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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 29 — Oct. 10, 1998
  • pp: 6911–6913

Analysis of the fractional Hilbert transform

Jeffrey A. Davis, Dylan E. McNamara, and Don M. Cottrell  »View Author Affiliations


Applied Optics, Vol. 37, Issue 29, pp. 6911-6913 (1998)
http://dx.doi.org/10.1364/AO.37.006911


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Abstract

The Hilbert transform is of interest for image-processing applications because it forms an image that is edge enhanced relative to an input object. Recently a fractional Hilbert transform was introduced that can select which edges are enhanced and to what degree the edge enhancement occurs. Although experimental results of this selective edge enhancement were presented, there was no explanation of this phenomenon. We analyze a one-dimensional fractional Hilbert transform acting on a one-dimensional rectangle function and show how it produces an output image that is selectively edge enhanced.

© 1998 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.6110) Fourier optics and signal processing : Spatial filtering
(100.0100) Image processing : Image processing
(100.2980) Image processing : Image enhancement
(100.5010) Image processing : Pattern recognition
(110.6980) Imaging systems : Transforms
(120.2440) Instrumentation, measurement, and metrology : Filters
(200.3050) Optics in computing : Information processing

History
Original Manuscript: December 8, 1997
Revised Manuscript: June 3, 1998
Published: October 10, 1998

Citation
Jeffrey A. Davis, Dylan E. McNamara, and Don M. Cottrell, "Analysis of the fractional Hilbert transform," Appl. Opt. 37, 6911-6913 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-29-6911

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