Page 272 - Digital Analysis of Remotely Sensed Imagery

234 Cha pte r S i x

x − X
i
Pixel Band 1 Band 2 Band 1 Band 2 Comp 1 Comp 2
1 2 4 −3 −1 3.83 2.30
2 4 5 −1 0 6.06 2.07
3 3 6 −2 1 5.75 3.45
4 4 3 −1 −2 4.99 0.38
5 7 8 2 3 10.20 2.99
6 7 6 2 1 9.13 1.30
7 8 5 3 0 9.43 −0.08
8 5 3 0 −2 5.83 −0.16
X 5 5 − −

TABLE 6.2 Coordinates of the Eight Pixels in the Two Spectral Bands in Fig. 6.22

− ⎛ ⎧ 3 ⎞ − ⎛ ⎞1 − ⎛ 2 ⎞
V = 1/(8 − 1) ⎜ ⎨ ⎟ (−3 − 1) + ⎜ ⎟ (−1 0) + ⎜ ⎟ (−2 1)
⎩ − ⎝ 1 ⎠ ⎝ ⎠ 0 ⎝ 1 ⎠

2 ⎛ ⎞
2 ⎛ ⎞
3 ⎛ ⎞
+ ⎜ − ⎛ 1 ⎞ ⎟ (−1 − 2) + ⎜ ⎟ (2 3) + ⎜ ⎟ (2 1) + ⎜ ⎟ (3 0) + ⎛ ⎜ 0⎞ ⎟ (0 −2)
− ⎝ 2 ⎠ 3 ⎝ ⎠ 1 ⎝ ⎠ 0 ⎝ ⎠ − ⎝ 2⎠
⎧⎛93 ⎞ ⎛ 10⎞ ⎛ 42⎞ ⎛ 12⎞
= 1/7 ⎨ ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟ + ⎜ ⎟
⎩ ⎝39 ⎠ ⎝ 00⎠ ⎝ 21⎠ ⎝ 24⎠

⎫
⎛ 46⎞ ⎛ 42⎞ ⎛ 90⎞ ⎛ 00⎞⎫
+ ⎜ ⎝ 69⎠ ⎟ + ⎜ ⎝ 21⎠ ⎟ + ⎜ ⎝ 00⎠ ⎟ + ⎜ ⎝ 04⎠ ⎟ ⎬
⎭
⎛ 42 15⎞ ⎛ 6 2 14⎞ ⎛ V V ⎞
.
12
= 1/7 ⎜ ⎝ 15 28⎠ ⎟ = ⎜ ⎝ 214 4 ⎠ ⎟ = ⎜ ⎝ V 11 V ⎠ ⎟ .
.
21
22
After the variance-covariance matrix V is determined, it is time to
calculate the correlation matrix R using Eq. (6.16):
⎡ 1 r ... r ⎤
⎢ 12 1n ⎥
R = ⎢ r 21 1 ... r 2n ⎥
⎢ ... ... ... ... ⎥
r ⎢ n ⎣ ⎣ 1 r n 2 ... 1 ⎥ ⎦