92 Computing in Geographic Information Systems
of (k, l) ∈ R
2
. In other words, for each pixel (i, j) in the output image, compute
its corresponding location (k, l) in input image, obtain the pixel value from
input image and put it in output image. Since a reverse computation of pixel
location is used, this process is also known as reverse transformation or inverse
transformation or output-to-input transformation. The above transformation
can be expressed through a pair of polynomials as 5.2 and 5.3
k = Q(i, j) = q
0
+ q
1
i + q
2
j + q
3
ij (5.2)
and
l = R(i, j) = r
0
+ r
1
i + r
2
j + r
3
ij (5.3)
These polynomial equations can be represented in matrix form. Since the
affine transformation is represented through a set of polynomials, it is called
PAT. The unknown co