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Frequency Domain Analysis of Translations with Piecewise Cubic Trajectories
April 1993 (vol. 15 no. 4)
pp. 411-416

Translations with piecewise cubic trajectories are studied in the frequency domain. This class of motion has as an important subcase: cubic spline trajectories. Translations with trajectories depending on time with general polynomial law are preliminarily considered, and a general theorem concerning this type of motion is introduced. The application of this theorem to the case of cubic time dependence and the consideration of finite-duration effects lead to the solution of the piecewise cubic trajectory case. The results, which are remarkably different from those concerning constant velocity translations, clearly indicate the importance of the role of velocity and time duration. In this respect, they confirm the validity of constant velocity motion as a first-order model for frequency domain analysis of motion.

[1] J. O. Drewery, "The filtering of luminance and chrominance signals to avoid cross-colour in a PAL colour system," BBC Tech. Rep. RD 1975/31, Dec. 1975.
[2] T.S. Huang,Image Sequence Analysis. Berlin: Springer-Verlag, 1983.
[3] D. J. Heeger, "Optical flow From spatiotemporal filters," inProc. IEEE Int. Conf. Comput. Vision(London), June 1987, pp. 181-190.
[4] D. J. Fleet and A. D. Jepson, "Hierarchical construction of orientation and velocity selective filters,"IEEE Trans. Patt. Anal. Machine Intell., vol. 11, no. 3, pp. 315-325, Mar. 1989.
[5] A. B. Watson and A. J. Ahumada Jr., "A took at motion in the frequency domain," NASA Tech. Memo. 84352, NASA-Ames Res. Cent., 1983.
[6] E. H. Adelson and J. R. Bergen, "Spatiotemporal energy models for the perception of motion,"J. Opt. Soc. Amer., vol. 2, pp. 284-299, 1985.
[7] M. Balanza and G. M. Cortelazzo, "On the effects of acceleration in the frequency domain," inProc. Third Int. Workshop HDTV(Torino, Italy), 1989.
[8] A. Papoulis,Systems and Transforms with Applications in Optics. New York: McGraw-Hill, 1968.
[9] A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi,Tables of Integral Transforms. New York: McGraw-Hill, 1954.

Index Terms:
frequency domain motion analysis; motion estimation; translations; piecewise cubic trajectories; cubic spline trajectories; finite-duration effects; constant velocity motion; first-order model; frequency-domain analysis; motion estimation; splines (mathematics)
G. Cortelazzo, M. Balanza, "Frequency Domain Analysis of Translations with Piecewise Cubic Trajectories," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 4, pp. 411-416, April 1993, doi:10.1109/34.206960
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