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EXTERIOR ORIENTATION IMPROVED BY THE COPLANARITY EQUATION 
AND DEM GENERATION FOR CARTOSAT-1 
Pantelis Michalis and Ian Dowman 
Department of Civil, Environmental and Geomatic Engineering, University College London, Gower Street, 
London WC1E6BT, UK 
[pmike,idowman]@ge.ucl.ac.uk 
Commission I 
KEYWORDS: rigorous model, rational polynomials, collinearity, coplanarity, along track satellite imagery, DEM, 
ABSTRACT: 
In this paper the sensor model evaluation and DEM generation for CARTOSAT-1 pan stereo data is described. The model is 
tested on CARTOSAT-1 data provided under the ISPRS-ISRO Cartosat-1 Scientific Assessment Programme (C-SAP). The 
data has been evaluated using the along track model which is developed in UCL, and the Rational Polynomials Coefficient 
model (RPCs) model which is included in Erdas Photogrammetry Suite (EPS). A DEM is generated in EPS. However, the 
most important progress that is represented in this paper is the use of the Coplanarity Equation based on the UCL sensor 
model where the velocity and the rotation angles are not constant. The importance of coplanarity equation is analyzed in the 
sensor modelling procedure and in DEM generation process. 
1. INTRODUCTION 
CARTOSAT-1 represents the third generation of Indian 
remote sensing satellites. The main improvement from the 
instrument point of view is the two panchromatic cameras 
pointing to the earth with different angles of view. The first 
one is looking at +26 deg. of nadir while the second one at -5 
deg. of nadir, giving the ability of collecting along track 
stereo images. 
In this paper, the rigorous sensor model developed in UCL 
and the RPCs model included on the Erdas Photogrammetry 
Suite (EPS) are used to evaluate Cartosat images along with 
DEM generation on EPS. However, the most important 
progress that is represented in this paper is the use of the 
Coplanarity Equation based on the UCL sensor model where 
the velocity and the rotation angles are not constant. The 
importance of the coplanarity equation is analyzed and 
evaluated in the sensor modelling procedure and in the DEM 
generation process. 
2. BACKGROUND 
A pushbroom image consists of sequence of ffamelets which 
are independent one-dimensional images with their own 
exterior orientation parameters, as the scanning effect of line 
CCD scanner on the ground is due to the motion of the 
satellite. In general, the pushbroom sensor model can be seen 
as a sophisticated model, which should simulate 
simultaneously the along track motion, that is closely related 
to the satellite trajectory and the across track perspective 
projection of the ffamelets. The main drawback of this 
approach is that the exterior orientation parameters of 
neighbouring framelets are highly correlated. 
The across track perspective could be represented with the 
well known collinearity equations which should be modified 
in a way that the satellite orbit is taken into consideration. 
The way that the satellite motion is represented leads to 
different sensor models. It is possible to have an even more 
correlated model in the case that more parameters are used in 
this procedure, than are really needed. 
Moreover, especially for the along track stereo images it 
sounds very attractive to establish the coplanarity equation 
which could relate conjugate points of images. The coplanarity 
equation establishes a geometric condition along the track 
which can improve the stability of the orientation and the 
accuracy of the DEM generation as the x-parallax is at this 
direction (along track). 
Kim (Kim, 2000) investigates the epipolar geometry of 
pushbroom images based on Gugan and Dowman model 
(Gugan and Dowman, 1988). In this model the position and 
kappa rotations are described by second order polynomials 
while the omega and phi rotations are constant. It is reported 
that the coplanarity in pushbroom is different than in frame 
cameras represented by epipolar curves instead of lines. 
However the most important conclusion is that for any two 
conjugate points the epipolar curves are different from each 
other, as the coefficients of the coplanarity equation that was 
developed are varied for each point. 
Habib (Habib et al., 2005) represents a comprehensive analysis 
of the epipolar geometry for pushbroom scanners moving with 
constant velocity and attitude trying to produce epipolar lines 
(not curves) and normalized images. It is confirmed that for a 
given point in the left image, there will be multiple epipolar 
planes in the right image. It is mentioned that the key 
difference between frame and line cameras is that the base 
vector will change as the scanner moves along its trajectory. 
Finally, it is concluded that even in that simplified case 
(constant velocity and attitude) the production of normalized 
images are not feasible without having a DEM since the 
normalized and original images do not share the same exposure 
station.