'. Part B3. Istanbul 2004 
respectively, X, Y,Z. The 
covered by the images, 
d coordinate referential 
> 
E 
X 
NA 
Y 
+ 
gi 
E 
Systems. 
ndle of convergent rays 
1metric observations as a 
ht line is defined by the 
ts (both image and object 
nter) The triangulation 
; collinearity equations as 
^hese equations must be 
ont using Least Squares 
ployed to determine the 
the images involved and 
points observed ( Lugnani, 
most precise and flexible 
|, MeGlone 2001). In this 
vations were previously 
he image, as presented in 
ion program developed in 
nbined adjustment method 
weight or position in the 
: formulation: 
(5) 
ljusted; 
rs. 
rs in the coordinates are 
‘erential. 
da, f, (6) 
- da, -Ÿ, (7) 
oma 72. (8) 
Y,) +m, (Z~-Z,) 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
rais my (X =X) +m, (Y =X) +m (Z-Z,) (9) 
Cm (X =X) +m, (Y =Y) +m (Z~Z,) 
  
M - R. (K).R, (Q).R, (d) (10) 
my ms, mp; ( 11 ) 
M=|m,, m, m 
Ha Hu m.s 
m,, = COS P.COS K 
M, = COSO.SENK + SENW.SENGP.COS K 
m,, — sena.senk — cos o.seng.cos k 
My, = —cOs Q.senk 
Hl, — COS QJ.COS K — sena.seng.senk 
Wl, — SenQ. COS K - COS Q.seng.senk 
ms, = senp 
m, =—Senw.cos @ 
H3, — COS. COS 
c = camera constant; 
X,Y,Z= ground coordinates; 
X,,Y,,Z, = ground coordinates of the perspective centre; 
m, 7 elements of the rotation matrix M; 
y 
ór €ór ^ symmetric radial distortion correction; 
x y 
ód €ód. - decentric distortion correction; 
x x 
oa € su = affine deformation correction; 
x Y 
J. ¢ gr, = photogrammetric refraction correction. 
3.4 LIDAR 
The laser profiling system generates a cloud of points 
irregularly distributed on the terrestrial surface. Its three- 
dimensional coordinates in a geodetic system are determined in 
function of the time of emission and return of a laser pulse. 
This process is called Light Detection and Ranging — LIDAR 
(Optech, 2003). A precise laser rangefinder scans the surface 
registering the pulses (distances). To correct the movements of 
the aircraft during the post-processing, the Euler angles 
(x,p,œ ) refering to each distance measured are determined 
through INS, during profiling. The positioning of the aircraft is 
determined by GPS through two receptors, one installed in the 
aircraft and other on the terrain, thus enabling differential 
correction and refinement of the coordinates (F igure 2). During 
the post-processing, the data generated are combined and 
determine the precise position of the ground points. The 
nominal precision of the system is around 15 cm (mean square 
error) for altimetry and around 30 cm for planimetry (Wever 
and Linderberg 1999, Optech 2003). See more details in 
Baltsavias, 1999. 
4. METHODOLOGY 
This research was carried out in two basic stages. The first stage 
verified the positional quality of the Laser Scanner data and the 
second one implemented procedures to carry out the 
triangulation through simultaneous adjustment of images 
(Bundle method), supported by data coming from the Laser 
Scanner. 
ew 
4 
  
Figure 2. LIDAR (Optech 2003). 
4.1 Verification of LIDAR Positional Quality Data 
To verify the positional quality of the Laser Scanner data 
existing in the work area, as reference, it was utilized 8 points, 
positioned by geodetic techniques (GPS and geometric 
leveling), which have planialtimetric coordinates with accuracy 
of few millimeters. These verification points are identifiable 
details in the intensity image generated with data from the Laser 
Scanner. On the terrain, they are concrete marks in the form of 
a pyramidal trunk with dimensions of 20 x 40 cm and 
approximate height of 30 cm in relation to the soil, and are 
distributed all over the test area (they are identified with * in 
Figure 4). The intensity image employed in this research was 
obtained from a regular grid with spacing of 40 cm. The 
intensity image was employed just to obtain the approximate 
coordinates of the points of verification selected. These 
approximate coordinates are input data in the search for the 
non-interpolated coordinates in the original text file proceeding 
from the Laser Scanner. The search process entailed the 
following stages: 
- in the original file, the neighbor points are separated to the 
approximate coordinate within a 1 m radius circle. 
- for the definition of the point coordinate, two criteria must be 
met: firstly, the proximity, and the secondly, the point 
researched must be the point of highest altitude (h). 
From the comparison of the geodetic coordinates of the check 
points and the respectives generated by LIDAR, one has the 
results presented in Table 1. 
The average planimetric discrepancy (dR) obtained in the 
verification conducted between the coordinates of the 
verification points and the ones obtained from LIDAR was of 
0.254 m. The averages resulting in dN, dE show a normal 
distribution of the discrepancies obtained, exempting the data 
from possible systematic errors. The results obtained in the 
altimetry also show a normal distribution in the residues and a 
standard error of 0.109 m. The accuracy results obtained in this 
verification are compatible with the nominal precision offered 
by the manufacturer of the system.