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2.6 Calculated corner coordinates 
Aller (wo lines forming corner are oblained, corner 
coordinate (Xc,yc) can be computed: 
Xc7 ( pj sin 02 - p? sin 01) / sin(05 - 01) 
yc= ( p2 cos 01 - p1 cos 0») /sin(05 - 01) (28) 
where (pj,01) and (p;,02) are the parameters of two 
straight lines. 
3 ACCURACY 
3.1 Internal accuracy 
Standard error of unit weight: 
0g= sqrl[ EVV/(n-4)] (29) 
where n is the number of observed value. 
Inversion of coefficient matrix of normal equation N is 
covariance matrix Q-092N"1. The covariance matrix of 
stright line parameters (p,0) is 
jo 4 
op’qpg 00“900 (30) 
The covariance matrix of two straight lines parameters 
(p, 01) and (pz, 62) 1s 
op^qpipi 01“api61 O 0 
op1’qp161 901790101 0 0 
0 0 ob qpzp2 902^dp262 
0 0 057^q5202 9927790202] (31) 
The derivations can be computed by equation 28: 
dx=FxTdL 
dy-FyldL (32) 
where 
'sin 05/sin (02-01) ] 
-p2 cos 01/sin(02-01)+xc atan(02-01) 
Fx =|-sin 01/sin(02-01) 
P1 cos 69/sin(02-01)-xc atan(02-01) | 
-cos 02/sin(02-01) ] 
-p2 sin 01/sin(02-01)+yc atan(02-61) 
Fy=| cos 01/sin(02-01) 
|p! sin 02/sin(02-01)-xc atan(02-01) | 
  
  
from covariance theorem: 
ox2 =FxI Dp 1 Fx 
oy2=kyl D1] Fy (33) 
oxy -FxlI Dy 1. Fy 
So internal accuracy and error ellipse can be obtained. 
3.2 exlernal accuracy 
If there are various errors in mathematical model. internal 
accuracy is higher than external accuracy. The external 
accuracy should be used in eveluation of location 
method. By comparing the coordinates of location (x.y) 
with rcal coordinates (X53): 
Dx-x -X 
Dy=y:Y 
Mx=sqrt( Z DxDx/n) 
My=sqrt( 2 DyDy/n) 
M = sqri( Mx2+My?) (34) 
where n is the number of samples, statistic results show 
that internal accuracy is almost equal to external accuracy 
in ideal condition (see table 1). 
4 EXPEREMENT RESULTS 
4.1 Relation between accuracy and the points near the 
corner 
The points near corner are used in method 1 and the 
points near corner are not used in method 2. From talbe 1, 
it can be seen that the location precision is higher with 
method 2 and the external accuracy corresponds with the 
internal one. So the points near the corner should be 
rejected. 
4.2 Compared with Forstner method 
Form table 2, the new method's accuracy is higher than 
Forsiner's. In ideal condition, the accuracy of new 
method is about 0.02 pixel size. 
4.3 Sensibility to noise 
From table 3, the accuracy of the new method is smaller 
than 0.1 pixel size, when there are some noises in image. 
4.4 Resuli on real images 
An image whose shape is like chessboard in produced by 
computer. So all intersection points' coordinates are 
known. After taken the photograph, it is digitised with 
25425 pixel size in scanner. Because scanner coordinates 
do not correspond with photo coordinates, we used the 
affine transformation for orientation and distortion 
correction. The new method is used for location, and the 
results see table 4 . 
The table 4 shows that the real accuracy is 0.091 pixel, 
the line's direction is obtained at the same time. 
4.5 Relative orientation 
The new location method and the method of high 
precision least squares maiching are used in relative 
orientation of a urban image (fable 5). Because of the 
influence of urban buildings, the surface is no smooth, 
and only affine transformation is used in the method of 
least squares matching for geometric correction. It can not 
completely compensate the errors. But the problem does 
not exist in the new method, so its accuracy is higher than 
that in the method of least squares matching.