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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
(GCPs). When no GCPs (and no inertial system telemetry) are
available, users cannot recover the exterior orientation of the
sensor and therefore unable to perform various mapping and data
collection operations.
With the introduction of generalized sensor models, this
situation has changed considerably. Generalized sensor models,
particularly the RFM (Hu et al., 2004), have alleviated the
requirement to obtain a physical sensor model, and with it, the
requirement for a comprehensive understanding of the physical
model parameters. Furthermore, as the RFM sensor model
implicitly provides the interior and exterior sensor orientation,
the availability of GCPs is no longer a mandatory requirement.
Consequently, the use of the RFM for photogrammetric
mapping is becoming a new standard in high-resolution satellite
imagery that has already been implemented in various high-
resolution sensors, such as Ikonos™ and QuickBird™. This has
led to various research efforts that have primarily focused on
the approximating accuracy (Tao and Hu, 2001), stereo
intersection (Tao and Hu, 2002), correction of biases in the
RFM parameters (Hu and Tao, 2002; Fraser and Hanley, 2003),
block adjustment (Grodecki and Dial, 2003), and 2D/3D
mapping applications (Croitoru et al., 2004).
Inspired by the advantages of the RFM and its capability to
provide an open approach to photogrammetric exploitation of
the commercial HRSI, the purpose of this paper is to explore
how the RFM could be further utilized for extraction of 3D
models. In particular, we are interested in the user's point of
view and in demonstrating how RFM information, together with
auxiliary data such as DEM, could provide an efficient, fast and
economical solution that can be handled by non-expert users.
2. THE RFM FRAMEWORK
2.1 The Rational Function Model
The RFM sensor model describes the geometric relationship
between the object space and image space. It relates object
point coordinates (X, Y, Z) to image pixel coordinates (/, s) or
vice versa using 78 rational polynomial coefficients (RPCs) that
allow users to perform photogrammetric processing in the
absence of the rigorous physical sensor model. For the ground-
to-image transformation, the defined ratios of polynomials have
the forward form (NIMA, 2000):
: P» (X, à Y. , z ) |
Ps ( X, , Y , Z, )
Ss =
, POLL LY, Li)
es MA Z,)
= (1)
7
where (/, s,) are the normalized row (line) and column
(sample) index of pixels in image space; X,, Y,, and Z, are
normalized coordinate values of object points in ground space;
and p;...p, are a set of rational polynomials with coefficients
dj Dj Cj, d;, respectively (also called rational function
coefficients (RFCs)). Each polynomial in Eq. 1 is of twenty-
term cubic form. Although several versions of different
permutations of the polynomial terms occur in the literature, the
order defined in NIMA (2000) has been adopted by Space
Imaging and Digital Globe, and thus has become the industry
standard. These RFCs can be solved by terrain-independent
scenario using known physical sensor models or by terrain-
dependent scenario without using physical sensor models (Tao
and Hu, 2001).
2.2 RFM Refinement
The RPCs provided by the vendors could be refined in image
space or in object (ground) space, when additional control
information becomes available. The RFM may be refined
directly or indirectly (Hu et al., 2004). For example, the Ikonos
Geo products and Standard stereo products will be improved to
sub-meter absolute positioning accuracy using one or more high
quality GCPs (Grodecki and Dial, 2003; Fraser et al, 2003; Tao
and Hu, 2004) or be close to the accuracy of the GCPs whose
quality is low (Hu and Tao, 2002; Tao et al. 2003). It should be
noted that from the user's point of view, the availability of
RFM refining methods is likely to promote the use of low cost
imaging products (with a lower processing level) for various
applications.
The refinement of the forward RFM can be accomplished by
appending a simple complementary transformation in image
space at the right-hand side of Eq. 1 in order to eliminate
various error sources. The use of first-order polynomials to
eliminate the image shift and drift errors as given in Eq. 2
defines an adjustable RFM model (Grodecki and Dial, 2003).
Al-l'-I7agtarltas (2)
ASSS'rgmhytb:ltb.-s
In Eq. 2, (A4 As) express the discrepancies between the
measured line and sample coordinates (/', s’) and the RFM
projected coordinates (/, s) of a GCP or tie point; the
coefficients ap, ay, as, by, bj, b, are the adjustment parameters for
each image. For narrow field-of-view CCD instruments with a
priori orientation data, these physical effects mainly behave like
a same net effect of displacements in line and sample directions
in image plane in total. Hence, for short images the error
sources can be modeled by a simple translation in image space,
and the above model becomes simply A/ = ay and As = by.
2.3 Single Image 3D Metrology
Using the refined RFCs it is possible to retrieve the 3D
coordinates of points with only a single image. This is done by
utilizing a dynamic measurement mode. By utilizing a DEM, it
is possible to extract, for example, the 3D location of a roof
point with user's cursor. Many techniques have been developed
to facilitate the measurement entire process from the single
image. A similar approach to the 3D point extraction could be
taken by utilizing shadow information. The sun altitude and
azimuth can be retrieved either from the image time or the
image metadata.
This approach is particularly suitable for the extraction of
building heights. However, this approach may be inapplicable
in some cases due to occluded shadows, visible shadows that
are projected on other objects. This approach also assumes the
availability of a DEM. Although a high resolution accurate
DEM will ensure the most accurate results, it is sufficient to use
an approximation of the DEM or even the average relief height
in some applications, such as relative building height
estimation. In these cases rough estimation of the relief height
may suffice due to the ratio between the building heights and
the range between the building and a satellite sensor.
2.4 Stereo based 3D Metrology
When the RPCs are provided by imagery vendors or are refined
using GCPs, 3-D feature extraction is possible since the RFM
provides the necessary interior and exterior orientation
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