Page 208 - Digital Analysis of Remotely Sensed Imagery

172 Cha pte r F i v e

5.5.4 Creation of the Output Image
The discussion so far has concentrated only on the geometric position
of pixels in the rectified image. Their radiometric values in the output
image have not been resolved yet. This issue is dealt with by resam-
pling the input image. As illustrated in Fig. 5.9, pixels in the output
image do not have a regular interval after the removal of geometric
distortions. This pixel spacing does not reflect the spatial resolution
of the original image anymore. Furthermore, the ground coordinates
calculated using Eqs. (5.13) and (5.14) rarely correspond to the ground
position where pixels are sampled. The output pixels do not have any
radiometric values associated with them. Therefore, the idea of trans-
ferring the value of pixels in the input image to the output image
directly, as discussed previously, has to be abandoned. Instead, the
process must be reversed for all pixels with the exception of the four
corner ones. After their location in the output image is determined
using the transformation equations. (5.13) and (5.14), the output
image is created in two steps:

• First, the position of all other pixels in the output image is
determined by sampling the newly created empty image at a
constant interval equivalent to the image’s spatial resolution
both horizontally and vertically, starting from the corner
pixels. In this way, it is guaranteed that the rectified image
will retain the same spatial resolution as the input image.
Once the position of all pixels in the output image is
determined, then their corresponding position in the input
image is estimated by inversing Eq. (5.15), or

−1
r = f (E, N) (5.21)
1
−1
c = f (E, N) (5.22)
2
• Second, the radiometry at the position calculated in step one
in the input image is estimated via a process known as radiometric
resampling in which the radiometric value is estimated from the
pixel values in the neighborhood. Resampling of radiometric
values at these positions is precipitated by the fact that the
inversed r and c from Eqs. (5.21) and (5.22) are likely to be
floating points. At these calculated positions there are no
pixels. Instead, radiometric values are available at pixels that
are spaced neatly in a regular grid in the original image. The
radiometric values at these calculated r and c coordinates
have to be estimated from the value of pixels in the vicinity.
The definition of the neighborhood size varies with the
resampling method.

There are three resampling methods in creating the output
image.