Sergey Zheltov 
  
2. PHOTOGRAMMETRIC FOUNDATION OF THE METHOD 
This section is devoted to exploring the stereophotogrammetric possibilities of the method. To estimate accuracy of 
object coordinates determination let us consider the case, when the camera orientation parameters are known. Let us 
introduce an external coordinate system X, Y,Z. The system is selected so that the surface has 2.5D-view Z(X, Y) in some 
neighborhood of the object. By (X, Y, Z;) denote the projection center of the left camera. Designate by a;,b;,c; elements 
of left camera rotation matrix, which is calculated from three rotation angles o5 € K. By (x,y) denote a projection of a 
3D-point to the left image. All variables corresponding to the right camera denote by (*). Thus the relation between 3D- 
scene and image points is given by the following equations: 
a(X-X MAC-FOre-7, (aX TX) Y) 2-2,) 
  
  
  
  
Fzx- =0 F,=v-f ae mr rrr 0 
Si End ire) : a,(X — Y,)*b4(Y -Y,) *c4(Z - Z,) 
Y -XO-MQ-YOote(iZ-Z,; ,a4(QX — Xy) bi -Yy) e c$(Z- Zy 
qm aX Xo) -Yyraz-z)., Emit as ( y)T53Q —Yy)tei 2 o 1) 
aX - Xy) *b;(Y -Yy) te3(Z - Zy) a,(X — Y y)*b5(Y -Y;) *c5(Z -Zy) s 
By B denote a basis of the stereosystem. The following additional condition also used: 
FB -(Q.-X,y-(Q.-Yy -(,-Z,y' 20 (2) 
3D-coordinates of the object are obtained by least square method: 
Ax= “AT (BKB" A] AT(BKB!)'!F, (3) 
where Ax - vector of corrections to some initial approximation of 3D -coordinates x — (X. Y;Z y , A — matrix of partial 
derivatives of functions (1),(2) on object coordinates X, Y, Z; B - partial derivatives matrix of functions (1),(2) on 
elements of observation vector Z — (xy x y Xs Ys Zs 0,0, K Xs, Ys, Zs, 0,0, K,B). K is the covariance matrix of 
observation vector Z , Fo=(F,F, FFF 2)! iS discrepancy vector of functions (1),(2). 
Accuracies of X, Y, Z are determined with the help of covariance matrix of spatial coordinates K,. This matrix is 
defined by following equation: 
K,-[A' (BKB)'A]' (4) 
It diagonal elements are the covariances of defined parameters. 
To simulate the process of spatial coordinates determination the following values of elements of exterior orientation of 
images in the SOXYZ coordinate system (S, - projection of the left origin projection to the horizontal plane) were used: 
Xs 20, Yg,20, Zgz-1m, a-0-K-0, Xs$-1.5m, Y4-0, Z;-1m, d'=œ"=x'=0. The following values of coordinates of 
three points of an object lying on the surface were used: X,2-4.25 m, X,20.75 m, X525.75 m, Y,250 m, Y,-50 m, 
Y;=50m, Z,=0, Z,=0, Z;=0. The following values of interior orientation elements were used: f=f=25 mm. 
Covariance matrix K which is included in (3) and (4), is accepted as diagonal with zero covariance between 
measurements. Mean square errors are accepted as: 
Ox = §, = Oy = GO; = Oy = CONSt, Oy; = Oy = Oy = Oy; = Oy; = Oy, = G, = Const, 
Oc = Oo = Ok = Ou= Ow= Ox= Oangle = const, 
In simulation based on typical Sony CCD camera parameters, the following combinations of errors were used: 
  
1042 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.