International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004
interest within the photogrammetric community to adopt
approximate models since they require neither a comprehensive
understanding of the imaging geometry nor the internal and
external characteristics of the imaging sensor. Approximate
models include Direct Linear Transformation (DLT), self-
calibrating DLT (SDLT), Rational Function Model (RFM), and
parallel projection (Vozikis et al., 2003; Fraser, 2000; OGC,
1999: Ono et al., 1999; Wang, 1999; Gupta et al., 1997; El-
Manadili and Novak, 1996). Among these models, parallel
projection is gaining popularity for its simplicity and accurate
representation of the perspective geometry associated with
scenes captured by a narrow angular field of view imaging
sensor that is travelling with constant velocity and constant
attitude. Another motivation for utilizing the parallel projection
is the straightforward procedure for generating normalized
imagery, which is necessary for increasing the reliability and
reducing the search space associated with the matching problem
(Morgan et al., 2004).
In this paper, the parallel projection will be used for
representing the perspective geometry and deriving a DEM
from high resolution satellite imagery. The following section
presents a brief overview of the parallel projection formulation
as well as the generation of resampled scenes according to
epipolar:geometry. Section 3 explains the DEM generation
methodology including primitive extraction, matching, space
intersection, and interpolation. This is followed by a description
of the incorporated real datasets captured by SPOT-1, SPOT-2,
and SPOT-5 as well as an evaluation of the performance of
proposed methodology for DEM generation in sections 4 and 5,
respectively. Finally, conclusions and recommendations for
future work are summarized in section 6.
2. PARALLEL PROJECTION: BACKGROUND
High resolution imaging satellites (e.g., IKONOS, SPOT,
QUICKBIRD, ORBVIEW, and EOS-1) constitute an efficient
and economic source for gathering current data pertaining to an
extended area of the surface of the Earth. Due to technical
limitations, two dimensional digital arrays that are capable of
capturing imagery with geometric resolution, which is
commensurate to that associated with traditional analogue
cameras, are not yet available. Therefore, high resolution
imaging satellites implement a linear array scanner in their focal
plane. Successive coverage of contiguous areas on the Earth’s
surface is achieved through multiple exposures of this scanner
during the system’s motion along its trajectory. For systems
moving with constant velocity and attitude, the imaging
geometry can be described by a perspective projection along the
scanner direction and parallel projection along the system’s
trajectory. Moreover, for imaging systems with narrow angular
field of view, the imaging geometry can be further
approximated with a parallel projection along the scanner
direction.
The smooth trajectories and narrow angular field of view
associated with high resolution imaging satellites (e.g., the
angular field of view for IKONOS is less than one degree)
contribute towards the validity of the parallel projection as a
highly suitable model for representing the mathematical
relationship between corresponding scene and object
coordinates. The following subsections present a brief overview
of the formulation of the parallel projection model. Also, the
conceptual procedure for resampling satellite scenes according
to epipolar geometry (i.e, normalized scene generation) is
summarized.
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2.1 Parallel Projection: Mathematical Model
The parallel projection model involves eight parameters: two
parameters for the projection direction — L, M, three rotation
angles — & , 9, K, two shifts — Ax, Ay, and one scale factor — s
(Ono et al., 1999). The non-linear form of the parallel projection
can be re-parameterized to produce the linear form, as
expressed in Equation 1.
xcdocEHY. dd kd (1)
y= AX +4Y +47 +4
where:
X. y are the scene coordinates,
X,Y,Z are the object coordinates of the corresponding object
point, and
di~4s are the
parameters.
re-parameterized parallel — projection
The imaging geometry of scenes captured by an imaging
scanner moving along a straight line trajectory with constant
velocity and attitude can be described by a parallel projection
along the flight trajectory and perspective geometry along the
scanner direction. The perspective projection along the scanner
direction can be approximated by a parallel projection for
systems with narrow angular field of view. However, additional
term (y) is introduced in the y-equation to make the projection
along the scanner direction closer to being a parallel one,
Equation 2 (Morgan et al., 2004).
Xni aui ad,
A, X + A,Y + A,Z + A, (2)
y= s
tan (i
j, 59i) )G x pul Xanh q.d.)
e
where:
c is the scanner principal distance, and
V is the scanner roll angle.
The parameters (4, — As, v) can be estimated for each scene if
at least five ground control points (GCP) are available.
2.2 Normalized Scene Generation
In addition to the simplicity of the parallel projection model, it
allows for resampling the involved scenes according to epipolar
geometry. Such a resampling is known as normalized scene
generation. The normalization process is beneficial for DEM
generation since the search space for conjugate points can be
reduced from 2-D to 1-D along the epipolar lines as represented
by the same rows in the transformed scenes. The resampling
process can be summarized as follows, refer to (Morgan et al.,
2004) for more technical details:
e The parallel projection parameters (4; — Ag, y), Equations
2, are determined for the left and right scenes using some
ground control points.
e Derive the parallel projection parameters L, M, c, q, x, Ax,
Ay, and s that correspond to the estimated parameters (4; —
Ag) in the previous step.
e Use the parallel projection parameters for the left and right
scenes to derive an estimate of a new set of parameters for
the normalized scenes. The newly derived parallel
projection parameters will ensure the absence of y-parallax
between conjugate points. Moreover, the x-parallax
between conjugate points will be linearly proportional to
the elevations of the corresponding object points.
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