On the deformation of image intensity and zero-crossing contours under motion

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. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-88-69. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/738 ON THE DEFORMATION OF IMAGE INTENSITY AND ZERO-CROSSING CONTOURS UNDER MOTION Jian Wu and K. Wohn MS-CIS-88-69 GRASP LAB 154 Department of Computer and Information Science School of Engineering and Applied Science University of Pennsylvania Philadelphia, PA 19104 September 1988 Acknowledgements: This research was supported in part by DARPA grant N00014-85K-0807, U.S. Postal Service Grant 104230-87-H-0001IM-0195, NSF grants MCS-8219196CER, IR184-10413-A02 and U.S. Army grants DAA29-84-K-0061, DAA29-84-9-0027. On the Deformation of Image Intensity and Zero-Crossing Contours Under Motion Jian FVu Laboratory for Sensory Robotics Boston University I<. Wohn Department of Computer and Information Science University of Pennsyvania July 10, 1988 revised August 25, 1988