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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 30, Iss. 9 — Sep. 1, 2013
  • pp: 1796–1805

Patterns with different phases but same statistics

Peyman Sheikholharam Mashhadi, Mahdi Aliyari Shoorehdeli, and Mohammad Teshnehlab  »View Author Affiliations

JOSA A, Vol. 30, Issue 9, pp. 1796-1805 (2013)

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Many successful methods in various vision tasks rely on statistical analysis of visual patterns. However, we are interested in covering the gap between the underlying mathematical representation of the visual patterns and their statistics. With this general trend, in this paper a relationship between phase structure of a class of patterns and their moments after and before filtering have been considered. First, a general formula between the phase structure and moments of the images is obtained. Second, a theorem is developed that states under which conditions two visual patterns with the same frequencies but different phases have the same moments up to a certain moment. Finally, a theorem is developed that explains, given a set of filters, under which conditions two visual patterns with both different frequencies and different phases have the same subband statistics.

© 2013 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(000.5490) General : Probability theory, stochastic processes, and statistics
(330.5000) Vision, color, and visual optics : Vision - patterns and recognition
(350.5030) Other areas of optics : Phase
(070.2615) Fourier optics and signal processing : Frequency filtering

ToC Category:
Vision, Color, and Visual Optics

Original Manuscript: November 15, 2012
Revised Manuscript: April 27, 2013
Manuscript Accepted: July 17, 2013
Published: August 21, 2013

Peyman Sheikholharam Mashhadi, Mahdi Aliyari Shoorehdeli, and Mohammad Teshnehlab, "Patterns with different phases but same statistics," J. Opt. Soc. Am. A 30, 1796-1805 (2013)

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