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In the iteration routine of the least squares solution, the 
convergence of rotated angles can be set as le-6 (rad) or le-7 
(rad), and the number of iterations may be less than 20. 
4.1 Data Description 
Two typical data sets were selected in this section. The 
scanning data from Hebei and Henan province, China was 
received by an ALS60 (Leica Geosystems) airborne laser 
scanner at 1000 meters above the ground. The Hebei data set is 
an urban scene, including buildings, roads, trees, rivers, etc. 
and the Henan data set is a mountainous area, including 
terraced field, scarps, isolated trees and a few low buildings. 
A 
  
EXE 
Figure 4. Two groups of LiDAR raw data sets: (a)~(b) Hebei 
data set of urban scene, (c)-(d) Henan data set of 
mountainous area. 
i 
  
  
Some other quantitative information of our experiment data 
sets can be seen in table 1. 
Table 1. Properties of the test data sets 
  
  
  
a points number data range overlap points density 
1. 00E+04 (m X m) (3) (points/m2) 
stripl (hebei) 514. 77 1999 X 1549 17 4.12 
strip2(hebei) 477. 12 1997 X 1545 18 4. 30 
strip3(hebei) 498. 10 1999 X 1547 17 3.92 
strip! (henan) 324. 17 1999 X 2515 15 2.11 
strip2(henan) 319. 30 1999 X 2504 14 2.43 
strip3(henan) 309. 46 1999 X 2523 13 2.27 
4.0 Results 
The purpose of this section is to show 2 categories of results 
from our proposed method: profiles registering, estimating 
results and accuracy assessment of unknown parameters. 
Profile results are shown in figure 5. Estimating results of 
unknown parameters are listed in table 2 and the corresponding 
accuracy assessments are in table 3. 
All of the results show that the LS3D proposed in our approach 
can achieve the transform parameters between two overlapping 
surfaces, and the conjugate points rule plays an important role 
in the LS3D procedure. 
5. CONCLUSIONS 
A general mathematical model for co-registration of two 3D 
surfaces is presented. Our proposed method, estimates the 
transformation parameters between reference surface and 
registration surface, using the generalized Gauss Markoff 
model which is a well-known method in geodesy and 
photogrammetry. Our mathematical adjustment model is 
generic to effective conjugate point rules. In this paper, there 
are three definitions of conjugate points presented and 
described. Finally, the LND definition shows the highest 
precision in the experiments of surface matching or strip 
adjustment. 
At last, the derived conclusions may be the following ones. 
Due to the influence of multiple echo points in laser scanner 
data, it is necessary to remove height anomaly points and 
irregular geometric shapes, e.g. tree points, using fast filtering 
technology or rough classification routines. These points 
discussed above can reduce the co-registration accuracy. 
Another important issue is that if there are not enough 
geometric features or enough overlap between conjugate 
surfaces, the iteration will fail. In this case, we can add some 
roof points to strengthen geometric constraints between 
surfaces. 
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