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

Classification of polarimetric SAR imagery 305

7.4 Classification of polarimetric SAR imagery

We saw in Chapter 6, Section 6.3, how to derive a Bayes maximum likeli-

hood classifier for normally distributed optical/infrared pixels. In the case

of the fully polarimetric m-look SAR data discussed in Chapter 5, the image

observations were expressed in complex covariance matrix form

¯

c =

1

m

x,

where

x =

m

X

ν=1

s(ν)s(ν)

†

, s = (s

hh

,

√

2s

hv

, s

vv

)

T

.

The corresponding random matrix X, as was pointed out, will follow a com-

plex Wishart distribution, Equation (2.58),

p

W

c

(x) =

|x|

(m−N)

exp(−tr(Σ

−1

x))

π

N(N−1)/2

|Σ|

m

Q

N

i=1

Γ(m + 1 − i)

, (7.27)

where N is the dimension of the covariance ...