265 
Figure 3. The distance from a point to the reference layer 
(4) The distance is calculated from the point to the relative 
local surface of the reference layer along to the normal vector 
of the calculating point (Figure 3). 
According to the calculated results two statistics tables are 
listed in the following. 
Distance 
[unit: mm] 
Scan 1 - Scan 2 
Method 1 
Method 2 
Method 3 
<10 
4357108 
4826722 
6031903 
10-20 
2156554 
1712486 
859421 
20-50 
574553 
549914 
197869 
>50 
6965 
6058 
5987 
Sum. 
7095180 
7095180 
7095180 
Table 1. Overlapping region distance statistics between 
registered Scanl and Scan 2 
Distance 
[unit: mm] 
Scan 2 - Scan 3 
Method 1 
Method 2 
Method 3 
<10 
4959896 
5622448 
7065586 
10-20 
2479985 
1985987 
992843 
20-50 
817398 
649691 
200395 
>50 
8087 
7240 
6542 
Sum. 
8265366 
8265366 
8265366 
Table 2. Overlapping region distance statistics between 
registered Scan2 and Scan 3 
Table 1 shows the results of the overlapping region distance 
statistics between registered Scanl and Scan 2, we found: 
(1) For method 1, over 60 percent of points have less than 
10mm distance, 30 percent of points have distance 
between 10mm to 20mm and less than 10 percent of 
points have more than 20mm distance. 
(2) For method 2, over 68 percent of points have less than 
10mm distance, 24 percent of points have distance 
between 10mm to 20mm and less than 8 percent of points 
have more than 20mm distance. 
(3) For method 3, over 85 percent of points have less than 
10mm distance, 12 percent of points have distance 
between 10mm to 20mm and less than 3 percent of points 
have more than 20mm distance. 
(4) 0.1 percent of points have more than 50mm distance in 
three different registration results. 
Table 2 shows the same results as table 1. 
From the test some conclusions are gotten: 
(1) For the test data method 3 has the best registration result, 
method 1 has the worst registration result, and method 2 
has the intermediate registration result. 
(2) For method 1, because all target-based control points are 
placed on the bottom of the Buddha, it brings on some 
systemic errors and makes the bottom point matching 
accuracy higher than the top. 
(3) For method 2, because transformation parameters are 
calculated from extracted features, to some extent the 
registration result depends on the quality and the quantity 
of the extracted features. 
(4) For method 3, Since ICP requires good initial values, the 
algorithm is often used for a fine registration stage in 
order to improve previous achieved results. Good initial 
values can speed registration procedure and the worse 
initial values results in more search expenses. 
(5) In order to improve the registration accuracy, all the 
points with gross errors should be removed firstly before 
registration. 
(6) Better registration results can be gotten if two or more 
methods are employed in registration procedure. 
5. SUMMARY 
Based on the point clouds captured for YUNGANG Grottoes, 
three registration methods are employed to merge multiple 
scans into a uniform reference datum. By comparing and 
analysing to the three registration results, “Cloud-to-cloud” 
registration is the most suitable method to meet our work in 
standalone use. If combine two registration methods (e.g. 
Populating a survey network with scans and “Cloud-to-cloud” 
registration) in a registration procedure, all the merits of the 
both can be used and better results can be gotten. Moreover, in 
order to connect all the YUNGANG Grottoes a uniform geo- 
referencing datum has been constructed, registration and geo- 
referencing can be done at the same time. 
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