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