Entropy uncertainty of multi-dimensional random variable
Dajun Li, Xia Yang, Jianya Gong · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
Research on positional uncertainty of point is the basis of modeling uncertainty of line segment and polygon. The positional uncertainty indices of point have been widely studied in topography and metrology. In this paper, the exist entropy uncertainty interval of one-dimensional random variable is extended to the circumstances of two-dimensional, three-dimensional and N-dimensional by introducing the theory of information entropy. The indices of entropy uncertainty ellipse, entropy uncertainty ellipsoid and entropy uncertainty super ellipsoid are presented, which can be considered as the indices of uncertainty degree of the random point in two-dimensional, three-dimensional and multidimensional. The entropy indices presented in this paper are unaffected by the objective selection of the confidence level. And they are especially suitable for uncertainty measurement of the random points with unknown distribution in GIS.