This Article 
 Bibliographic References 
 Add to: 
The Frequency Structure of One-Dimensional Occluding Image Signals
February 2000 (vol. 22 no. 2)
pp. 200-206

Abstract—We present a theoretical investigation of the frequency structure of 1D occluding image signals. We show that image signal occlusion contains relevant information which is most easily extractable from its representation in the frequency domain. For instance, the occluding and occluded signal velocities may be identified as such and translucency phenomena may be understood in the terms of this theoretical investigation. In addition, it is found that the structure of occluding 1D signals is invariant under constant and linear models of signal velocity. This theoretical framework can be used to describe the exact frequency structure of non-Fourier motion and bridges the gap between such visual phenomena and their understanding in the frequency domain.

[1] J. Aisbett, “Optical Flow with Intensity-Weighted Smoothing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 5, pp. 512-522, May 1989.
[2] C. Chubb and G. Sperling, “Drift-Balanced Random Stimuli: A General Basis for Studying Non-Fourier Motion Perception,” J. Optical Soc. Am. A, vol. 5, no. 11, pp. 1,986-2,007, 1988.
[3] D.J. Fleet, Measurement of Image Velocity. Norwell,Mass.: Kluwer Academic, 1992.
[4] D.J. Fleet and A.D. Jepson, “Computation of Component Image Velocity from Local Phase Information,” Int'l J. Computer Vision, vol. 5, no. 1, pp. 77-104, 1990.
[5] D.J. Fleet and K. Langley, “Computational Analysis of Non-Fourier Motion,” Vision Research, vol. 34, no. 22, pp. 3,057-3,079, 1995.
[6] J.D. Gaskill, Linear Systems, Fourier Transforms and Optics. Wiley&Sons, 1978.
[7] A.D. Jepson and M. Black, “Mixture Models for Optical Flow Computation,” Proc. Computer Vision and Pattern Recognition, pp. 760-761, June 1993.
[8] H.-H. Nagel, “Constraints for the Estimation of Vector Fields from Image Sequences,” Proc. Int'l JCAI, pp. 945-951, Aug. 1983.
[9] H.-H. Nagel, “Displacement Vectors Derived from Second-Order Intensity Variations in Image Sequences,” Computer Vision, Graphics, and Image Processing, vol. 21, pp. 85-117, 1983.
[10] H.-H. Nagel, “On the Estimation of Optical Flow: Relations between Different Approaches and Some New Results,” Artificial Intelligence, vol. 33, pp. 299-324, 1987.
[11] J.D. Victor and M.M. Conte, “Coherence and Transparency of Moving Plaids Composed of Fourier and Non-Fourier Gratings,” Perception and Psychophysics, vol. 52, no. 4, pp. 403-414, 1988.
[12] M.J. Zanker, “Theta Motion: A Paradoxical Stimulus to Explore Higher-Order Motion Extraction,” Vision Research, vol. 33, pp. 553-569, 1993.

Index Terms:
Occlusion, Fourier transforms, optical flow, non-Fourier motion.
Steven S. Beauchemin, John L. Barron, "The Frequency Structure of One-Dimensional Occluding Image Signals," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 2, pp. 200-206, Feb. 2000, doi:10.1109/34.825758
Usage of this product signifies your acceptance of the Terms of Use.