Int 
height of approximately 750 meters, resulting in a spatial 
resolution on the terrain of 0.25 meters. 
3. BACKGROUND 
Non-metric digital cameras are not provided with fiducial 
marks, which allow the recovery of the projective geometry. 
Having the need of a reference system to recover the geometry 
through a procedure of camera calibration, an intermediary 
referential, called image referential for the referencing of 
photogrammetric observations conducted on the image, was 
utilized in this research. The referentials of image space and 
object space employed in this work are: 
3.1 Reference System in the Image Space 
- Digital System (x",y") defined as a two-dimensional 
rectangular system, left-handed system, with the origin at the 
image's left top corner, being x" coincident with the first line 
and ," coincident with the first column; 
- [mage System (y, y) is two-dimensional rectangular system 
coordinates with the origin in image's geometric center, right- 
handed system. 
The two systems are assumed as being parallel. The 
transformation between digital and image systems can be done 
using the following equations (Jain et al. 1995): 
  
voco x (1) 
2 
ADEL n Q) 
= 3 ; 
x", y" 7 coordinates in the digital system; 
x, y = coordinates in the image system; 
Col = image’s number of columns; 
Row = image’s number of rows; 
- the system of photogrammetric coordinates (x', y',c)» the 
photo coordinate system is a three-dimensional, rectangular, 
right-handed system with its origin at the perspective center and 
by definition parallel to image’s referential (Merchant 1988). 
Knowing the coordinates of the principal point in the image’s 
referential (x, y,)> the transformation from one system into 
another takes place through, a simple translation in the plan, as 
presented in equations 3 and 4. 
X=y-—x, (3) 
y-y-» (n 
S photogrammetric coordinates; 
XM principal point coordinates (image system). 
3.2 Reference System in Space Object 
The reference system for the space object, adopted for the 
present work, consists of a hybrid system in which the geodetic 
coordinates in the UTM projection system and SAD69 
reference system (E,N) and the orthometric height (h), were 
ernational Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Ista! 
ibul 2004 
equaled to the rectangular coordinates, respectively, X, Y,Z. The 
small area of approximately 2 km?, covered by the images, 
enabled the utilization of this hybrid coordinate referential 
without damage to the accuracy. 
CEN 
Figure 1. Reference Systems. 
2.3 Bundle Method 
The block triangulation through bundle of convergent rays 
(bundle method) considers photogrammetric observations as a 
bundle of straight lines. Each straight line is defined by the 
condition of collinearity of three points (both image and object 
spaces points, and perspective center). The triangulation 
through bundle adjustment (BA) uses collinearity equations as 
fundamental mathematical model. These equations must be 
linearized to perform the adjustment using Least Squares 
Adjustment — LSA. Which is employed to determine the 
parameters of exterior orientation of the images involved and 
the coordinates of photogrammetric points observed ( Lugnani, 
1988). It can considered to be the most precise and flexible 
triangulation method (Mikkail, Bethel, McGlone 2001). In this 
paper, the photogrammetric observations were previously 
corrected from systematic errors of the image, as presented in 
equations 6 and 7. The aerotriangulation program developed in 
MATLAB (BundleH) employed Combined adjustment method 
(Gemael 1994) with constraints of weight or position in the 
control points. Here follows the basic formulation: 
F(La, Xa) « 0 (5) 
La = vector of the observed values adjusted; 
Xa = vector of the adjusted parameters. 
The components of systematic errors in the coordinates are 
calculated in the photogrammetric referential. 
x'=x- No ri or, = ód. ox oa, = J (6) 
y = y ES Yo FE or, = od zT óa US of, u) 
Si mx — Xm {Y- Y+m(Z-2,) (8) 
  
c mj (X — X,)o my (Y - Y) e mys(Z - Z5) 
     
   
     
  
   
  
  
  
  
  
  
  
  
    
  
  
   
  
   
   
  
   
    
   
   
  
  
  
   
   
  
    
   
  
    
    
   
   
   
  
  
  
     
    
  
   
    
    
  
  
   
  
    
International Archi 
paco Phi 
epa Hi 
M 
My =C 
m, =C 
nya =S 
m, =- 
My =C 
My =S 
m,, — St 
By -— 
Ma = Ct 
¢ = camera constan 
X,Y, z= ground coc 
XN ground 
m, elements of th 
e e symmetric 
Xd © öd = decentri 
da, © a, = affine de 
g.e d = photogram 
3.4 LIDAR 
The laser profiling 
irregularly distribut 
dimensional coordin 
function of the time 
This process is call 
(Optech, 2003). A 
registering the pulse 
the aircraft during 
(x, o, c) refering tc 
through INS, during 
determined by GPS 
aircraft and other « 
correction and refine 
the post-processing, 
determine the preci 
nominal precision of 
error) for altimetry 
and Linderberg 19¢ 
Baltsavias, 1999. 
This research was ca 
verified the positiona 
second one imple 
triangulation throug