Page 199 - Digital Analysis of Remotely Sensed Imagery

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requires provision of 3D GCP coordinates in the format of (E, N, H)
with a balanced spatial distribution both horizontally and vertically.
Elevation information is indispensable in building the model for
removing relief displacement from the input image. Image coordi-
nates are first geometrically corrected for Earth rotation and cell-size
variations caused by oblique viewing. Direct linear transform models
are purely solvable based on the principle of the least-squares adjust-
ment through the use of a minimum of six GCPs to determine the 11
orientation parameters of a scene. However, more GCPs are needed
to achieve a satisfactory solution in practice. The least-squares adjust-
ment also removes systematic residuals after the preliminary process-
ing. With this model submeter accuracy can be achieved using as few
as six GCPs for SPOT data.

5.4.6 Polynomial Model
The polynomial model is a popular generic model completely inde-
pendent of the imaging sensor, and hence highly suited for rectifying
satellite images whose geometry and distortions are difficult to
model. This model is generic in that it can be applied to all sorts of
images, even though some of them may be more accurately georefer-
enced with other sensor-specific models. Its high flexibility allows
customization of geometric correction via polynomial equations that
can have a varying number of terms. The complexity of the model
can be adapted to suit the availability of the numbers of GCPs and to
meet different transformation precision requirements. It is possible to
use the first-order polynomials to project raw satellite imagery with
satisfactory accuracy if there is not much distortion in it. Higher-order
polynomials are preferred for images suffering from nonlinear geo-
metric distortion. Irrespective of the model complexity, only the hori-
zontal position of pixels is dealt with in all polynomial model–based
image transformations. Three-dimensional GCPs are not required in
performing image rectification based on this model. All geometric
distortions of the input image (e.g., sensor-caused distortion, relief
displacement, Earth curvature, and so on) are addressed in one trans-
formation. However, relief displacement cannot be inadequately
removed from the rectified image.

5.4.7 Rubber-Sheeting Model
The rubber-sheeting model is a piecewise polynomial model for geo-
metrically correcting severely warped images in a number of steps.
The first step is to form a triangulated irregular network (TIN) from
all the available GCPs. The image area encompassed by each triangle
in the network is rectified using the first- (linear) or fifth- (nonlinear)
order polynomials. Because of geometric uncertainty, the areas out-
side the convex hull of the TIN (i.e., extrapolation) should not be recti-
fied using this model. The rubber-sheeting model is appropriate for