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Frequency domain analysis of rotational motion

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Abstract

The consideration of translational motion in the frequency domain has rendered valuable service in many applications, such as television signal analysis, motion estimation, image registration, and visual perception studies. This work presents rotational motion in the frequency domain, developing theoretical results parallel to those relative to translations. The analysis can support the extension of frequency —domain—based approaches to specific applications concerning rotations, an operation successfully carried out by recent image registration works.

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References

  • T.S. Huang,Image Sequence Analysis, Berlin: Springer-Verlag, 1983.

    Google Scholar 

  • A.B. Watson, A.J. Ahumada Jr., “A Look at Motion in the Frequency Domain,” NASA Techn. Memorandum 84352, NASA-Ames Research Center, 1983.

  • J.O. Drewery, “The Filtering of Luminance and Chrominance Signals to Avoid Cross-Colour in a PAL Colour System,” BBC Techn. Report RD 1975/31, Dec. 1975.

  • J. Biemond, L. Looijenga, D.E. Boekee, and R.H.J.M. Plompen, “A Pel-Recursive Wiener-based Displacement Estimation Algorithm,”Signal Processing, vol. 13, 1987, pp. 399–412.

    Google Scholar 

  • C.D. Kuglin and D.C. Hines, “The Phase-Correlation Image Alignment Method,” inProc. IEEE 1975 Int. Conf. Cybernetics and Society, pp. 163–165, 1975.

  • S. Alliney and C. Morandi, “Digital Image Registration Using Projections,”IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, 1986, pp. 222–233.

    Google Scholar 

  • E.H. Adelson and J.R. Bergen, “Spatio-temporal Energy Models for the Perception of Motion,”J. Opt. Soc. Amer., vol. 2, 1985, pp. 284–299.

    Google Scholar 

  • E. De Castro and C. Marconi, “Registration of Translated and Rotated Images Using Finite Fourier Transforms,”IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-9, 1987, p. 700–703.

    Google Scholar 

  • S. Alliney, “An Algorithm for the Digital Analysis of Rotated Images,”IEEE Trans. Pattern Anal. Machine Intell., to appear.

  • M.R. Portnoff, “Time-Frequency Representation of Digital Signals and Systems Based on Short-Time Fourier Analysis,”IEEE Trans. Acoust. Sp. Signal Proc, vol. ASSP-28, 1980, pp. 55–68.

    Google Scholar 

  • S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation,”IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-I, 1989, pp. 674–693.

    Google Scholar 

  • M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies, “Image Coding Using Wavelet Transform,”IEEE Trans. Image Processing, vol. IP-1, 1992, pp. 205–213.

    Google Scholar 

  • G. Cortelazzo and M. Balanza, “Frequency Domain Analysis of Translations with Piecewise Cubic Trajectories,”IEEE Trans. Pattern Anal. Machine Intell., vol. 15, April 1993.

  • G. Cortelazzo and G. Nalesso, “A Differential Equation Approach to the Computation of the Fourier Transform of the Images of Translating Objects,” Report DEI 90/16, Dipartimento di Elettronica e Informatica, Universita' di Padova, Padova, 1993.

    Google Scholar 

  • L. Jacobson and H. Weehster, “Derivation of Optical Flow Using a Spatiotemporal-Frequency Approach,”Computer Vision, Graphics, and Image Processing, vol. 38, 1987, pp. 29–65.

    Google Scholar 

  • D. Heeger, “Optical Flow Using Spatiotemporal Filters,”Int. J. Computer Vision, 1988, pp. 279–302.

  • A. Papoulis,Systems and Transform with Applications in Optics, New York: McGraw-Hill, 1968.

    Google Scholar 

  • A. Erdelyi, W. Magnus, F. Oberhettinger, and F.G. Tricomi,Tables of Integral Transforms, New York: McGraw-Hill, 1954.

    Google Scholar 

  • A. Papoulis,The Fourier Integral and Its Applications, New York: McGraw-Hill, 1962.

    Google Scholar 

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Cortelazzo, G., Monti, C.M. & Balanza, M. Frequency domain analysis of rotational motion. Multidim Syst Sign Process 4, 203–225 (1993). https://doi.org/10.1007/BF00985889

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  • DOI: https://doi.org/10.1007/BF00985889

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