The linearized form of equation (1) is: 
-f9 (Xy) f Ay, -f, ATv 
where g,29g?(xy)/8xg , g,=09°(xy)/dyg 
fom of (xy)ox, , f 20f? (xy)/9y, 
Using the notations 
x T=(ATy |, ATy |, ATy ATyg AS4, AS), AR, AR) 
1=19(xy)-g°(xy) 
1 
Aj 2 (fy fy B gy OxXR.GyYR 9xYn: 9yXn)j 
A La i-th row of the design matrix A 
equation (3) result in 
-e(xy)s Ax-1 ; P 
expressed in linearized form as: 
ATy | + (dF /9Z)AZ + FXO) +x,°=0 
ATyı+(9F,Y /9Z)AZ +FLY©® «y,?-0 
ATy g+ (9Fp* 132) AZ « Fg) +xp°=0 
ATy p+ (Fg! /9Z) AZ «Fg! +yp°=0 
  
  
where FX, FY ..... nonlinear collinearity conditions ; i=L, R 
x 9 ,y P ..... initial image coordinates of patch centers 
; i=L,R 
t y 
X.......vector of parameters 
B, .....design matrix of parameters 
| 
equations (9) result in 
B; X li = 0 
Equations (8) and (11) form the joint system 
-e(xy)=Ax-1 ; P 
Bx+t=0 
- 286 - 
  
-e(xy)=0g°(xy) +0, ATy g +9, XgAS +0, YR AR, +9, ATy gp +0, XR AR, +g, YRAS  - 
With the assumption of given interior and exterior orientation and fixed X,Y-object point 
coordinates, the geometric constraints as derived from the collinearity conditions can be 
(3) 
(4a) 
(4b) 
= 
(8) 
(9a) 
  
(12a) 
(12b)