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resampling process 
s onto a common 
plane, whose orientation is determined by the orientation 
parameters of the original images. Moreover, original and 
normalized scenes share the same perspective centre. In this 
case, an object point, P, is projected onto the left and right 
normalized images as p and p', respectively. Although the 
normalization process is straightforward when dealing with 
frame images, it is not possible using the rigorous modelling of 
linear array scanners as will be discussed in Section 2.3. But 
first, some terminologies for linear array scanners as well as 
their geometric modelling will be introduced. 
Right original image 
     
Left original image 
Left normalized image 
P 
Figure 1. Epipolar resampling of frame images 
2.2 Differences between Image and Scene 
It is important to distinguish between the two terms “image” 
and “scene” throughout the analysis of linear array scanners, 
Figure 2. 
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Figure 2. À sequence of 1-D images (a) constituting a scene (b) 
An image is defined as the recorded sensory data associated 
With one exposure station. In the case of a frame image, it 
contains only one exposure station, and consequently it is one 
complete image. In the case of a linear array scanner, there are 
many 1-D images, each associated with a different exposure 
station. The mathematical model that relates a point in the 
object space and its corresponding point in the image space is 
the collinearity equations, which uses Exterior Orientation 
Parameters, EOP, of the appropriate image (in which the point 
appears). 
In contrast, a scene is the recorded sensory data associated with 
one (as in frame images) or more exposure stations (as in linear 
array scanners) that covers near continuous object space in a 
short single trip of the sensor. Therefore, in frame images, the 
image and scene are identical terms, while in linear array 
scanners, the scene is an array of cons” «tive 1-D images. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
2.3 Rigorous Modelling of Linear Array Scanners 
Rigorous modelling of linear array scanners involves the 
scanner interior orientation parameters, IOP, and the exterior 
orientation parameters, EOP, for each image in the scene. Lee 
and Habib (2002) explicitly dealt with these parameters in pose 
estimation problems. Alternatively, other researchers reduced 
the number of involved parameters using functional 
representations of the EOP (Lee et al., 2000; Wang, 1999; 
McGlone and Mikhail, 1981; Ethridge, 1977). The underlying 
reason is that EOP do not abruptly change between consecutive 
images within the scene. For indirect estimation of the EOP 
using GCP, instability of the bundle adjustment exists, 
especially for space-based scenes (Wang, 1999; Fraser et al., 
2001). This is attributed to the narrow Angular Field of View 
(AFOV) of space scenes, which motivates the investigation of 
the parallel projection model. Such a model will be discussed in 
more detail in the next section. 
Before proceeding with the analysis of the parallel projection 
model, one has to note that rigorous modelling of linear array 
scanners does not allow straightforward epipolar resampling. 
One of the reasons is that it results in non-straight epipolar lines 
(Morgan et al., 2004a; Kim, 2000). However, in frame images, 
epipolar lines are straight in the original and normalized images 
(Cho et al., 1992). For this reason, a different model, parallel 
projection, will be sought for the analysis in Section 3. 
3. PARALLEL PROJECTION 
This section discusses the rationale behind selecting the parallel 
projection model. Linear and non-linear forms of the parallel 
projection model are presented. Finally, a prerequisite prior to 
handling scenes according to parallel projection is presented. 
3.1 Motivations 
The motivations for selecting the parallel projection model to 
approximate the rigorous model are summarized as follows, 
Figure 3: 
e Many space scanners have narrow AFOV — e.g., it is 
less than 1? for IKONOS scenes. For narrow AFOV, 
the perspective light rays become closer to being 
parallel, Figure 3a. 
e Space scenes are acquired within short time — e.g., it 
is about one second for IKONOS scenes. Therefore, 
scanners can be assumed to have the same attitude 
during scene capturing. As a result, the planes, 
containing the images and their perspective centres, 
are parallel to each other, Figure 3b. 
e For scenes captured in very short time, scanners can 
be assumed to move with constant velocity. In this 
case, the scanner travels equal distances in equal time 
intervals. As a result, same object distances are 
mapped into equal scene distances, Figure 3c.