The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
603 
5. EXPERIMENTAL RESULTS 
There is no need to search rotation matrix values for 
a ll R e 50(3) area in laser scanning practice. Most of laser 
3x3 
scanners have a compensatory mechanism which guarantees the 
parallelism of Z axis for all scans. Therefore, we have found 
the correlation function considering rotation of the coordinate 
system of the second scan around Z axis only by angle 
k e (-180°, 180°) with step of 3°. The pre-alignment results 
using orientation histograms are presented on figure 2(B). The 
size of V is limited to 75x75x75 voxels. The size of each scan 
is about 500 000 points. 
6. CONCLUSIONS 
We have presented the fully automated pre-alignment algorithm 
using orientation histograms. The accurate solution of the whole 
problem can be found after applying ICP based algorithm using 
founded initial estimations. Presented algorithm is effective 
even with large initial angles (> 100°) between registered point 
clouds. This algorithm is simple in the implementation. The 
practical tests show robust and reliable results. 
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APPENDIX A 
Lets y and y be the binary voxel presentations of scans 
MxNxK MxNxK 
P x (Xj ,y x ,z 1) and P 2 (jc 2 ,y 2 ,z 2 ) respectively with the same 
angular orientation. Lets 
P x = P 2 + AT , 
(5) 
where 
AT = 
, is a vector that corresponds to the maximum 
of correlation function (4). 
Adds additional zero values to y and y : 
MxNxK MxNxK 
and 
K 
= [V 0 
K 
v 0 ] 
(3M-2)x(3N-2)x(3K-2) 
MxNxK 
V 2 
= [ 
K0 
V 0 ] 
3M-2)x(3N-2)x(3K-2) 
MxNxK 
(6) 
where V n = 0 • 
M-\xN-\xK-\ 
Values of corresponding normalized correlation function G can 
be calculated using (8): 
G = 
> < 8 > 
2M IN 2K M N K 
, ittwj.u-tttwj,*)- 
\ I M j=N l=K i=1 7=1 /=1 
where 
Jft () - discrete forward Fourier transform on R3, 
ifft () - discrete inverse Fourier transform on R3, 
COnj () - function for calculation of complex conjugating 
elements of matrix. 
Accordingly, 
'i 0m -M-2' 
min(x,) N 
min(x 2 )^ 
A T = 
jc„-N-2 
■S v + 
min(y,) 
- 
min(y 2 ) 
min(z,)^ 
,min(z 2 ) y 
where 
(i n , / ~ ,k r )-indices of the maximal element of G, 
V G^ Omax ’ ^max ' 
S v - the size of the voxel side.