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International Journal of Advanced Network, Monitoring and Controls          Volume 04, No.01, 2019 
48 
Rotation center calibration based on  
line laser rotating platform 
Lei Doudou 
School of Computer Science and Engineering 
Xi’an Technological University  
Xi’an, 710032, China 
e-mail: ccdd007123@qq.com 
Liu Baolong 
School of Computer Science and Engineering 
Xi’an Technological University  
Xi’an,710032 China 
e-mail: liu.bao.long@hotmail.com 
 
Yao Huimin 
Eighth of production plant, the company china 
petrdeum, Changqing oilfield, Xi’an 
Xi’an, 710021, China 
 
 
 
 
 
 
 
 
 
 
 
Abstract—Line lasers are of great significance in many 
fields such as industrial inspection, machine vision, 
cultural relics identification, mechanical design, and 
medical oral cavity. The three-dimensional 
reconstruction of the line laser can accurately obtain the 
three-dimensional information of the surface of the 
object, and quickly complete the three-dimensional 
contour reconstruction of the object to be tested. In the 
online laser rotation scanning, the object rotates around 
a certain point, which is a rotation center, and the 
calibration of the rotation center is the main factor that 
restricts the accuracy of the three-dimensional contour. 
At present, the calibration of the center of rotation is 
mainly obtained by the characteristics of a circle (ball, 
cylinder, cone, etc.). This paper mainly introduces the 
basic process of rotating scanning, rotating center, and 
rotating methods as well as their advantages and 
disadvantages. First, the basic process of rotating 
scanning is briefly introduced. Secondly, the definition 
and content of the rotating center are introduced. Then, 
the calibration methods of three rotating centers (ellipse 
fitting method, symmetry method, plane fitting method) 
are introduced. Finally, the advantages and 
disadvantages of the three calibration methods and their 
respective applications are summarized. 
Keywords-Line laser; rotary scanning; Rotation center; 
calibration 
I. INTRODUCTION  
In today's life, two-dimensional information can no 
longer meet people's daily needs. The three-
dimensional information has thus been deeply 
researched and developed. Among them, the line laser 
is widely used in the three-dimensional reconstruction 
process. Line laser three-dimensional scanning is to 
project one or more line lasers to the measured object, 
extract the laser stripe in the image, and calculate the 
three-dimensional data of the surface of the laser line, 
usually using high-precision three-coordinate, rotating 
platform or camera alignment The laser sensor 
performs positioning to complete three-dimensional 
scanning of the surface of the object to be measured, 
and obtain surface data of the three-dimensional 
object[1][2]. 
According to the different mechanical displacement 
platforms, mechanical scanning mainly has two 
implementations of translation platform and rotary 
platform. Rotating scanning is more convenient and 
faster. A more accurate rotation center calibration can 
improve the accuracy of point cloud reconstruction and 
improve the 3D contour reconstruction of the measured 
object. 
The reconstruction of the rotating platform can be 
divided into three types according to the different 
movement modes: the first is that the camera rotates 
around the rotating axis [3], and the measured object 
does not move; the second is that the camera does not 
move, and the object rotates with the rotating platform 
[4] The third is that the camera and the object are 
combined and rotated at the same time[5]. 
The rotating platform is suitable for scanning 
objects with swivel features. The object is placed on a 
rotating platform for linear laser rotation scanning. At 
DOI: 10.21307/ijanmc-2019-033
International Journal of Advanced Network, Monitoring and Controls          Volume 04, No.01, 2019 
49 
this time, the visible object is rigidly transformed 
around the axis of the rotating platform [6], and the left 
and right camera point clouds can be constructed by 
using the rotation center and the rotation angle obtained 
after the platform calibration process. The rotation 
matrix between the two, the rotation matrix is 
multiplied by the current point cloud, the point cloud 
obtained by the left and right cameras can be registered 
to the same coordinate system, thereby realizing the 
automatic registration of the point cloud on the surface 
of the rotating platform [7]. 
II. CAMERA CALIBRATION 
Calibration is simply a matter of establishing a 
reference point between a pixel coordinate system of an 
image and a world three-dimensional coordinate 
system. The essence of the transformation relationship 
is the geometric principle of camera imaging. The 
ultimate goal of calibration is to obtain the camera's 
internal parameters as well as external parameters. The 
internal parameters of the camera are determined by the 
camera's own characteristics. The external parameters 
of the camera are used to establish the mutual 
conversion relationship between the local world 
coordinate system and the camera coordinate system in 
the actual process [8][9]. The camera's parameters have 
a direct impact on the accuracy of the reconstructed 
model, so the accuracy of the camera parameters is 
very important. In general, camera calibration is 
required before solving the center of rotation. 
III. ROTATION CENTER CALIBRATION 
Because the line laser scans once, it can only 
measure the surface of the object to be measured at a 
given angle of view. If you want to measure the 
contour of an object for a week, you can measure it by 
rotation, measure the object from multiple angles of 
view, and point cloud data from multiple angles of 
view. Spliced in the same coordinate system. 
Accurately calibrating the center of the turntable 
(rotation center) is the key to rotating measurements 
and multi-view assembly. 
Rotation Center: In a plane, a figure rotates a certain 
angle around a point O to get the other figure to change 
into rotation, and point O is the center of rotation. 
During the rotational scanning, the measured object 
starts from a fixed angle and starts to rotate 360 
degrees around the axis of rotation or the center of 
rotation. However, the center of rotation of the rotating 
platform is unknown. In order to obtain the three-
dimensional contour of the rotating object, it is 
necessary to obtain the rotation center of the rotating 
platform by means of a calibration block or a pasting 
marker point. After the center of rotation is obtained, 
the subsequent rotation and splicing can be performed. 
Since the subsequent splicing work is spliced according 
to the position of the center of rotation, the extraction 
work of the center of rotation is very important. 
The schematic diagram of the line laser double 
triangle rotation scan is shown in the figure below, 
where the center of rotation is the center of the stage. 
 
