65
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
The calculation formula of the parameter sin (p can be
analyzed with the following Figure 2:
Figure.2 The triangulation relationship for the bearing of
radicalization distance of photo nadir point (p
sin (p =| COS /? 1=1
T,Oi-■*„) +TdT-T,)
\l x n 2 +y n 2 •>/(*! -*„) +(y, - y„ f
With the help of the spin matrix relationship, we can get the
formula: COS CC = C 3 , so,
buildings are same, so the height of the top point can be
calculated with the formula: Z' = Z + Ah (Z is the height of
the bottom point), then we can get the three-dimensional
coordinates of the top point.
4. EXPERIMENT RESULTS
In the experiments, the scale of the image is: 1/3750, the focus
is 152.908mm, collimating marks distance is 212mm, the flying
height is about 575m, the exterior parameters are :
X s =511826.68
Y s = 4145628.60
Z s = 572.793(unit:meter),
a x =0.00194005
co = 0.007211
K — -0.0646547 (uinitradian).
I — I T , The partial experiment results are listed in the table. 1 and table
sin2a = 2sina • cosa = 2cosav 1 - cos 2 a = 2C 3 y 1 - C 3 (sina >0) 1 * ie
coordinates X and Y of the bottom and top point of the
Index
Height
Projection
error
Radiation
distance
Horizontal
Error 1
Titled 1
Error 2
Titled 2
Error 3
1
18.74
0.3053
10.8696
15.9327
-2.8073
15.9384
-2.8016
15.9383
-2.8017
2
19.35
1.6049
48.7857
18.6603
-0.6897
18.6973
-0.6527
18.6961
-0.6539
3
2.35
0.3322
84.0154
2.2260
-0.124
2.2282
-0.1218
2.2281
-0.1219
4
17.13
2.7183
89.1277
17.3172
0.1872
17.3913
0.2613
17.3891
0.2591
5
21.87
3.3841
89.1363
21.5578
-0.3122
21.6168
-0.2532
21.6146
-0.1554
6
49.40
9.7975
112.9627
49.2436
-0.1564
49.4334
0.0334
49.5169
0.1169
7
17.27
3.5224
115.1690
17.3675
0.0975
17.4651
0.1951
17.4621
0.1921
8
17.27
3.8548
127.0017
17.2349
-0.0351
17.3425
0.0725
17.3392
0.1692
9
19.35
2.3895
71.5043
18.9543
-0.3957
19.0071
-0.3429
19.0054
-0.3446
10
2.55
0.3322
84.0154
2.3260
-0.224
2.3282
-0.2218
2.3281
-0.1219
11
17.13
2.7183
89.1277
17.3172
0.1872
17.3913
0.2613
17.3891
0.2591
12
21.87
3.3841
89.1363
21.5578
-0.3122
21.6168
-0.2532
21.6146
-0.1554
13
17.13
2.7289
89.8093
17.2527
0.1227
17.3272
0.1972
17.3249
0.1949
14
49.40
9.7975
112.9627
49.2436
-0.1564
49.4334
0.0334
49.5169
0.1169
15
49.40
9.8528
113.8897
49.1183
-0.2817
49.3103
-0.0897
49.2936
-0.1064
16
17.13
3.5939
117.5893
17.3556
0.2256
17.4553
0.3253
. 17.4523
0.3223
Table. 1 The experiment results when we consider the nadir point is the principal point of photograph
Index
Height
Projection
error
Radiation
distance
Horizontal
Error 1
Titled 1
Error 2
Titled 2
Error 3
1
18.74
0.3060
10.9174
15.8967
-2.8433
15.8975
-2.8425
15.8974
-2.8426
2
18.74
0.5658
18.2346
17.6014
-1.1386
17.6162
-1.1238
17.6158
-1.1242
3
18.74
0.7428
24.0134
17.5466
-1.1934
17.5635
-1.1765
17.5630
-1.1770
4
18.74
0.9623
30.7724
17.7387
-1.0013
17.7578
-0.9822
17.7572
-0.9828
5
18.74
1.3299
41.5118
18.1724
-0.5676
18.1973
-0.5427
18.1965
-0.5435
6
19.35
1.6052
49.8017
18.2821
-1.0679
18.3220
-1.028
18.3207
-1.0293
7
18.74
1.6823
52.2102
18.2772
-0.4628
18.3023
-0.4377
18.3015
-0.4385
8
19.35
2.2913
69.5359
18.6897
-0.6603
18.7332
-0.6168
18.7318
-0.6182
9
19.35
2.3896
72.2990
18.7466
-0.6034
18.7932
-0.5568
18.7916
-0.5584
10
2.35
0.3323
84.0363
2.2416
-0.1084
2.2462
-0.1038
2.2461
-0.1039
11
21.87
3.3596
86.0195
22.1772
0.3072
22.2569
0.3869
22.2538
0.3838
12
17.13
2.7289
89.8093
17.2527
0.1227
17.3272
0.1972
17.3249
0.1949
13
49.40
9.8530
113.2326
49.4045
0.0045
49.5617
0.1617
49.5480
0.1480
14
17.27
3.5225
116.2019
17.2136
-0.0564
17.3026
0.0326
17.2999
0.0299
15
17.13
3.5939
118.6099 1
17.2063
0.0763
17.2962
0.1662
17.6934
0.1634
16
17.27
3.8548
128.0410
17.0951
-0.1749
17.1932
-0.0768
17.1902
-0.0798
Table.2 The experiment results for the nadir point
