Image Analysis, Classification and Change Detection in Remote Sensing, 3rd Edition

Multivariate alteration detection (MAD) 379

due to the Ce ntral Limit Theorem (Theorem 2.3), the quantities involved are

increasingly well described by the normal distribution.

To anticipate somewhat, in performing C C A on a bitemporal image, one

maximizes the correlation ρ between the random variables U and V . The

correlation is given by (see Chapter 2)

ρ =

cov(U, V )

p

var(U)

p

var(V )

. (9.3)

Arbitrary multiples o f U and V would cle arly have the same correlation, so a

constraint must be chosen. A convenient one is

var(U) = var(V ) = 1. (9.4)

Note that, under this co nstraint, the variance of the difference image is

var(U − V ) = var(U) + var(V ) − 2cov( ...