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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
projections, and parameter partial derivatives for use by the
block adjustment engine. By encapsulating the math model in
COM modules, ISDM Satellite Triangulation is easily adapted
to work with many different models. The modules developed
by Z/1 Imaging for use with Landsat, SPOT, IRS, and
QuickBird images all implement rigorous collinearity-based
mathematical models. The module developed for IKONOS
images implements a mathematical model based on rational
polynomial functions modified by an affine transformation
using control points (Grodecki, J., 2001 and Fraser, et al, 2001).
2.1 Rational Functions
While the satellite triangulation itself may be performed using a
variety of mathematical models, third-order rational polynomial
functions are used as a sensor independent math model for
working with satellite images within the Z/I Imaging suite of
products (Madani, 1999). These rational polynomial functions
have the form:
nm AZ
Gl ius)
Zod:
=: DC X y
n
n?
C
: GM 2.)
where r and c are the row and column of an image point, X, Y,
Z are coordinates of an object point, and p;, p», q,;, q; are third-
order polynomials in X, Y, and Z. These polynomials have 20
terms each.
By setting selected coefficients to zero, the power of the
rational functions can vary for each dimension as well as for the
numerator and the denominator. In fact, by setting all non-
constant denominator coefficients to zero, the rational functions
can be reduced to polynomial functions.
It is not uncommon to encounter coordinate systems with
extremely large coordinate values. If, in addition to large
coordinates, a relatively high-order polynomial is employed,
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numerical instability or overflow can occur. In order to avoid
such problems, a normalization scheme has been implemented.
Each object point coordinate variable is normalized to a range
of -1 to 1 before they are used in the rational polynomial
functions. The ranges of the rational polynomial functions are
also —1 to 1, so the final row and column values are obtained by
“de-normalizing” the results.
Image-to-ground calculations are performed using a remote
sensor module in order to populate a regular grid that captures
the mapping between image coordinates and ground
coordinates at different ground elevations. This grid is then
used to produce RPCs that approximate the mapping from
ground coordinates to image coordinates. Initial RPCs are
produced for each image as its photo is created within
ImageStation Project Manager (ISPM) or ISDM. After
triangulation has been performed on one or more images, new
RPCs are produced for the images using the adjusted values of
the satellite image parameters. The initial or adjusted RPCs are
used by ISDM and other applications when measuring points
on images, creating stereo views, etc.
3. ISDM SATELLITE TRIANGULATION
WORKFLOW
3.1 Project Initialization
The general ISDM Satellite Triangulation workflow begins
with creating a new project. When the New Project command
is executed in ISPM or ISDM, the “New Project” wizard guides
the user through the project creation process. If the user selects
a project type of "Satellite Imagery", the project is configured
for use with the Satellite Triangulation block adjustment engine
and the currently registered remote sensor modules. It is
important to note that Satellite Triangulation projects are
currently configured to use a WGS84 geographic coordinate
system with an ellipsoidal vertical datum, and all functions are
performed within that coordinate system basis. Once the project
has been created, the Edit Photos command is used to create
photos from satellite images and their associated support data
files (Figure 1). These images have been processed using the
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