Page 221 - Digital Analysis of Remotely Sensed Imagery

Image Geometric Rectification 185

Usually carried out for large scale hyperspatial resolution
images or airborne photographs, orthorectification is recom-
mended for mountainous terrains and for remote sensing mate-
rials that are to be used to construct 3D models of the scene.
Orthorectification, however, is not beneficial if the scene has a
relatively flat terrain. It is not recommended for small-scale
images obtained at an altitude much higher than the topo-
graphic relief as the amount of topography-induced displace-
ment in pixel position is negligible on such images.

5.7.2 Methods of Image Orthorectification
The precondition of image orthorectification is the establishment
of a relationship between image coordinates (r, c) and the ground
coordinates (E, N, Z). For spaceborne satellite imagery, the con-
struction of this relationship relies on the exterior and interior ori-
entation parameters (e.g., position and orientation) of the sensor,
with the assistance of 3D GCPs. Image orthorectification may be
implemented nonparametrically or parametrically (Hemmleb and
Wiedemann, 1997). Nonparametric approaches such as polyno-
mial transformation and projective transformation are very simi-
lar to the 2D polynomial-based image rectification covered in Sec.
5.5 except that the height of GCPs is also considered. No informa-
tion on the sensor is utilized in the rectification, in drastic contrast
to parametric approaches in which the image coordinates of all
pixels are transformed to ground coordinates based on the infor-
mation on the interior and exterior orientation of the sensor. These
approaches include differential rectification, sensor-specific model
rectification, and RFM rectification. Differential rectification refers
to individual transformation of pixel values from the input image
to an output image that has the right geometry (i.e., distortion
free). Both camera distortions and relief displacement are removed
from the rectified photographs and satellite images, which may be
further refined using GCPs. A sufficiently large number of 3D
GCPs is essential in both parametric and nonparametric approaches.
This number may be reduced through the deployment of mathe-
matical models, such as the bundle-adjustment model for over-
lapping 3D aerial photographs. Through photogrammetric bundle
adjustment, satellite images can be orthorectified from satellite
orbital parameters. It is possible to integrate the parametric meth-
ods with the nonparametric ones.
Image orthorectification may be based on a physical model or
sensor-specific model such as the rigorous collinearity equations. In
this model the ground coordinates of pixel A(E , N , H ) in the ground
A A A
coordinate system are calculated from its image coordinates (x , y )
a a
(Fig. 5.20) directly using the collinearity equations [Eqs. (5.25) and
(5.26)]. The establishment of these equations is based on the principle