For Z=0 condition these equations can be written in general 
form: 
P,X + PY +P, 
9 Q) 
= Ps X + PY + Pi 
Ya Q 
where 0 =P. X + PY +1, and P - (P, ... P.) — parameters 
of perspective transformation. 
In case of external orientation reference coordinates of test field 
and their image coordinates are known. Then unknown 
parameters P, , .., P; could be found by least mean square 
solution from (2), which after multiplying by Q become a linear 
function from P. So the vector of unknowns can be found by 
one step. 
The design matrix has the following form: 
a 0 = 0 -X 0 Yxi XX 
L —1 0 Ey 0 -X Yysi i 
(3) 
The estimation of vector of unknowns P is derived from 
equation: 
— 
A'AP AIL, (4 
T 
where L, =(...~ x, c» 
For determination of initial values for exterior orientation 
parameters the condition of coefficient equality in (1) and (2) at 
each matrix element a; is used. 
After performing necessary calculation matrix A could be 
written in the next form: 
— Paw —Pyw 
A Ls 
f f 
as cf IPS 0 (5) 
y Jf 
P,w Pgw 433 
where w = —(X ja, + Yay + 2003) 
„The values of unknowns w and a;3, a,3 as; are to be found. For 
unknowns determination the condition of equality to 1 for sum 
of squares for each row and each column of matrix A is used, 
because A is rotation matrix. This condition allows to write the 
next system of equations: 
H PA hé |^ 0 0 
w^ f 2 1 
7 b = pip? 0i d Ü (6) 
a 53 f^ 1 
ass Pri o 9 1] i 
0 1 1-1 
from which w and a;;, 275 a5; are found. 
Then angle parameters of exterior orientation are derived from 
equations: 
à — -arctg (a3; / A33) 
Q — -arcsin (a53) (7) 
K = arctg (a;;/ az) 
The initial values for X» Yo Ze are found from system of 
equations: 
w — (X95; * Yod35 * Zod33); 
Py — f(Xoajj + YoA12 + Z0913)/W; 
resulting in: 
x Pow! f 
Y, |=a’| Bw! f (9) 
Zo mM 
Thus initial approximation for camera location Xy, Yo, Zo and 
angle position a, c x are found. 
3.2 Interior parameters estimation 
The plane including 36 reference points is used as a test field, 
the dimensions of the test field being about 1.5 m x 1.8 m. The 
test field provides approximately equal targets density in 
captured images. Reference points are marked with original 
coded targets (Knyaz V., 1998) which provide robust and 
precise reference point coordinate determination in the image 
and reliable recognition of reference point number. 
Using of coded contrast targets as reference points allows 
achieving high degree of automation for interior parameters 
estimation procedure. The only manual part of the procedure is 
assessment of test field respectively camera in required 
position. 
2S0— 
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