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2, Dublin, Ireland, p. 654–672, 2000. , “Camera Calibration a head-eye system for Active Vision”, in E KLUNDH J. ), Proc. of 3rd European Conf. on Computer Vision, ECCV94, Stockholm, vol. 1, p. 543–554, May 1994. [LI 95] L I M. , “Some aspects of zoom lens calibration”, Technical Report KTH-NADA-CVAP, no. 172, 1995. Calibration of Vision Sensors 59 [LI 96] L I M. , “Some aspects of zoom lens calibration”, IEEE PAMI, vol. 18, no. 11, 1996. , V ETTERLING W. , 1992. , “Accuracy Improvement in Close Range Photogrammetry”, Schriftenreihe, Wissenschaftlicher Studiengang Vermessungswesen, Hochschule der Bunderwehr München, vol.
Reminder and notation A projective camera model is assumed. This model appeals to projective geometry, of which some basic recalls and concepts can be found in [MOH 93, FAU 93, MUN 92]. 1) ˆ is such where s is an arbitrary scale factor, but non-zero, and the notation p ˆ = [x, y, . . , 1]t . that if p = [x, y, . ]t , then p We consider a system of stereo cameras and provide two 2D points m1 and m2 resulting from the projection of the same physical point M in space. 2) If we place ourselves in the reference mark associated with the 1st camera, the projection matrices are then given by: P1 = [A | 0], P2 = [A R | A t], where R and t respectively represent the rotation matrix and the translation vector associated with the rigid movement between the 2 cameras.
This implies that for any point m on tangents to ω in the second image, we have: (e × m)t AAt (e × m) = 0 The epipolar line Ft m corresponding to m in the ﬁrst image is also a tangent at ω . 15) where β is a non-zero, arbitrary scalar. Since the intrinsic parameters are ﬁve in number, theoretically, three views are sufﬁcient to calculate them. 2. An algebraic derivation of Kruppa equations In this section, an algebraic derivation of Kruppa equations is developed. 5), which gives the form of the fundamental matrix.