ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS’’, Bangkok, May 23-25, 2001 
288 
Polynomial function was applied for all data. 
Model of relationship between x,y,v,u and x,y,z,u were 
generated. 
Based on the model, comparing between calculated data 
and referenced data were pursued by considering E value, 
and then defined the best-fit polynomial function for data. 
Accuracy of data can be defined as E value. 
4.ACCURACY ASSESSMENT OF POLYNOMIAL DATA 
As it can be observed (as Figure 2), the buildings can in 
principal be reconstructed. Obviously the procedures to extract 
all these features were very demanding. In stead of automatic 
extraction, using the manual extraction of control points (x,y,z) of 
the picture was undertaken, then linked those data with picture’s 
column and row respectively. The height (z) of buildings can be 
defined with its difference physically and obviously. All works 
were being run under manual measurement with approximated 
value. Then, the polynomial function was setup and taken as 
linkage among x, y, z, u(column) and row(v) (as in Table 1) and 
also compared their calculated values with referenced control 
points. Finally the accuracy was resulted in E value format. 
Laser data (x,y,z) Aerial photograph data (u,v) 
Figure 2. Laser data and photograph of study area. 
It was twenty-four control points extracted manually from both 
laser data and corresponding point in photograph. 
Table 1. Input data, 24 control points 
Coordinate 
of X 
Coordinate 
of Y 
Coordinate 
of Z 
Coordinate 
of U 
Coordinate 
of V 
25 
51 
144 
30 
48 
118 
13 
103 
127 
8 
97 
16 
136 
102 
14 
86 
28 
144 
93 
25 
117 
85 
115 
127 
80 
49 
63 
160 
53 
59 
55 
63 
160 
61 
58 
55 
68 
160 
61 
65 
49 
68 
156 
53 
65 
67 
63 
173 
71 
59 
74 
63 
165 
80 
59 
74 
68 
160 
80 
65 
67 
68 
160 
72 
64 
7 
15 
90 
10 
11 
6 
58 
115 
6 
56 
42 
66 
70 
47 
62 
42 
60 
132 
47 
76 
56 
79 
140 
61 
76 
56 
74 
148 
61 
71 
28 
32 
123 
34 
30 
42 
32 
119 
46 
30 
42 
39 
119 
46 
36 
28 
39 
107 
34 
36 
48 
22 
144 
53 
20 
4.1 Altimétrie accuracy based on polynomial function of 
x,y,z,u 
best value of E in each boundary of data, which started from 8 
until 24 control points. 
Table 2. Result of altimétrie accuracy, based on x,y,z,u 
Calculated 
value - E 
CT point No. 
Number of 
CT 
Combinations 
0.924191 
1234567 
8 
8 
0.989992 
0123458 
9 
36 
0.994972 
0123459 
10 
100 
0.995255 
0 1 2345 10 
11 
253 
0.995412 
0 1 2348 11 
12 
595 
0.997793 
1 34589 12 
13 
1290 
0.997793 
1 34589 12 
14 
2601 
0.997793 
1 34589 12 
15 
4932 
0.998318 
1 359 12 13 15 
16 
8856 
0 998412 
1 3 10 11 13 15 16 
17 
15182 
0.998432 
1 3 10 11 13 15 17 
18 
25028 
0.998451 
1 3 10 11 15 17 18 
19 
39907 
0.998451 
1 3 10 11 15 17 18 
20 
61822 
0.998451 
1 3 10 11 15 17 18 
21 
93367 
0.998451 
1 3 10 11 15 17 18 
22 
137845 
0.998451 
1 31011 1517 18 
23 
199390 
0.998480 
1 3 11 13 15 1623 
24 
282133 
The E value was going up near to 1, when a number of control 
points were increased. This situation indirectly showed that the 
accuracy was also improved by this increasing, even more 
combinations. In addition, the changing of E value can be seen 
clearly in the form of line graph (as in Figure 3). 
0.08 
0.06 
0.04 
0.02 
0 
-0.02 
-0.04 
Calculated 
value - E (+ 
• % of changes (x 
100) 
! 
Figure 3. (a) the deviation of E value of relationship model of 
x,y,z,u (b) the corresponding relative changes of E value. 
It was E curve moving clearly up at the beginning (by 8 control 
points). Then, at nine control points, it appeared a little bit 
changes until almost certain at ten control points onward. 
According to this result, ten control points were enough for 
generating 3D building objects under the accuracy of 0.99 (E) in 
terms of altimetric accuracy. 
The height accuracy of the laser measurements was strongly 
related to the building geometry. A suitable polynomial function 
was derived to fit the position of x,y,z,u through a least squares 
solution, and then E values can be generated and also ranked 
up to highest value accompanied with chosen control points (as 
in Table 2). The process of computation was set to find out the 
4.2 Planimetric Accuracy based on Polynomial Function of 
x,y,v,u 
The accuracy in x,y and v,u of laser measurement and 
photograph were computed by identifying the same points in the 
laser data and in photograph data. And then the polynomial 
model was applied for this data, as well as the previous method