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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 20 — Oct. 3, 2005
  • pp: 8097–8121

Uniform estimation of orientation using local and nonlocal 2-D energy operators

Kieran G. Larkin  »View Author Affiliations

Optics Express, Vol. 13, Issue 20, pp. 8097-8121 (2005)

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Two new two dimensional (2-D) complex operators for estimating the energy and orientation of 2-D oriented patterns are proposed. The starting point for our work is a new 2-D extension of the Teager-Kaiser energy operator incorporating orientation estimation. The first new energy operator is based on partial derivatives and can be considered a local (point-based) estimator. Using a nonlocal (pseudo-differential) operator we derive a second and more general energy operator. A scale invariant nonlocal operator is derived from the recently proposed spiral phase quadrature (or Riesz) transform. The Teager-Kaiser energy operator and the phase congruency local energy are unified in a single equation for both 1-D and 2-D. Robust orientation estimation, important for isotropic demodulation of fringe patterns is demonstrated. Theoretical error analysis of the local operator is greatly simplified by a logarithmic formulation. Experimental results using the operators on noisy images are shown. In the presence of Gaussian additive noise both the local and nonlocal operators give improved performance when compared with a simple gradient based estimator.

© 2005 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(070.5010) Fourier optics and signal processing : Pattern recognition
(100.2550) Image processing : Focal-plane-array image processors
(100.2650) Image processing : Fringe analysis
(100.2960) Image processing : Image analysis

ToC Category:
Research Papers

Original Manuscript: August 8, 2005
Revised Manuscript: September 19, 2005
Published: October 3, 2005

Kieran Larkin, "Uniform estimation of orientation using local and nonlocal 2-D energy operators," Opt. Express 13, 8097-8121 (2005)

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