Page 197 - Digital Analysis of Remotely Sensed Imagery

162 Cha pte r F i v e

only. Other sensor-specific models include those designed to rectify
Synthetic Aperture Radar (SAR) images and Indian National Remote
Sensing Agency–generated (Indian Remote Sensing) IRS-1C/1D data.
These sensor-specific models are computationally and mathemati-
cally rigorous and complex, and produce more accurate geometric
rectification than generic models. However, with increasing availabil-
ity of diverse sensors, such as frame camera, panoramic camera,
pushbroom scanner, whiskbroom sensor, and radar antenna, it is not
always feasible to find all sensor-specific models in an image analysis
system. It may be difficult to add new models or to revise existing
ones. Moreover, sensor parameters for commercial remote sensing
satellites (e.g., IKONOS) are not routinely supplied to the user. Instead
of sensor-specific models, the rectification of these images has to rely
on generalized sensor models. One particular type of generalized
sensor model is the Rational Function Model (RFM) (Tao and Hu,
2001).

5.4.3 RPC Model
Generalized rectification models are independent of sensor platforms
and sensor types. They model the relationship between the image
space and the Earth’s surface as some general function instead of the
physical process of imaging, so it is called RFM. This model is com-
monly realized through rational polynomial coefficients or rapid
positioning coordinates (RPC). The rational coefficients describe the
geometric relationship between the sensor and the Earth’s surface.
These coefficients pertain to the interior and exterior orientation
parameters of the sensor at the instant of imaging. With these coeffi-
cients, it is even possible to rectify images without using GCPs, even
though it is desirable to further refine RPC models with the use of
GCPs because this refinement can further improve the accuracy of
image rectification. RFM is very suited to rectification of images at a
high accuracy level and in rectifying very high resolution satellite
imagery such as IKONOS and QuickBird.
The RPC model can be implemented in two modes, standard and
fast. In the standard mode, the transformation equations are estab-
lished pixelwise for every pixel. The calculation of each pixel’s loca-
tion using elevation and geoid information is a lengthy process. This
can be sped up by using the fast mode in which the equations are
established for a grid of points spaced throughout the image. A faster
speed is achieved at the expense of losing some accuracy, but usually
not a substantial amount (Leica Geosystems, 2006).

5.4.4 Projective Transformation
This transformation is applicable to frame aerial photographs that do not
contain warping. The photograph plane is projected to a corresponding
plane on the ground (Fig. 5.12) via the following equations: