EL OF 
, Parameters 
1eration of digital 
e practical. But at 
|, based on affine 
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any control points 
ljustment with the 
fter the new strict 
nent with the new 
for IKONOS and 
ared with the new 
responding to the 
tellite images are 
(fore, a new strict 
tion, for the high- 
parameters, was 
2002). In this new 
nd one slantwise 
revealed this new 
no less than that 
ustment (Jianging 
order to calculate 
points are needed. 
d in a block. It is 
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based on the new 
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e angle) of each 
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ONOS images has 
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f the images. 
   
     
  
   
    
    
   
   
     
    
  
  
    
    
  
    
   
   
     
   
   
     
    
     
   
   
    
   
   
   
   
   
   
    
     
   
    
  
     
   
   
     
   
      
    
  
  
  
2. BLOCK ADJUSTMENT BASED ON THE NEW 
STRICT GEOMETRIC MODEL 
Jianging Zhang and Zuxun Zhang (2002) have proposed a 
three-step image orientation model for HRSI based on parallel 
projection. In this new strict geometric model, a similarity 
transformation is first employed to reduce 3D object space to 
2D image space, which is then projected to a level plane via 
affine projection, and finally the level image is transformed to 
the actual inclined image. The equation between the image 
coordinates of the point and the terrain coordinates of the points 
is described as the below: 
Z 
mcosa 
f-G-x)tna 
(1) 
(x-xX)-a taX-taY-caZ 
Y=Yo=b,+bX+bY+bZ 
For the purpose of simplification, in the below, x-x, and 
y- y, Will be substituted by x and y respectively. 
This model comprises eight affine transformation parameters 
and one slantwise angle. The influence of the slantwise angle 
can be derived as the below (Fraser, 2003): 
AZ 
AX &g —————— X (2) 
f cosa 
where AZ is the terrain height variation. For IKONOS imagery, 
Fraser pointed out that the influence of the slantwise angle in 
equation (1) could be ignored when the height variations in the 
image is less than or about 500m. But this conclusion is not 
always the truth for other satellite imagery with high resolution. 
In the second test case of this paper, the calculated values of the 
slantwise angles of the satellite images are about 7-8 degree 
and the correction of x coordinates can reach to 9.4 pixels for 
AZ =300 meter. 
If the orientation parameters of the images are all known, the 
terrain coordinates of the tie point in the block can be calculated 
As follows: 
  
  
d T 
(4 P4). X — A' PL (3) 
where: 
[ X | Js; 
qüubdoh da hue BÀ e TUI de 
mcosa,(f — x, tana,) J =x tna, 
b, b, Bi YO 
X fs. 
Us du 4 ee ee 
J fe JS . . jo 
d mcosa (f —x,tana,) f f - x, lane, 
b 5. b y bs 
A A K K 
5 x fX 
Gu Ay a, + —————— dH c Ay 
5 mcosa,(f —x,tana,) f=, ana, 
| nl n2 b x YT bs 
  
  
  
  
The equation (1) is linearized as following error equation: 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXX V, Part B3. Istanbul 2004 
V, =cyda, +c da, +c, da, +c da, +c,da + 
c,dX t c,dY *c,dZ -I, (4) 
v, =d,db, +d\db, +d,db, +d db, + 
d,dX +d;dY+d,dZ —1, 
where: 
Z 
lomo ere ts Yi tl Lot een EEC 
: f-xtana 
l, = -hX-by- b,Z+y (5) 
Le X, 6, =Y, 6 =Z 
d, =L d = X, d, =fY, d,=Z 
Zz 
z : mS EEE 
Zxsina + mcosao 
  
4 = . 2 3 . 2 2 
m(f-xtana)cos «y (f —xtana)' cos? 
X 
  
€5 7 40,,C, —0,,€, 0, o : 
mcosa(f — xtana) 
djmh. db db 
3 
In addition, the control points are also treated as observations 
with appropriate weight. Then the error equations of the block 
adjustment are: 
V, p A A, ; X, i L, [^ (6) 
0 BIN) KFZ 
NS 
In equation (4), X, is the corrections vector of the orientation 
parameters of the images and the unknown terrain coordinates 
and A, is the coefficients matrix of the error equation (2). Y, is 
the corrections vector of the terrain coordinates of the control 
points and. £, is unit matrix. 
In each iterative step, the statistical hypothesis of the 
significance tests for all the slantwise angles of the images is 
executed. Assuming E(q.) = 0, the statistical variable of the t- 
1 
distribution is obtained as follows: 
[= v=n-u (7) 
where , is the mean square error of unit weight, 
ro 
  
obtained from adjustment computations, and its expectation is 
c, q, 13 taken from the corresponding diagonal element of the 
" 
cofactor matrix Q of the unknowns in the adjustment. When 
the significance level is given, then we can find the critical 
value ; from the t-distribution table. If t<1,» then the null 
hypothesis is accepted, which means that the slantwise angle a, 
is not significant and can be eliminated in the next iterative 
adjustment.