International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
  
100 : » Ns : x M. i 
  
Y Direction (mm) 
e 
7 
-50 i i sv À 
40022... Me RE a La 
  
  
dd veins i i LEN 
-100 -50 0 50 100 
X Direction (mm) [mens 
-— 1 micron 
Figure 7. The vector plot of the residual errors for the reseau 
grid 
3. COMPUTATION OF THE OBJECT COORDINATE 
The approximate values for the camera orientation parameters 
were calculated using the well known DLT equations given by: 
LX LYALL I+], 
LY vir Zn 
(4) 
LX+LY+l,Z+L, 
LX +L, Y+L,Z+] 
y= 
Where x, y are the image coordinates in comparator coordinate 
system; X,Y, Z are the corresponding object coordinate and 
L1,..., L11 are the DLT coefficients. The approximate values 
for the interior and exterior orientation parameters are given by: 
a U L, t LL. T LL, y 05 + Li de 2) 
Yom Lt Ils tA Mu 2) 
  
  
(5) 
o BRE EB eR 
¢, = (Li + Li + BL + Ly + 1) ~ 33 
c={c. + c,)/2 
Er Lou mV 
| Lt i 5 Ly 
LZ. L, L, L, 1 
w=tan"'(-L,/L,) 
(6) 
a 
9 = sin” C taf 5 + Ly * £ | 
K= cos” (CL, Xs yt Cos Ó- & + L. + Dr ) 
As residual systematic errors inevitably remain in the observed 
data and the conventional approaches for the coordinates 
refinement can not be entirely eliminated, a self calibration 
approach is adopted. 
(X—XMnjit(Y-Yynst(Z-Z yn. 
x» ta, ——C E EE LE ; 
(X - ma + cYymst( -ZYn. (7) 
(X - X,)m, *(Y -Y. m, -(Z —Z,ym,, 
(X X m TO -yun,t-273)m. 
  
  
yy, ta, =< 
sp 
The following additional parameters are implemented for this 
project: 
(a) Brown 1975 additional parameters, given by: 
Ax, =a,x+a,y+ ax’ +a, xy + a)’ + ax y + a, xy’ 
X ? 3 ^ > 
"hr xe ey cy’ he d are xor ey*) 
S 
(8) 
ni x 5 2 A ~ X. o 
+ x(Kr? + Kort + Kr) + p] 3x) Y2p,xy t &, - (—)& 
T rre 
Ay, - bx by bx? * buxy t b, y) buxo yt buxy? 
ya ; 2 2 
(ex -exyey ex tex ytexv toy) 
r 
7 > 2h Y 
+ 2K? + Kort + Kr) + 2p xy + py (x° +337) + &, +(=)de 
(b) Brown 1976 additional parameters, given by: 
Ax, =a x+a,y+axy+ a,y’ +a,x’y+axy’ +a, x’y’ 
X 2 2 2 4 4 
ta (fv Ya x ya (0 oy) 
C 
y > > : 2 (9) 
wh xa, (5° ty y +a, (7 +07) a(x yy ) 
2 2 2 3.2 
Ay, —dXVta4X tax ytaxy HA OX V 
y : 2 
+2 (a; (x -y+a,x’y +a (xt - py? )) 
c 
 y(a (x? ty yaQ xy) +a, (07 + »°)6) 
(c) Ebner 1976 additional parameters given by: 
Ax, =ax+a,y —a,(2x —4r*/3)+ a,xy t a,(y^ — 2171/3) 
(10) 
tax(y! -27 f) 0a y(x - 23/3) +a, (FF -2 ray y! —2r*/3) 
Ay,=-ay+ay+axy-a(2y"- 4r*/3) tax - 2,2 f3) 
7 
N 
tay -27/3) e auxi y? -2rf3)* a,Q -2r!fay y -2r!f3) 
(d) El-Hakim 1977 additional parameters given by: 
Ax, =(x=x,)T 
Ay, =(y-v, I 
T=a 
tar cos A br? sin A ar^ cos34 * b, r^ sin3A --- 
00 * 44, €05 A b, sin AF ar t ar cos^ A b,,r sin 2A (11) 
ry Va 
xx 
À = tan 
(e Moniwa 1977 additional parameters given by: 
Ax, - dr, t dp, * dg, 
Av, = dr, - dp, +dg, 
dr, = (x — WK rE + Kr +Kır“) (12) 
dr, = (y= yp Kr? + Kr + Kr) 
dp, = pr’ + Ua=5Y 1+ 29,0: =x, X13 ~¥%,) 
dp, =p, vrac Aa Sa) 
dg. = A(x— x) 
dg, z B(y— 9) 
    
  
   
     
    
    
   
    
  
   
    
   
    
   
   
    
   
  
    
    
      
   
    
  
   
    
   
    
     
     
     
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Church, VA 
Brown, D.C 
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Remote Sens 
Ebner, H, 19 
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El-Hakim, S 
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