ON THE PRINCIPLES AND THE APPROACHES OF IMPLEMENTING THE STRICT DIGITAL GEOMETRIC RECTIFICATION FOR SPOT IMAGERY 
SHU NING 
DEPARTMENT OF PHOTOGRAMMETRY AND REMOTE SENSING 
WUHAN TECHNICAL UNIVERSITY OF SURVEYING AND MAPPING 
WUHAN P.R. CHINA 
COMMISSION II 
ABSTRACT 
This paper presents the theories and the approaches of carrying out the digital geometric rectification for the 
focuses on the mathematical model of calculating the exterior 
SPOT imagery by means of collinearity equations. It 
orientation elements according to the image-forming mechanism of the SPOT imagery, 
the principles of realizing the 
indirect method for the anchor points’ coordinates using the strict formula, and specially, the first employment of 
direct method in digital geometric rectification and its advantages in use. The experiments using SPOT image window in 
Yiyang area and the precision analysis show us that the 
tion are correct and reasonable, 
proposed approaches and key techniques using collinearity equa- 
KEY WORDS, Linear array scanning imagery, Collinearity equations, Rectification for anchor points, Indirect and direct 
methods, 
SPOT images are of the central projection only at 
lines, Each scan line has its own projective center, The 
exterior orientation elements vary with the change of scan 
line number, Therefore, SPOT images are different . from 
aerophotographs in imaging geometry. The collinearity 
equations based on the special geometric nature must be 
taken when using SPOT image for strict rectifications. 
1. The projective deformation due to relief 
The frame size of SPOT image is of generally 150mm 
x150mm which can cover the ground area of 60kmx60km. If 
taking into account a point with the distance to the nadir 
r=75mm, and hight difference h=800m, the estimated projec- 
tive. deformation will be Dh=0.0723 at that point. The 
displacement will be 1.112mm when creating a photomap of 
the scale 1,50000 without geometric processing. It is 
almost 3 times of allowable mapping error. So the projec- 
tive deformation is very distinct, even in the general 
case, The necessity of employing collinearity equations 
can be seen according to the estimation above, 
2. The solution for the exterior orientation 
elements of central line 
2.1 Mathematic model 
One can define the collinearity equations for SPOT 
image as the same formula as that for aerial photographs. 
But the position and the attitude parameters of CCD 
sensor in those equations are not for whole image, but 
only for one line, and x-(, because of the image geometry. 
€ here, x represents the flight direction ) Further more, 
each exterior element must be expressed as that at central 
line added with its change rate per line multiplicated by 
line change number to central line, Thus the unknowns in 
the equations are the exterior orientation elements for 
central line and the change rate of those elements. As 
CCD oblique scanning can be performed by SPOT system, the 
y direction expression in the equations should be written 
as the following formula while considering scanning angle, 
Yi =fx(y xcos@ +fxsin® )/(y xsing -fxcosy ) (D 
where y is the raw image coordinate, 
^ Usually, the SPOT 1A level image, not other level, 
is used in rectification, But the image coordinates (seq- 
uence number of line and column ) should be transformed to 
those of a new coordinate system which origin is the 
32 
center of image. Since earth curveture effects are very 
significant, one has to chose tangent plane coordinate 
system as ground coordinate system, The corresponding 
round point to the center of image must be determined as 
the origin of tangent plane system. 
In order to avoid the strong correlation between 
the Linear and angular elements ( i.e. the position and 
attitude of sensor ), one must calculate them separately 
during the iteration. While computing one type of exterior 
orientation element (the position, for example), the other 
type could be considered as constant(the attitude remained 
unchanged, in this case). This has been proved effective in 
the experiments, 
2.2 Preparation for basic data 
For the solution of exterior orientation elements 
and the estimation of precision, it is needed to select 
sufficient number of control points and check points. The 
importance is the determination of image coordinates with 
subpixel accuracy as much as possible. 
As to the origin of tangent plane system, one can 
firstly fit up a second order of polinomial by means of 
control points, then calculate the ground coordinates (Xc, 
Yc ) for the corresponding point of image center. The 
elevation value of that point could be read from topomap 
according to Xc and Yc. Because the attitude of satellite 
can be read from ^" Leader File " of SPOT CCT tape, the 
equivalent focal length therefore should be evaluated for 
the image of interest, 
The preliminary values of exterior orientation 
elements must be assigned since it is meaningful for the 
rapid convergence of solutions, Generally, the angle ele- 
ments and all the change rate parameters should be zero 
when starting iteration, but the position of sensor must 
be determined using satellite altitude in "Leader File" as 
the preliminary value of Zs for central line, and assig- 
ning the zero-order terms as Xs and Ys after fitting up 
first order polinomial by four control points at the 
corners of image frame, 
3. Indirect approach for anchor point grid 
As each scan line of SPOT image has its own orien- 
tation elements, the line sequence number has to be esti- 
mated firstly for a ground point for which the correspon- 
ding image coordinates should be calculated by means of 
collinearity equations, Therefore, one must fit up second 
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