ınbul 2004 
| model is 
the model 
he longest 
9 triangles 
only 6 had 
e ability of 
dinate sys- 
(8 3.2), 5 
sumed then 
53.3). The 
was under- 
eters, then 
e algorithm 
n was mea- 
1sformation 
ormation, 
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The set was 
reater New- 
iter Newcas- 
nce of 0.Im 
ts. A com- 
>d from sur 
0.25m. Only 
yf the set was 
ints, and one 
departure of 
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matched sets 
ng programme 
arse GPS set 
nse data. The 
Il triangles 
t represent ae 
clusters. After 
lise numeric 
resulting in? 
ected tO occ! 
to planimetr 
  
  
International Archives of the Photo grammetry, R 
200 
  
100 4 Lor Ca 
„450 7) 100 
-100 
-200 ^ -200 
-300 
Figure 2: ALS and GPS Data Sets 
errors (Huising and Gomes Pereira, 1998), and the set used 
was part of a much larger set adjusted globally. Moreover, 
the programme matches 5$» on the triangulated model S, 
not on the true surface. The accuracy of the matching to 
the true surface depends on the faithfulness of the model 
to the true surface and is a function of the density of the 
reference surface S, (Páquet, 2003b). The parameters of 
the adjustment are: 
Rotation Angles (degrees): w = 0.0159 
Q = 0.0072 
Ko om -00650 
Translation (m): Ix = 0.0773 
Ty = "0.0031 
Ty = —0.0496 
Scaling: Sod es 0.9999 
It is assumed that the position of S5 after the prepara- 
tion adjustment accurately describes the true surface. No 
checks are available to determine this accuracy. The sole 
measure of precision is that provided by the least squares 
method. The separation between the two surfaces after it- 
eration termination can only be assessed with the residuals 
ofthe least squares adjustment. 
The residuals of the least squares are not directly indica- 
tive of the accuracy of the registration: some of the resid- 
uals occur in the large patches formed by the triangula- 
tion between the six clusters of GPS data. The total num- 
ber of triangles in S, is 1,719. The number of triangles 
With an area under 6m? is 1,569. Their combined sur- 
face area is 28,637m?, which represents 38.3796 of the 
total triangulated area of 74,638m?. The total number of 
residuals obtained in the matching is 14,649 (out of 27,748 
points: see explanation below). Assuming that the small- 
est residuals occur within the smallest triangles, the matrix 
ofresiduals is sorted by size. The 5,620 smallest residuals 
(or 38.37% of the matrix of residuals) have values rang- 
ing from 0.000038m to 0.4918m. The mean and standard 
deviation are respectively 0.2123m and 0.1420m. By con- 
rast, the largest residual in the matrix of residuals has a 
Value of 4.4123m, and the mean and standard deviation 
are 1.1466m and 1.0356m respectively. This assumption 
1175 
emote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004 
is validated in Figure 3(c), which shows residuals of value 
smaller than 0.1 m produced within the six clusters. 
200 - 
150 - 
-50 - 
-100 - 
-150 - 
  
-200 ~ L ! e 1 H t . 
-200 -150 -100 -50 0 50 100 150 200 
(a) Reference Surface S 
200 
150 
50 
-100 - 
-150 
   
-200 
-200 -150 50 100 150 
(b) All Residuals 
    
0.05m 
  
  
-209 1 i 1 
50 
100 
(c) Smaller Residuals 
Figure 3: Configuration and Magnitude of Residuals 
52 has a total area of approximately 149,740m?. The six 
clusters of Sy represent an area of approximately 28,637m? 
or 19.196 ofthe ALS surface. Of the 27,748 points of 5S5, 
only 14,649 were included in the last iteration of the pro-