Abstract
We have developed direct methods for recovering the motion of an observer in a static environment in the case of pure rotation, pure translation, and arbitrary motion when the rotation is known. Some of these methods are based on the minimization of the difference between the observed time derivative of brightness and that predicted from the spatial brightness gradient, given the estimated motion. We minimize the square of the integral of this difference taken over the image region of interest. Other methods presented here exploit the fact that surfaces have to be in front of the observer in order to be seen.
We do not establish point correspondences, nor do we estimate the optical flow. We use only first-order derivatives of the image brightness, and we do not assume an analytic form for the surface. We show that the field of view should be large to accurately recover the components of motion in the direction toward the image region. We also demonstrate the importance of points where the time derivative of brightness is small and discuss difficulties resulting from very large depth ranges. We emphasize the need for adequate filtering of the image data before sampling to avoid aliasing, in both the spatial and temporal dimensions.
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References
A.R. Bruss and B.K.P. Horn, “Pasive navigation,”Computer Vision, Graphics, and Image Processing, 21, pp. 3–20. 1983.
G. Adiv, “Determining 3-D motion and structure from optical flow generated by several moving objects,” COINS TR 84-07, Computer and Information Science, University of Massachusetts, Amherst, MA, April 1984.
S. Negahdaripour and B.K.P. Horn, “Direct passive navigation”IEEE Trans. PAMI-9(1), pp. 168–176, January 1987.
A.M. Waxman and S. Ullman, “Surface structure and 3-D motion from image flow: A kinematic analysis,”Intern. J. Robotics Res., 4(3), pp. 72–94, Fall 1985.
A.M. Waxman and K. Wohn, “Contour evolution, neighborhood deformation, and global image flow: Planar surfaces in motion,”Intern. J. Robotics Res. 4(3), pp. 95–108, Fall 1985.
B.K.P. Horn and B.G. Schunck, “Determining optical flow,”Artificial Intelligence, 17, pp. 185–203, 1981.
H.C. Longuet-Higgins and K. Prazdny, “The interpretation of a moving retinal image,”Proc. Roy. Soc. London B 208, pp. 385–397, 1980.
S. Negahdaripour, “Direct methods for structure from motion,” Ph.D. Thesis, Mechanical Engineering, MIT, September 1986.
Y. Aloimonos and C. Brown, “Direct processing of curvilinear motion from a sequence of perspective images,”Proc. Workshop on Computer Vision, Representation and Control, Annapolis, Maryland, 1984.
B.K.P. Horn and E.J. Weldon Jr., “Computationally efficient methods of recovering translational motion,”Intern. Conf. Computer Vision, London, England, June 8–11, 1987.
P.R. Wolf,Elements of Photogrammetry, McGraw-Hill: New York, 1983.
S.K. Gosh,Theory of Stereophotogrammetry. Ohio State University Bookstores, 1972.
M. Minsky and S. Papert.Perceptrons: An Introduction to Computational Geometry. MIT Press: Cambridge, MA, 1969.
R.O. Duda and P.E. Hart,Pattern Classification and Scene Analysis Wiley: New York, 1973.
S. Negahdaripour and B.K.P. Horn, “Using depth-is-positive constraint to recover translational motion,”IEEE Workshop on Computer Vision, Miami Beach, Florida, 1987.
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This research was supported by the National Science Foundation under Grant No. DMC85-11966. Additional support was provided by NASA (Grant No. GSFC 5-1162) and by the Veteran's Administration.
BKPH on leave from the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.
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Horn, B.K.P., Weldon, E.J. Direct methods for recovering motion. Int J Comput Vision 2, 51–76 (1988). https://doi.org/10.1007/BF00836281
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DOI: https://doi.org/10.1007/BF00836281