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

348 Unsupervised Classification

8.4.2 Spa tial clustering

As described in Chapter 4, class labels for multispectral images can be

rep-

resented by realizations of a Markov random field, for which the label of a

given pixel may be influenced only by the class labe ls of other pixels in its

immediate neighborhood. According to Gibbs-Markov equivalence, Theorem

4.3, the probability density for any co mplete labeling ℓ of the imag e is given

by

p(ℓ) =

1

Z

exp(−βU(ℓ)), (8.48)

where Z is a normalization and the energy function U(ℓ) is given by a sum

over clique potentials,

U(ℓ) =

X

c∈C

V

c

(ℓ), (8.49)

relative to a neighbo rhood system N. If we restrict discussion to 4- ...