parameters of camera interior orientation. In this contribution these constraints are expressed directly in 3D Euclidean space by imposing the equality of the dihedral angle of epipolar planes defined by the optical axes of the two cameras or by suitably chosen corresponding epipolar lines. By means of these constraints, new closed form algorithms are proposed for the estimation of a variable or common camera constant value given the fundamental matrix and the principal point position of a stereopair.