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

Algorithms that minimize the simple cost functions 333

Equating the likelihood and prior terms in this expression to give E(C) = 0

and taking p

k

≈ 1/

˜

K, where

˜

K is some a priori expected number of c lusters,

then gives

α

E

≈ −

m

2 log(1/

˜

K)

. (8.22)

The parameter σ

2

in Equation (8.21) (the within-cluster varianc e) can be

estimated fro m the data, see below.

The extended K-means (EKM) algorithm is then as follows. First an initial

configuratio n U with a very large number of clusters K is chosen (for single-

band data this might conveniently be the K ≤ 256 gray values that an ima ge

with 8-bit quantization can possibly have) and initial values

ˆ

µ

k

=

1

m

k

m

X

ν=1

u

kν ...