Page 182 - Introduction to Statistical Pattern Recognition

164 Introduction to Statistical Pattern Recognition

p[x(i,j),x(i+k,j+t)] = pf'py) . (4.13 1)

That is, the correlation coefficient between x(i,j) and x(i+k,j), which is called
the column correlation coefficient, pf), depends only on k. The same is true
for the row correlation corncient, py). The correlation coefficient between

x(i,j) and x(i+k,j+!) is assumed to be the product of pf) and pf'')*
If we form a vector with nm variables by stacking columns of the
received image as

x = [x(l,l). . .x(n, 1). . .x(l,m). . .x(n,m)lT (4.132)

the correlation matrix has the block toeplitz form

R, @R, = , (4.133)