Fundamental matrix for cameras with radial distortion

When deploying a heterogeneous camera network or when we use cheap zoom cameras like in cell-phones, it is not practical, if not impossible to off-line calibrate the radial distortion of each camera using reference objects. It is rather desirable to have an automatic procedure without strong assumptions about the scene. In this paper, we present a new algorithm for estimating the epipolar geometry of two views where the two views can be radially distorted with different distortion factors. It is the first algorithm in the literature solving the case of different distortion in the left and right view linearly and without assuming the existence of lines in the scene. Points in the projective plane are lifted to a quadric in three-dimensional projective space. A radial distortion of the projective plane results to a matrix transformation in the space of lifted coordinates. The new epipolar constraint depends linearly on a 4 × 4 radial fundamental matrix which has 9 degrees of freedom. A complete algorithm is presented and tested on real imagery.