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Image intensity and edge are two major sources of information for estimating the motion in the image plane. The 2-D motion obtained by analyzing the deformation of intensity and/or edges is used to recover the 3-D motion and structure. In this paper we show that the motion defined by the image intensity differs from the motion revealed by the (zerocrossing) edge. Understanding of this discrepancy is important since most of the 3-D motion recovery algorithms reported so far require accurate 2-D motion as their input.
We begin the discussion by assuming the invariance of intensity, that the evolution of image intensity manifests the underlying transformation of the image due solely to the motion of objects. We then raise the question if the zerocrossing of the Laplacian operating on the image intensity is invariant too. The change of perspective view due to relative motion results the zerocrossing not being preserved as the image evolves, thereby deteriorating the accuracy of the 2-D motion obtained from the zerocrossing contour. We derive how much the zero-crossing contour deviates from its "correct" position due to motion. The result may be used to determine the reliability of the zerocrossing contours for the purpose of the motion estimation.
Jian Wu and K. Wohn, "On the Deformation of Image Intensity and Zero-Crossing Contours Under Motion", . August 1988.
Date Posted: 15 November 2007