Simultaneous linear estimation of multiple view geometry and lens distortion

Abstract

A problem in uncalibrated stereo reconstruction is that cameras which deviate from the pinhole model have to be pre-calibrated in order to correct for nonlinear lens distortion. If they are not, and point correspondence is attempted using the uncorrected images, the matching constraints provided by the fundamental matrix must be set so loose that point matching is significantly hampered. This paper shows how linear estimation of the fundamental matrix from two-view point correspondences may be augmented to include one term of radial lens distortion. This is achieved by (1) changing from the standard radial-lens model to another which (as we show) has equivalent power, but which takes a simpler form in homogeneous coordinates, and (2) expressing fundamental matrix estimation as a quadratic eigenvalue problem (QEP), for which efficient algorithms are well known. I derive the new estimator, and compare its performance against bundle-adjusted calibration-grid data. The new estimator is fast enough to be included in a RANSAC-based matching loop, and we show cases of matching being rendered possible by its use. I show how the same lens can be calibrated in a natural scene where the lack of straight lines precludes most previous techniques. The modification when the multi-view relation is a planar homography or trifocal tensor is described.