
184 Image Enhancement and Correction
5.3.6 A quality index
Several quantitative measures have been suggested for determin
ing the degree
to which the spectral pro perties of the multispectra l bands have been degraded
in the pan-sharpening process (Tsai, 1982). Wang and Bovik (2002) suggest
a particularly simple and intuitive measure of spectral fidelity between two
image bands with pixel intensities repre sented by f and g:
QI =
σ
fg
σ
f
σ
g
·
2
¯
f¯g
¯
f
2
+ ¯g
2
·
2σ
f
σ
g
σ
2
f
+ σ
2
g
=
4σ
fg
¯
f¯g
(
¯
f
2
+ ¯g
2
)(σ
2
f
+ σ
2
g
)
, (5.18)
where
¯
f (¯g) and σ
2
f
(σ
2
g
) are mean, and variance of band f (g) and σ
fg
is the
cova riance of the two bands; see Listing 5.9. The first factor in (5.18) is