Active Intrinsic Calibration Using Vanishing Points

Co-authored with Jörg Ernst

Short version appeared in CVPR'96, pp.708-713, June '96, S.F., CA
Long version published in Pattern Recognition Letters, 17:1179-1189, 1996.

Abstract

We propose a new method for the estimation of the intrinsic parameters of an active camera. During a fixed axis camera rotation every point is moving on a conic section. If the point used is a vanishing point the conic section is invariant to possible translations of the observer. Given the rotation axis and the inter-frame correspondence of a set of parallel lines we are able to compute the intrinsic parameters without knowledge of the rotation angles. We propagate the error covariances and we remove the bias in the computation of the conic. We experimentally study the sensitivity of calibration to the amount of rotation and we compare our performance to the performance of a recent active calibration technique.

Notes

Key concepts

When a camera is arbitrarily moving the vanishing points change their position only due to camera rotation.
If the rotation axis remains fixed the projection is a conic section.
The image centers can be computed more reliably than the scaling factors. The main factor affecting accuracy is the amount of rotation carried out by the camera.
Intrinsic parameters encoded in the image of the absolute conic can be obtained from point correspondences in 3 to 4 views.

Algorithm

Camera Rotation axis is assumed known.
Camera rotations will translate to vanishing points moving along hyperbolas.
The image center coincides with the hyperbolas center.
The procedure is as follows:
- Rotate around the pan axis y and fit a conic to the trace of VPs; from the coefficients of the conic compute the center and axes of the hyperbolas to recover x0 & sx (scale).
- Rotate around the axis x (parallel to the xz-plane) and fit a conic to the trace of VPs; from the coefficients of the conic compute the center and axes of the hyperbolas to recover y0 & sy (scale)
Computation of line intersections, to retrieve VPs loci, is performed via a Hough Transform and MLE.
Fitting of a conic also uses MLE, together with linearization and matrix perturbation theory.

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