
Exercises 125
FIGURE 3.12
Two classes of observations in a two-dimensional feature space. The solid
lines are the principal axes; see Listing 3.10.
where C
B
= (m
1
− m
2
)(m
1
− m
2
)
⊤
.
(b) Show that the desir ed projection directio n is given by
w = (C
1
+ C
2
)
−1
(m
1
− m
2
). (3.82)
(c) Modify the program in Listing 3.10 to calculate and plot the projec-
tion direction w.
14. Using the code in Listings 3.6 a nd 3.8 (IDL) or Listing s 3.7 and 3.9
(Python) as a starting point, write a procedure to perform the MNF
transformatio n on a multispectral image. If you are using ENVI/IDL,
compare your output with ENVI’s MNF procedure.
15. Show from Equation (3.50) tha t the variance ...