Simultaneous linear estimation of multiple view geometry and lens distortion

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Abstract
A bugbear of uncalibrated stereo reconstruction is that cameras which deviate from the pinhole model have to be pre-calibrated in order to correct for nonlinear lens distor- tion. If they are not, and point correspondence is attempted using the uncorrected images, the matching constraints pro- vided by the fundamental matrix must be set so loose that point matching is significantly hampered. This paper shows how linear estimation of the funda- mental 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 co- ordinates, and (2) expressing fundamental matrix estima- tion 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 es- timator is fast enough to be included in a RANSAC-based matching loop, and we show cases of matching being ren- dered 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.

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