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

Algebra of vectors and matr ices 11

1.3 Algebra of vectors and matrices

It is very convenient, in fact essential, to use a vector representation for multi-

sp ectral or SAR image pixels. In this book, a pixel will be represented in the

form

g(i, j) =







g

1

(i, j)

.

.

.

g

N

(i, j)







, (1.4)

which is understood to be a column vector of spectral intensities or gray-scale

values at the image position (i, j). It can be thoug ht of as a point in N -

dimensional Euclidean space, commonly referred to as input space or feature

space. In the case of SAR images, the vector components may be complex

scattering a mplitudes.

Since we will be making extensive use of the vector ...