Classification Methods for Remotely Sensed Data, Second Edition

Page 236

where w′={w₁,…,w_r−1, w′_r,…,w_m} is any configuration, which agrees with w at all sites except r, and L is the set of labels (user-defined classes). The combination of Equations (6.1) and (6.3) yields:

and, similarly,

Substituting Equation (6.6) into Equation (6.5) gives:

If clique C is subdivided into two sets A and B with A consisting of pixels containing r and B being the pixels not containing r, then Equation (6.7) can be written as:

Since V_c(w)=V_c(w′) for any set of pixels c that does not contain pixel r,