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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • 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)

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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

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

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)

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  1. See, for example, the Image Processing tutorial in WOLFRAM MATHEMATICA, www.wolfram.com/mathematica .
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  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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Fig. 1. Fig. 2. Fig. 3.

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