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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 7 — Jul. 1, 2014
  • pp: 1531–1535

Unitary rotations in two-, three-, and D-dimensional Cartesian data arrays

Guillermo Krötzsch, Kenan Uriostegui, and Kurt Bernardo Wolf  »View Author Affiliations


JOSA A, Vol. 31, Issue 7, pp. 1531-1535 (2014)
http://dx.doi.org/10.1364/JOSAA.31.001531


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Abstract

Using a previous technique to rotate two-dimensional images on an N×N square pixellated screen unitarily, we can rotate three-dimensional pixellated cubes of side N, and also generally D-dimensional Cartesian data arrays, also unitarily. Although the number of operations inevitably grows as N2D (because each rotated pixel depends on all others), and Gibbs-like oscillations are inevitable, the result is a strictly unitary and real transformation (thus orthogonal) that is invertible (thus no loss of information) and could be used as a standard.

© 2014 Optical Society of America

OCIS Codes
(100.6890) Image processing : Three-dimensional image processing
(350.6980) Other areas of optics : Transforms
(070.2025) Fourier optics and signal processing : Discrete optical signal processing

ToC Category:
Image Processing

History
Original Manuscript: March 11, 2014
Revised Manuscript: May 13, 2014
Manuscript Accepted: May 14, 2014
Published: June 19, 2014

Citation
Guillermo Krötzsch, Kenan Uriostegui, and Kurt Bernardo Wolf, "Unitary rotations in two-, three-, and D-dimensional Cartesian data arrays," J. Opt. Soc. Am. A 31, 1531-1535 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-7-1531


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References

  1. See, for example, the Image Processing tutorial in WOLFRAM MATHEMATICA, www.wolfram.com/mathematica .
  2. S.-C. Pei and C.-L. Liu, “Discrete spherical harmonic oscillator transforms on the Cartesian grids using transformation coefficients,” IEEE Trans. Signal Process. 61, 1149–1164 (2013). [CrossRef]
  3. M. Moshinsky, The Harmonic Oscillator in Modern Physics: From Atoms to Quarks (Gordon & Breach, 1969).
  4. V. D. Efros, “Some properties of the Moshinsky coefficients,” Nucl. Phys. A 202, 180–190 (1973). [CrossRef]
  5. N. M. Atakishiyev and K. B. Wolf, “Fractional Fourier–Kravchuk transform,” J. Opt. Soc. Am. A 14, 1467–1477 (1997). [CrossRef]
  6. L. Barker, Ç. Çandan, T. Hakioğlu, A. Kutay, and H. M. Ozaktas, “The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform,” J. Phys. A 33, 2209–2222 (2000). [CrossRef]
  7. N. M. Atakishiyev, G. S. Pogosyan, L. E. Vicent, and K. B. Wolf, “Finite two-dimensional oscillator. I: the Cartesian model,” J. Phys. A 34, 9381–9398 (2001). [CrossRef]
  8. L. E. Vicent and K. B. Wolf, “Analysis of digital images into energy-angular momentum modes,” J. Opt. Soc. Am. A 28, 808–814 (2011). [CrossRef]
  9. R. Simon and K. B. Wolf, “Fractional Fourier transforms in two dimensions,” J. Opt. Soc. Am. A 17, 2368–2381 (2000). [CrossRef]
  10. K. B. Wolf and T. Alieva, “Rotation and gyration of finite two-dimensional modes,” J. Opt. Soc. Am. A 25, 365–370 (2008). [CrossRef]
  11. L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics, Theory and Application, G.-C. Rota, ed., Vol. 8 of Encyclopedia of Mathematics and Its Applications (Addison-Wesley, 1981).
  12. K. B. Wolf, “A recursive method for the calculation of the SOn, SOn,1, and ISOn representation matrices,” J. Math. Phys. 12, 197–206 (1971). [CrossRef]
  13. K. B. Wolf, “Linear transformations and aberrations in continuous and in finite systems,” J. Phys. A 41, 304026 (2008). [CrossRef]

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