Stability of Phase Information 1

This paper concerns the robustness of local phase information for measuring image velocity and binocular disparity. It addresses the dependence of phase behaviour on the initial lters as well as the image variations that exist between diierent views of a 3d scene. We are particularly interested in the stability of phase with respect to geometric deformations, and its linearity as a function of spatial position. These properties are important to the use of phase information, and are shown to depend on the form of the lters as well as their frequency bandwidths. Phase instabilities are also discussed using the model of phase singularities described by Jepson and Fleet 14]. In addition to phase-based methods, these results are directly relevant to diierential optical ow methods and zero-crossing tracking.

[1]  Hans Knutsson,et al.  Hierarchical Phase Based Disparity Estimation , 1992 .

[2]  K. Langley,et al.  Vertical and Horizontal Disparities from Phase , 1990, ECCV.

[3]  Juyang Weng,et al.  A theory of image matching , 1990, [1990] Proceedings Third International Conference on Computer Vision.

[4]  D J Field,et al.  Relations between the statistics of natural images and the response properties of cortical cells. , 1987, Journal of the Optical Society of America. A, Optics and image science.

[5]  H. Knutsson,et al.  A multiresolution stereopsis algorithm based on the Gabor representation , 1989 .

[6]  David J. Fleet,et al.  Phase singularities in scale-space , 1991, Image Vis. Comput..

[7]  Peter J. Burt,et al.  Object tracking with a moving camera , 1989, [1989] Proceedings. Workshop on Visual Motion.

[8]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[9]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[10]  D. Burr,et al.  Feature detection in human vision: a phase-dependent energy model , 1988, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[11]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[12]  D Marr,et al.  A computational theory of human stereo vision. , 1979, Proceedings of the Royal Society of London. Series B, Biological sciences.

[13]  W. Root,et al.  An introduction to the theory of random signals and noise , 1958 .

[14]  David J. Fleet,et al.  Phase-based disparity measurement , 1991, CVGIP Image Underst..

[15]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[16]  Hans Knutsson,et al.  Preattentive gaze control for robot vision , 1992 .

[17]  Michael Jenkin,et al.  The Measurement of Binocular Disparity , 1988 .

[18]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[19]  David J. Fleet.  Measurement of image velocity , 1992 .

[20]  C. D. Kuglin,et al.  The phase correlation image alignment method , 1975 .

[21]  Alan L. Yuille,et al.  Scaling Theorems for Zero Crossings , 1987, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[22]  Thomas J. Olson,et al.  Real time vergence control , 1989, Proceedings CVPR '89: IEEE Computer Society Conference on Computer Vision and Pattern Recognition.