Overview of Image Processing
Swath edge
Satellite
________ ~. ~_-- ~ -=====~o
Earth
Swath center
Fig. 2.1. Effect of earth curvature on pixel size
55
The above distortions are systematic in the sense that the errors are predictable. For example, once a satellite's glide path is known, it is easy to predict
the square to rhombus transformation due to the Earth's rotation. Often, the
agency-supplied data are systematic corrected. However, there are also nonsystematic distortions. These arise mainly due to unpredictable occurrences
such as random variations in platform velocity, altitude and attitude. Obviously, such changes result in changing the FOV thus leading to distortion.
A common approach to correcting shape distortions is to geometrically
transform the coordinates of the image to coincide with ground control points
(GCP). A geo-referenced data set such as a map of the imaged area or an
actual ground survey, conducted these days using global positioning systems
(GPS), is required to collect the GCP. A GCP is a point on the reference data
set that is also identifiable in the recorded image. For example, this could be
a mountain peak or a cape or human-made features such as road intersections.
Several GCPs are identified and their geographical coordinates are noted.
A coordinate transformation is determined to relate the image coordinates to
the true coordinates,
(2.2)
Here R is the rectification mapping that maps the set of image coordinates
(subscripted 1) to the true coordinates (subscripted T). The simplest coordinate transformation that one can choose is linear or affine. While this works
for simple distortions such as the square to rhombus alluded to above, it is insufficient for other distortions. Polynomial transformations are more general.
For example, a second order transformation has the form
b12] [XT] + [Cll
b22 YT
C2l
(2.3)
If we choose exactly 12 GCPs we can solve for the constants in (2.3) through
12 simultaneous linear equations. If we choose more GCPs we will have an
overdetermined set of linear equations for which we can get a least squares
solution.
Once the parameters of the mapping have been determined, we need to
adjust the intensity values in the rectified image. This is because pixel centers
in the original image do not necessarily map to pixel centers in the rectified
Swath edge
Satellite
________ ~. ~_-- ~ -=====~o
Earth
Swath center
Fig. 2.1. Effect of earth curvature on pixel size
55
The above distortions are systematic in the sense that the errors are predictable. For example, once a satellite's glide path is known, it is easy to predict
the square to rhombus transformation due to the Earth's rotation. Often, the
agency-supplied data are systematic corrected. However, there are also nonsystematic distortions. These arise mainly due to unpredictable occurrences
such as random variations in platform velocity, altitude and attitude. Obviously, such changes result in changing the FOV thus leading to distortion.
A common approach to correcting shape distortions is to geometrically
transform the coordinates of the image to coincide with ground control points
(GCP). A geo-referenced data set such as a map of the imaged area or an
actual ground survey, conducted these days using global positioning systems
(GPS), is required to collect the GCP. A GCP is a point on the reference data
set that is also identifiable in the recorded image. For example, this could be
a mountain peak or a cape or human-made features such as road intersections.
Several GCPs are identified and their geographical coordinates are noted.
A coordinate transformation is determined to relate the image coordinates to
the true coordinates,
(2.2)
Here R is the rectification mapping that maps the set of image coordinates
(subscripted 1) to the true coordinates (subscripted T). The simplest coordinate transformation that one can choose is linear or affine. While this works
for simple distortions such as the square to rhombus alluded to above, it is insufficient for other distortions. Polynomial transformations are more general.
For example, a second order transformation has the form
b12] [XT] + [Cll
b22 YT
C2l
(2.3)
If we choose exactly 12 GCPs we can solve for the constants in (2.3) through
12 simultaneous linear equations. If we choose more GCPs we will have an
overdetermined set of linear equations for which we can get a least squares
solution.
Once the parameters of the mapping have been determined, we need to
adjust the intensity values in the rectified image. This is because pixel centers
in the original image do not necessarily map to pixel centers in the rectified