PARALLEL PROJECTION MODELLING FOR LINEAR ARRAY SCANNER SCENES
M. Morgan®, K. Kim”, S. Jeong”, A. Habib?
? Department of Geomatics Engineering, University of Calgary, Calgary, 2500 University Drive NW, Calgary, AB,
T2N 1N4, Canada - (mfmorgan@ucalgary.ca, habib@geomatics.ucalgary.ca)
^ Electronics and Telecommunications Research Institute (ETRI), 161 Gajeong-Dong, Yuseong-Gu, Daejeon, 305-350,
Korea — (kokim, soo) @etri.re.kr
PS WG I11/1: Sensor Pose Estimation
KEY WORDS: Photogrammetry, Analysis, Modelling, Method, Pushbroom, Sensor, Stereoscopic, Value-added
ABSTRACT:
Digital frame cameras with resolution and ground coverage comparable to those associated with analogue aerial cameras are not yet
available. Therefore, linear array scanners have been introduced on aerial and space borne platforms to overcome these drawbacks.
Linear array scanner scenes are generated by stitching together successively captured one-dimensional images as the scanner moves.
Rigorous modelling of these scenes is only possible if the internal and external characteristics of the imaging system (interior
orientation parameters and exterior orientation parameters, respectively) are available. This is not usually the case (e.g., providers of
IKONOS scenes do not furnish such information). Therefore, in order to obtain the parameters associated with the rigorous model,
indirect estimation has to be performed. Space scenes with narrow angular field of view can lead to over-parameterization in indirect
methods if the rigorous model is adopted. Earlier research has established that parallel projection can be used as an
alternative/approximate model to express the imaging process of high altitude linear array scanners with narrow angular field of
view. The parallel projection is attractive since it involves few parameters, which can be determined using limited number of ground
control points. Moreover, the parallel projection model requires neither the interior nor the exterior orientation parameters of the
imaging system. This paper outlines different parallel projection alternatives (linear and nonlinear). In addition, forward and
backward transformations between these parameters are introduced. The paper also establishes the mathematical relationship
between the navigation data, if available, and the parallel projection parameters. Finally, experimental results using synthetic data
prove the suitability of parallel projection for modelling linear array scanners and verify the developed mathematical
transformations.
1. INTRODUCTION
The limited number of pixels in 2-D digital images that are
captured by digital frame cameras limits their use in large scale
mapping applications. On the other hand, scenes captured from
linear scanners (also called pushbroom scanners or line
cameras) have been introduced for their great potential of
generating ortho-photos and updating map databases (Wang,
1999). The linear scanners with up-to one-meter resolution from
commercial satellites could bring more benefits and even a
challenge to traditional topographic mapping with aerial images
(Fritz, 1995).
Careful sensor modelling has to be adapted in order to achieve
the highest potential accuracy. Rigorous modelling describes the
scene formation as it actually happens, and it has been adopted
in a variety of applications (Lee and Habib, 2002; Habib et al.,
2001; Lee et al., 2000; Wang, 1999; Habib and Beshah, 1998;
McGlone and Mikhail, 1981; Ethridge, 1977).
Alternatively, other approximate models exist such as rational
function model, RFM, direct linear transformation, DLT, self-
calibrating DLT and parallel projection (Fraser et al., 2001; Tao
and Hu, 2001; Dowman and Dolloff, 2000; Ono et al., 1999;
Wang, 1999; Abdel-Aziz and Karara, 1971). Selection of any
approximate model, as an alternative, has to be done based on
the analysis of the achieved accuracy. Among these models,
parallel projection is selected for the analysis. The rationale and
the pre-requisites behind its selection are discussed as well as its
linear and non-linear mathematical forms are presented in
Section 3. But first, background information regarding linear
array scanner scenes is presented in Section 2. In cases where
scanner navigation data are available, Section 4 sets up their
relationship to the parallel projection model. Due to the
complexity of the derivation of the developed transformations,
Section 5 aims at verifying them by using synthetic data.
Finally, Section 6 includes the conclusions and
recommendations for future work.
2. BACKGROUND
2.1 Motivations for using Linear Array Scanners
Two-dimensional digital cameras capture the data using a two-
dimensional CCD array. However, the limited number of pixels
in current digital imaging systems hinders their application
towards extended large scale mapping functions in comparison
with scanned analogue photographs. Increasing the principal
distance of the 2-D digital cameras will increase the ground
resolution, but will decrease the ground coverage. On the other
hand, decreasing the principal distance will increase the ground
coverage at the expense of ground resolution.
One-dimensional digital cameras (linear array scanners) can be
used to obtain large ground coverage and maintain a ground
resolution comparable with scanned analogue photographs.
However, they capture only a one-dimensional image (narrow
strip) per snap shot. Ground coverage is achieved by moving the
scanner (airborne or space borne) and capturing more 1-D
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