Devlaminck V, Terrier P
LAGIS-FRE CNRS 3303 Université Lille 1, Sciences et Technologies, Lille 59655, France.
J Opt Soc Am A Opt Image Sci Vis. 2010 Aug 1;27(8):1756-63. doi: 10.1364/JOSAA.27.001756.
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.
我们定义了一种与非奇异相干矩阵的极化空间相关的测地距离。它在HPD(2)（二维埃尔米特正定矩阵流形）上的引入可直接与琼斯计算相关联。还给出了在这个特定度量空间中距离的表达式以及均值的相关概念。我们研究了这种测地距离和经典欧几里得距离的性质，以及它们在成像偏振测量背景下用于像素间比较的适用性。最后，给出了经典K均值聚类算法的测地版本在模拟数据和真实数据上的结果。结果证明了测地方法的优势。
