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. 
394 
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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