doi:10.1016/S0031-3203(99)00033-3 
Copyright © 1999 Pattern Recognition Society. Published by Elsevier Science B.V.
Calibrating a video camera pair with a rigid bar
a Laboratory of Human Motion Study and Virtual Reality, Istituto Neuroscienze e Bioimmagini CNR, Via f.lli Cervi, 93 - 20090 Segrate, Milano, Italy
b Department of Bioengineering, Centro di Bioingegneria, Fondazione ProJuventute, Politecnico di Milano, Via Capecelotro, 66, 20148 Milano, Italy
Received 4 June 1998.
Available online 30 May 2000.
References and further reading may be available for this article. To view references and further reading you must
purchase this article.
Abstract
In this paper a new procedure to determine all the geometrical parameters of a stereo-system is presented. It is based on surveying a rigid bar carrying two markers on its extremities moved inside the working volume and it does not require grids or complex calibration structures. The external parameters are estimated through the epipolar geometry up to a scale factor which is determined from the true length of the bar. The focal lengths are determined using the properties of the absolute conic in the projective space. The principal points are computed through a non-linear minimisation carried out through an evolutionary optimisation. The accuracy of the method is assessed on real data and it compares favourably with that obtained through classical approaches based on control points of known 3D coordinates.
Author Keywords: Epipolar geometry; Evolution strategy; Calibration; Fundamental matrix
Fig. 1. The geometrical arrangement of a stereo-pair. The point P is projected in p1 and p2 on the image plane of the two cameras. The optical axis intersects the image plane at a point cj(xoj, yoj) called principal point. The distance between the perspective centre and the image plane, fj, is the focal length of the camera. The epipolar plane, Π, contains the points P, p1, p2, and the line (the relative position T), which joins the perspective centres of the two cameras. The points of intersection between and the image planes are the epipoles, e1 and e2. The intersection between Π and the two image planes originates two lines, lp1 and lp2, called epipolar lines. They are corresponding epipolar lines in the homography generated by P, C1 and C2.
Fig. 2. The absolute conic, Σ∞, and its projection over the two image planes, σ1 and σ2. The intersection of the two tangent planes with the absolute conic gives the two points P∞ and P∞′ which project into p1 and p1′ on the first image plane and into p2 and p2′ on the second one. Through these points the two pairs of epipolar lines, lp1 and lp1′, and lp2 and lp2 are identified.
Fig. 3. The flow chart of the calibration procedure is reported on the left. On the right the flow chart of the block calibration and fitness evaluation is exploded in its main components.
Fig. 4. The reconstructed distances between the two markers on the bar extremes frame by frame. They have been computed from the parameters obtained with bar calibration (a) and with ILSSC (b). The data are referred to the second experiment (wide-angle lens with focal length=8.5 mm).
Fig. 5. The trajectory of the principal points is reported in (a) for TV1 and in (b) for TV2. The initial position of each pair of principal points is plotted as empty circles and the final one by filled circles. The 2D coordinates are expressed in target units (t.u.). In (c), the fitness, the mean error on the bar length and the mean intersection error are reported for each step of the calibration in experiment 1.
Table 1. The accuracy obtained with ILSSC and bar calibration when the cameras were equipped with zoom lens (focal length
30 mm). The data from two different calibrations by using the bar are indicated as Bar, 1st and 2nd calibration
Table 2. The accuracy obtained with ILSSC and bar calibration when the cameras were equipped with wide-angle lens (focal length=8.5 mm). The data from two different calibrations by using the bar are indicated as Bar, 1st and 2nd calibration
Abstract
Purchase PDF (475 K)
E-mail Article
Add to my Quick Links
Cited By in Scopus (14)
Purchase PDF (355 K)
, 
and P. Cerveria, b
