This Article 
 Bibliographic References 
 Add to: 
Separability of Spatiotemporal Spectra of Image Sequences
December 1992 (vol. 14 no. 12)
pp. 1210-1213

The authors calculate the spatiotemporal power spectrum of 14 image sequences in order to determine the degree to which the spectra are separable in space and time and to assess the validity of the commonly used exponential correlation model. They expand the spectrum by a singular value decomposition into a sum of separable terms and define an index of spatiotemporal separability. as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model, which corresponds to a product of exponential autocorrelation functions separable in space and time.

[1] N. S. Jayant and P. Noll,Digital Coding of Waveforms: Principles and Applications to Speech and video. Englewood Cliffs, NJ: Prentice-Hall, 1985.
[2] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.
[3] M. V. Srinivisan, S. B. Laughlin, and A. Dubs, "Predictive coding: A fresh view of inhibition in the retina,"Proc. Roy. Soc. Lond. B, vol. 216, pp. 427-459, 1982.
[4] D. J. Field, "Relations between the statistics of natural images and the response properties of cortical cells,"J. Opt. Soc. Amer. A, vol. 4, no. 12, pp. 2379-2394, 1987.
[5] D. J. Connor and J. O. Limb, "Properties of frame-difference signals generated by moving images,"IEEE Trans. Commun., vol. COM-10, pp. 1564-1575, 1974.
[6] L. E. Franks, "A model for the random video process,"Bell Sys. Tech. J., pp. 609-630, 1966.
[7] D. C. Coll and G. K. Choma "Image activity characteristics in broadcast television,"IEEE Trans. Commun., vol. COM-12, pp. 1201-1206, 1976.
[8] W. Chen and D. Hein "Recursive temporal filtering and frame rate reduction for image coding,"IEEE J. Spec. Areas Commun., vol. SAC-5, no. 7, pp. 1155-1165, 1987.
[9] A. K. Jain, "Partial differential equations and finite-difference methods in image processing, Part 1: Image representation,"J. Optim. Theory Appl., vol. 23, no. 1, pp. 65-91, 1977.
[10] S. Treitel and J. L. Shanks, "The design of multistage separable planar filters,"IEEE Trans. Geo. E., vol. GE-9, pp. 10-27, 1971.
[11] D. E. Dudgeon and R. M. Mersereau,Multidimensional Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1981.
[12] R.C. Gonzalez and P. Wintz,Digital Image Processing, Addison-Wesley, Reading, Mass., 1987.
[13] J. E. Dennis and D. J. Woods, "Optimization in microcomputers: The Nelder-Meade simplex algorithm," inNew Computing Environments: Microcomputers in Large-Scale Computing(A. Wouk, Ed.). New York: SIAM, 1987, pp. 116-122.
[14] A. B. Watson, "Perceptual-components architecture for digital video,"J. Opt. Soc. Amer. A, vol. 7, no. 10, pp. 1943-1954, 1990.

Index Terms:
image sequences; spatiotemporal power spectrum; exponential correlation model; singular value decomposition; spatiotemporal separability; image sequences; spectral analysis
M.P. Eckert, G. Buchsbaum, A.B. Watson, "Separability of Spatiotemporal Spectra of Image Sequences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 12, pp. 1210-1213, Dec. 1992, doi:10.1109/34.177387
Usage of this product signifies your acceptance of the Terms of Use.