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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. 27, Iss. 8 — Aug. 1, 2010
  • pp: 1756–1763

Geodesic distance on non-singular coherency matrix space in polarization optics

V. Devlaminck and P. Terrier  »View Author Affiliations


JOSA A, Vol. 27, Issue 8, pp. 1756-1763 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001756


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Abstract

We define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of this geodesic distance and the classical Euclidean one and their appropriateness for interpixel comparisons in a context of imaging polarimetry. Finally, results are presented for a geodesic version of the classical K-means clustering algorithm with simulated data and real data. The results demonstrate the advantages of the geodesic approach.

© 2010 Optical Society of America

OCIS Codes
(120.5410) Instrumentation, measurement, and metrology : Polarimetry
(260.2130) Physical optics : Ellipsometry and polarimetry
(260.5430) Physical optics : Polarization
(100.4995) Image processing : Pattern recognition, metrics

ToC Category:
Physical Optics

History
Original Manuscript: March 18, 2010
Revised Manuscript: May 20, 2010
Manuscript Accepted: June 7, 2010
Published: July 6, 2010

Citation
V. Devlaminck and P. Terrier, "Geodesic distance on non-singular coherency matrix space in polarization optics," J. Opt. Soc. Am. A 27, 1756-1763 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-8-1756

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