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Direct methods for recovering motion
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Direct methods for recovering motion Berthold K. P. Horn1 and E. J. Weldon Jr.1 | (1) | Department of Electrical Engineering, University of Hawaii at Manoa, 96822 Honolulu, Hawaii |
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. 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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