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Sergey Zheltov 
Op =0.008 mm, Op» =0.016 mm, Go3z3 =0.032 mm, Oo4 =0.064 mm, 
Op: =0.001 m, op, =0.002 M, O angle 1 =0.015°, G angle 2 =0.03°, O angle 3 =0.1° 
The results of mathematical simulation have shown, that: 
e convergence of an iterative process is rather high (2-3 iterations); 
e initial approximations for determination X, Y, Z could be rather far from a true value; 
e symmetry of errors is observed, when the points are lying on the equal distances from a central part of the surface; 
e 
more rough of all coordinates the distance Y is determined, its errors are practically not depend on distribution of 
points on the line, perpendicular to axial lines of the surface; 
e measurement errors of basis are in the range from 06g,-20.001m to 055;-0.002m causing practically identical 
influence on accuracy of spatial coordinates determination. 
For various accuracy of images points coordinates o, and various accuracy of exterior orientation angles oy, the 
variance curves of X (Fig.1(a,b)), Y (Fig.1(c)), and Z (Fig.1(d)) are built. 
The variance curves of X determination are given both for object points located on one of the axial lines of the surface 
(Fig.1(a)), and for object points located on an average part of the surface (Fig.1(b)). 
For example, from the figures follows if the accuracy of pixel coordinates is 2 pixels (0520.016mm) and 6 ge =2’, 
then the distance is determined with the error 6y=2m, and object height is determined with the error 6,=0.04m. 
0.12 
  
  
  
   
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
0.8 
0.1 4 
0.08 e n 0.6 
0.06 ec ee eee —— 0.4 
0.04 : - 02 
0.02 
0 0 
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08 
—9$— 0.1 grad —B— 0.03 grad 0.015 grad 0.1 grad 0.03 grad 0.015 grad 
(a) (b) 
8 0.2 
6 0.15 
4 0,1 + 
0.05 + 
2 
0 
0 0 0.02 0.04 0.06 0.08 
0 0.02 0.04 0.06 0.08 —e—0.1 grad —#-0.07 grad 0.05 grad 
——0.1 grad —#—0.07 grad 0.05 grad 0.03 grad —%—0.015 grad 
0.03 grad —— 0.015 grad 
(c) (d) 
Fieure 1. Accuracy of the object 3D-coordinates determination. The horizontal axis on all graphs shows accuracy of 
image coordinates o, (mm) 
(a) Variance curves of X determination in average part of the surface for various accuracy of angular elements of 
images exterior orientation (6,={0.1°,0.03°,0.015°}). The vertical axis shows 6x (m). 
(b) Variance curves of X determination in one of the axial lines of the surface for various accuracy of angular elements 
of images exterior orientation (c,={0.1°,0.03°,0.015° }); The vertical axis shows 0x (m). 
(c) Variance curves of Y determination for various accuracy of angular elements of images exterior orientation 
(c,={0.1°, 0.07°, 0.05°, 0.03°, 0.015°}). The vertical axis shows ox (m). 
(d) Variance curves of Z determination for various accuracy of angular elements of images exterior orientation 
(0, (0.19, 0.075, 0.05?, 0.03*, 0.015? }). The vertical axis shows 0; (m). 
Thus, the results of simulation show that detection ability of the method is 4-8cm on a distance up to 80m, at use Sony 
CCD cameras with a digital format of 640x480 pixels. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 1043