Direct Passive Navigation: Analytical Solution for Planes

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Abstract
This paper derives a closed form sloution for recovering the motion of an observer relative to a planar surface directly from image brightness gradients. The optical flow is not computed as an intermediate step, only the spatial and temporal intensity gradients at a minimum of eight points. A linear matrix equation is solved for the elements of a 3x3 matrix. The eigenvalue decomposition of its symmetric part is then used to compute the motion parameters and the plane orientation. Keywords Passive navigation; Optical flor; Structure and motion; Planar surfaces; Least squares method.

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