Free Trial

Safari Books Online is a digital library providing on-demand subscription access to thousands of learning resources.


132 Image Fusion: Algorithms and Applications not exist either on the space of SS random variables. Instead, quantities like covaria- tions or codifferences, which under certain circumstances play analogous roles for SS random variables to the one played by covariance for Gaussian random variables have been introduced [21]. Specifically, let X and Y be jointly SS random variables with > 1, zero location parameters and dispersions X and Y , respectively. The covariation of X with Y is defined in terms of the previously introduced FLOMs by Samorodnitsky and Taqqu [21]: [X, Y ] = E(XY p-1 ) Y E(|Y | p ) (5.21) where the p-order moment is defined as x p = |x| p sign(x). Moreover, the covariation coefficient of X with Y , is the quantity X,Y = [X, Y ] [Y, Y ] for any 1 p< (5.22) Unfortunately, it is a well-known fact that the covariation coefficient in (5.22) is neither symmetric nor bounded [21]. Therefore, in [10] we proposed the use of a symmetrised and normalised version of the above quantity, which enables us to define a new match measure for SS random vectors. The symmetric covariation coefficient that we used for this purpose can be simply defined as [X, Y ] [Y, X]