Geodesic distance on non-singular coherency matrix space in polarization optics.
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.
Devlaminck
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LAGIS-FRE CNRS 3303 Université Lille 1, Sciences et Technologies, Lille 59655, France. vincent.devlaminck@univ-lille1.fr
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