Abstract
How we manage to reconstruct the three-dimensional character of the world from the two-dimensional representations on our retinae has been a lively subject of research in the last ten or fifteen years. One principle that has emerged unifying many of these ideas is the need for constraints to allow the visual system to interpret the images it receives as three-dimensional. These constraints come from assumptions about the nature of the situation that produced the image. We have looked at how gravity can be used as a constraint in the case of a free fall trajectory projected onto an image plane by central projection. We have examined several possible methods for deriving the initial conditions of the trajectory from the two-dimensional projection, and examined their behavior under noisy and noiseless conditions, using both image simulations and videotapes of a real ball. We show that there are several ways to robustly compute the initial conditions of the parabolic trajectory from the image data in the presence of noise.
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References
Hildreth EC (1983) The computation of the velocity field. MIT AI Memo 734
Hoffman DD (1980) Inferring shape from motion fields. MIT AI Memo 592
Hoffman DD, Flinchbaugh BE (1982) The interpretation of biological motion. Biol Cybern 42:195–204
Korn GA, Korn TM (1968) Mathematical handbook for scientists and engineers. McGraw-Hill, New York, p 771
Longuet-Higgins HC (1981) A computer algorithm for reconstructing a scene from two projections. Nature 293:133–135
Longuet-Higgins HC, Prazdny K (1980) The interpretation of a moving retinal image. Proc R Soc Lond (Biol) 208:385–397
Marr D (1982) Vision. Freeman, San Francisco
Poggio T, Torre V (1984) III-posed problems and regularization analysis in early vision. MIT AI Memo 773
Poggio T, Voorhees H, Yuille A (1985) A regularized solution to edge detection. MIT AI Memo 833
Prazdny K (1980) Egomotion and relative depth map from optical flow. Biol Cybern 36:87–102
Saxberg BVH (1987) Projected free fall trajectories. II Human Experiments Biol Cybern 56:177–184
Todd JT (1981) Visual information about moving objects. J Exp Psych 7:795–810
Tsai RY, Huang TS (1984) Uniqueness and estimation of three-dimensional motion parameters of rigid objects with curved surfaces. IEEE Trans Patt Anal Mach Intel 6:13–27
Ullman S (1979) The interpretation of visual motion. MIT Press, Cambridge, MA
Van Trees HL (1968) Detection, estimation, and modulation theory. Wiley, New York
Wallach H, O'Connell D (1953) The kinetic depth effect. J Exp Psych 45:205–217
Waxman AM, Wohn K (1984) Contour evolution, neighborhood deformation and global image flow: planar surfaces in motion. Univ M Cent Autom Res TR 58
Webb J, Aggarwaal JK (1981) Visually interpreting the motion of objects in space. Computer 14:40–46
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Saxberg, B.V.H. Projected free fall trajectories. Biol. Cybern. 56, 159–175 (1987). https://doi.org/10.1007/BF00317991
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DOI: https://doi.org/10.1007/BF00317991