Structure from motion with wide circular field of view cameras

This paper presents a method for fully automatic and robust estimation of two-view geometry, autocalibration, and 3D metric reconstruction from point correspondences in images taken by cameras with wide circular field of view. We focus on cameras which have more than 180 degrees field of view and for which the standard perspective camera model is not sufficient, e.g., the cameras equipped with circular fish-eye lenses Nikon FC-E8 (183 degrees), Sigma 8mm-f4-EX (180 degrees), or with curved conical mirrors. We assume a circular field of view and axially symmetric image projection to autocalibrate the cameras. Many wide field of view cameras can still be modeled by the central projection followed by a nonlinear image mapping. Examples are the above-mentioned fish-eye lenses and properly assembled catadioptric cameras with conical mirrors. We show that epipolar geometry of these cameras can be estimated from a small number of correspondences by solving a polynomial eigenvalue problem. This allows the use of efficient RANSAC robust estimation to find the image projection model, the epipolar geometry, and the selection of true point correspondences from tentative correspondences contaminated by mismatches. Real catadioptric cameras are often slightly noncentral. We show that the proposed autocalibration with approximate central models is usually good enough to get correct point correspondences which can be used with accurate noncentral models in a bundle adjustment to obtain accurate 3D scene reconstruction. Noncentral camera models are dealt with and results are shown for catadioptric cameras with parabolic and spherical mirrors.