1 registering LiDAR 
nce between image 
en the application of 
cerned, resolution of 
from Sem to several 
figuration of modern 
icing of LiDAR point 
What is the optimal 
registered to LiDAR 
view this problem as 
ywledge, there is no 
'gistration of LiDAR 
ges are as following: 
z to complete in two 
rientation is used to 
t clouds; second, 
register with LiDAR 
ition of registration 
of registration method 
> and multiple frame 
nuously; (4) there is 
RESSION OF 
TIVES 
tives 
ning the LiDAR data 
| also be decomposed 
ction of registration 
ity measurement, the 
nd the strategy for 
remote sensing data's 
tribution and easy to 
ifferent sensor data's 
se, scene changes and 
e used for registration 
ch as forest, lake and 
Goshtasby, 1986) and 
nt of lines intersection 
with large radian(Ali, 
ding ground objects' 
ction lines. 
gistration primitives, 
of discreteness, which 
its. Moreover, linear 
f scalability. Any two 
whole linear feature; 
ransformation model, 
onstrained condition 
ire are various, which 
expressed by any two 
ye expressed by line 
| points from LiDAR 
jle, since LiDAR data 
discrete return echoes 
e values. Therefore, it 
DAR data and image 
n primitives. Though 
egistration primitives, 
  
the extraction of them is not an easy task neither from imagery 
nor from point clouds. So straight lines are chosen as the 
registration primitives in our algorithm especially in urban area 
22 The Extraction of Linear Primitives 
In our procedure, we use accurate lines as the registration 
primitives in our transformation function. Bearing this in mind 
and considering the line extraction strategies mentioned above, 
we propose a new algorithm which is based on the fact that 
many sidewalls of buildings could reflect laser pulses, since 
most of time the data acquisition scanning angle is not zero 
degree. So many laser echoes are reflected from the sidewalls of 
the buildings (Fig. 1) .From above, we proposed a so-called 
Differential Volume Statistics Method (DVSM) method to 
extract precise linear features, which makes use of the property 
that the density of point clouds increases dramatically in the 
vicinity of edge lines (Fig.2) (Ma, 2010) . 
  
Figure 1: extraction of linear features. The red ones are the ideal 
linear features 
The details of DVSM are as following: 
(1) Firstly, use the progressive TIN filtering method to 
get the ground points and grid DEM; 
(2) Secondly, using Gradient operator to detecte edges as 
the initial Linear features from depth-image which is 
generated from the LiDAR points by height ; 
(3) Scanning the initial linear features, project the current 
line onto the DEM, then the feature plane is formed 
whose normal vector is  ,as shown in figure 3. 
     
Figure2- The side wall of the building - 
A 
te 
Figure3- The formulation of the feature voxel 
(4) The feature plane move a tiny distance dn in the 
direction of the vector "? , then the feature voxel dv is 
generated. 
(5) Counting the point number N in dv, if N>T, turn to 
(6),or else turn to (3); 
(6) Sort the laser points by Z values. Define P is the point 
with median Z value, then search point Q that meet 
the following two conditions: (a) zZ, — Zz] «bh un (0 
make sure the point Q is also in the wall area;(b) 
D= x md, «|x, - y » D ,where h 
  
mééthoit AS the 
elevation difference threshold, D is the distance 
threshold in the x-y plane,in order to make sure that 
the point P and Q are not very close. (c)Z values of 
the point P and Q can be interpolated using the 
corresponding original linear feature, and turn to (3) 
unless all the original linear features have been 
analysised.; 
(7 Output all the linear features which can be used as 
registration primitives. 
2.3 Registration Primitives’ Expression 
si s2 
  
A 
TB 
Figure 4. The line AB on the LiDAR point data and the 
corresponding points in the image space 
Firstly, take line AB (Figure.5) extracted from LiDAR points 
data as a line in object space. As points data is three- 
dimensional data, AB is three-dimensional line. P, a point in AB, 
has a correspondent corresponding image point P'in image. 
A , an unknown parameter, is introduced. So P’s true value 
coordinate can be expressed by coordinates of A and B, as well 
as 4, tobe[X ¥ Zr as shown by formula (1): 
p?^p? 
X, X X AM, 
y [ex ay e 
Z, Z Z2. 
Where, 
(X,,Y,Z,) is the three-dimensional coordinate of A 
point in line in LiDAR space; 
(X, 1.2.) is the three-dimensional coordinate of A 
point in line in LiDAR space’ 
Since this P point should be a corresponding point P' in image 
space (assumed not in the occluded area), ( Y.2) can be 
considered as the corresponding point of P in LiDAR points 
space. Different parameters À, correspond to a series of such 
corresponding points. It can be seen that P can be expressed by 
line AB and parameter A, , without seeking corresponding 
points in LiDAR data, therefore, it overcomes the difficulty of 
selecting tie points in LiDAR points data. 
3. THE REGISTRATION MODEL BASED ON 
COLLINEARITY EQUATION 
LiDAR points are taken as images' object space, by collinearity 
equation (Wang Zhizhuo,1979), principal point of photograph, 
image point and object space point are in the same line, being 
expressed to be mathematical equation shown as formula (2): 
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