H. C. Longuet-Higgins. The visual ambiguity of a moving plane. Proceedings of the Royal Society, London, B223:165--175, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....APPENDIX A INSTANTANEOUS MOTION MODEL The notations describing the 3D motion of the camera and the corresponding 2D motion of the planar surfaces in the image plane, for the fully uncalibrated camera model, are introduced in this section. These are similar to the ones first suggested by [15], only there the camera calibration was assumed robe fixed and, here, we allow for varying camera calibration. A.1 The Case of the Uncalibrated Camera Let ) X,Y, Z) r and : X , Y , Z ) T denote a scene point with respect to two different camera views, respec tively. Let 0 = x,y, 1) and = ....

.... d db a x v Po ad J z a2tx b2tv d2tz d e ( P d d d )x ( a aa P z dtt e ttz a a d e PC d c be balk ) bd z d et (e )tz P7 = l fy ttz a P8 X dY (I)2tz (25) 8 2 d ad be 3 = This result is equivalent to the ones showed by [15], 2] 4] 10] only they assumed fixed camera calibration and, here, we allow for varying camera calibration. A.2 The Longuet Higgins Model The notations introduced in Appendix A.1 are true for the general case of uncalibrated camera. For readability purposes, we chose to use in the body of ....

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H.C. Longuet-Higgins, "Visual Ambiguity of a Moving Plane," Proc. The Royal Soc. of London B, vol. 223, pp. 165-175, 1984.

....since in most cases, possible rotations are restricted to a combination of pan and tilt. The problem of using the coefficients a 1 : a 8 of the optical flow field along with Eqs. 5) to recover the motion and orientation of a moving planar surface has been extensively studied in the past [8, 17]. It has been shown that there exist two possible motions and plane orientations that give rise to the same optical flow field. In other words, the problem is ambiguous, having two possible dual solutions (see for example [17] p. 212) It is also known that these two solutions have distinct ....

H.C. Longuet-Higgins. The Visual Ambiguity of a Moving Plane. In Proc. of the Royal Society B, volume 223, pages 165--175. London, 1984.

....1 1. Introduction The problem of determining rigid body motion and surface structure from image data has been the topic of many research papers in the area of machine vision [1 22] Many approaches based on, tracking feature points [5,11,19,20] or contours [9] using motion flow field [1,3,4,10,12,16,17,21,22], texture [2] or image intensity gradients [14,15] have been proposed in the literature. In the feature point matching schemes, information about a finite number of well seperated points is used to recover the motion (general 8 point 2 frame algorithms of Longuet Higgins [11] Tsai and Huang ....

....methods while mathematically elegant are very sensitive to errors in the optical flow data since second order derivatives of noisy data are used. At the expense of more computation, more robust algorithms have been suggested using the optical flow at every image point [1,3,4] Longuet Higgins [12] has presented a closed form solution for planar surfaces, very similar to ours, using the coefficients of the second order optical flow equations. However, it is assumed that both components of the flow field have already been computed for a minimum of 5 image points. By representing a planar ....

Longuet-Higgins, H.C., "The Visual Ambiguity of a Moving Plane," Proceddings of the Royal Society of London, B 223, pp. 165-175, 1984.

No context found.

H. C. Longuet-Higgins. The visual ambiguity of a moving plane. Proceedings of the Royal Society, London, B223:165--175, 1984.

No context found.

H.C. Longuet-Higgins "The visual ambiguity of a moving plane ," Proceedings of the Royal Society of London, Series B, Vol. 223, 1984.

No context found.

H. C. Longuet-Higgins. The visual ambiguity of a moving plane. Proceedings of the Royal Society, London, B223:165--175, 1984.

No context found.

H.C. Longuet-Higgins. Visual ambiguity of a moving plane. Proceedings of The Royal Society of London B, 223:165--175, 1984.

No context found.

H. C. Longuet-Higgins. The visual ambiguity of a moving plane. Proceedings of Royal Society of London, Series B, 223:165--175, 1984.

No context found.

H. C. Longuet-Higgins. The visual ambiguity of a moving plane. Proceedings of Royal Society of London, Series B, 223:165--175, 1984.

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