The simulated cameras are defined to be independent 
of each other, i.e. the parameters for each camera can 
be calculated independently. 
3.1 Adjustment of the parameters 
DLT Parameters: Parameters of the linear DLT, case 
A equation (8) and (9), are calculated using adjustment 
of indirect observations of the form [Mikhail 1976]: 
v+BA =f (14) 
where v is the vector of residuals of the measure- 
ments, B is the matrix of parameter coefficients, A is 
the vector of parameter estimates, and f is the vector of 
observations. 
In order to calculate the parameters of the iterative 
DLT, case B, equations (10) and (11) are linearised by a 
Taylor series using only the first order terms. The 
linearized DLT equations look like: 
LT 
+ $= +... 
aea i, 
MO E M (15) 
Ple TX dx + —"dy = 
ôL11 H Ox x dy y 
0 OF, OF, 
F tie, +... 
cn 
Sm dL Sr d Sm dy —0.. (16 
+ == += dx + = 
nn d 5 y (16) 
The parameters are calculated using general least squ- 
are adjustment. Expressing the coefficients of the 
measured image points by matrix A, and the para- 
meter corrections by vector A results in: 
Av + BA =f (17) 
Matrix A and B are based on equations (15) and (16). A 
have the structure: 
Ref (18) 
Tax 
where sub-matrix J,, is the jacobian for image 
measurement of control point i: 
SE, GE. 
öx dy 
0e 
à 
öx Sy 
(19) 
38 
The number of control points is k. Matrix B have the 
structure: 
Jp; 
J 
B=| 12 (20) 
Um 
where the sub-matrix J. is the jacobian of parameters 
for control point i: 
BF, BF, BF, 
SL, So 7 84 
Ji = (21) 
BF, SF, BF, 
dL; OL, - dL; 
Collinearity equation parameters: The unknown 
parameters are calculated by linearization of equations 
(12) and (13) in the same way as for the DLT equations. 
Case C uses nine and case D six unknown parameters, 
see table 2. The resulting equations for nine para- 
meters looks: 
Renee Dw 
+ —dQ + —d® + —dK + 
> Ag 8% ôK 
ôF ôF ôF ôF 
— dX, * — dY, * — dZ, + —dx, + 
dX. dY, oZ. x, P 
Sr d si S ac eve ee z0 (22) 
oy, = Ox dy 7 
0 OF, OF, OF 
— qo. — — qK 
Fo + 35d 307 ak + 
OF, SF, SF, oF, 
— dy —Ó = d 
ES av d taz i s 
Se n, poii on e qf ovium 
oy, tk EC dy y e» 
The system of equations is solved using the general 
case least square in equation (17) where A is identical 
to the jacobian in equation (18) and (19) and B is 
identical to equation (20) but J, is substituted by: 
Fs 8E Fs ôFs 
60 606 ^ 6 oc 
Joi = d (24) 
Fg OF, OF, OF, 
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