  Laser Right 
camera
Left 
camera
objectiv
e table
Rotating 
platform
rotation 
direction
 
Figure 1.  Schematic diagram of line laser double triangle rotation 
scanning 
IV. ROTATION CENTER CALIBRATION METHOD 
A. Ellipse fitting method 
The center of rotation can also be obtained by 
dividing the plane edge of the rotating platform in the 
left and right images, and then performing ellipse 
fitting on the obtained plane edge, and obtaining the 
center coordinates of the ellipse by the least squares 
fitting method. It is the center of rotation of the rotating 
platform [10]. 
x
y
F
L1 L2O
 
Figure 2.  Ellipse Fitting 
International Journal of Advanced Network, Monitoring and Controls          Volume 04, No.01, 2019 
50 
As shown in Figure 2 above, Point ),( yxF  is a 
point on the ellipse, and the focus of the ellipse is 
),(
111
yxL  and ),( 222 yxL . 
 
cOLOL 2
21
  
Since the sum of the distances from any point on the 
ellipse to the two focal points is a constant 2a, there is 
an error between the sum of the actual distances, and 
the error is θ. As shown in the following formula (2): 
  aFLFL 2
21
 
The above formula (2) is specifically expanded as 
follows: 
 ayyxxyyxx 2)()( 2
2
2
2
2
1
2
1
）（）（  
Using the above formula, the point cloud of the 
elliptical edge can be fitted by the least squares method, 
and the estimated values of the five parameters are 
obtained, and then linearized and solved iteratively. 
The criteria for the iterative solution process are: 
It is necessary to eliminate the edge point cloud data 
whose absolute value of the error θ is greater than or 
equal to 2.6β after each ellipse fitting. (β: standard 
error of unit weight after each iterative fitting) 
Between two adjacent iterative fittings, the absolute 
value of the distance of any elliptical focus position 
must be less than a certain pixel value (typically 0.001 
pixels). If it is greater than or equal to this pixel, the 
iteration will end immediately. 
In the formula (3), the order: 
 21
'2
1
'
1
)( yyxxl  ）（  
 22
'2
2
'
2
)( yyxxl  ）（  
Let 1FL ， 2FL  be partial to 1x ， 2x ， 1y ， 2y . 
Then the above formula expands to: 








0212
2
2
'
2
2
2
'
1
1
1
'
1
1
1
'
22 allay
l
yy
x
l
xx
y
l
yy
x
l
xx
 
'
1
x ， '1y ，
'
2
x ， '2y represents the initial value of the 
coordinate of the focus, and the focus satisfies the 
relationship as follows: 

11
'
1
xxx  ，
22
'
2
xxx   

11
'
1
yyy  ，
22
'
2
yyy   
 aaa 
0
 
The initial position obtained is used as the initial 
value, and the point cloud data of the ellipse edge is 
fitted by the least squares method step by step iteration 
[11], then the parameter ( 1x ， 2x ， 1y ， 2y ， a ）
can be solved, and the elliptical center ),( 00 yxO  of the 
last fitting is: 
 2
21
0
xx
x

 ， 2
21
0
yy
y


 
B. Symmetry method 
Since the image on the rotating platform has 
symmetry after being rotated by 180 degrees and is 
symmetrical about the center of rotation, a plurality of 
laser lines can be selected on the auxiliary pattern to 
perform calculation of the center of rotation to ensure 
accuracy. Finally, the parameters obtained can be 
optimized by methods such as BP neural network. 
In order to accurately calibrate the center of rotation, 
the straight line equations of the two straight lines 21ss  
and 
'
2
'
1
ss  are fitted on the premise that the rotation angle 
of the rotating platform is known. Find the intersection 
O between the two lines. The intersection point O is the 
rotation center of the rotating platform. The point 1s  is 
located at the position of the point 
'
1
s  after being 
rotated by 180 degrees, and point 2s  is rotated 180 
degrees and is located at point 
'
2
s . 1s ， O， 
'
1
s  three 
points are collinear, and after rotation, are symmetric 
with respect to the rotation center O before rotation 
[12]. The principle of symmetry is shown in Figure 4.2 
below. 
O
),x(
111
yS
),x(
222
yS
),x( 2
'
2
'
2
' yS
),x( 1
'
1
'
1
' yS
 
Figure 3.  Symmetrical view of the center of rotation 
International Journal of Advanced Network, Monitoring and Controls          Volume 04, No.01, 2019 
51 
The calibration process of the symmetrical rotation 
platform is: 
(1) Firstly, the rotating platform is adjusted to the 
working position, the auxiliary pattern is pasted on the 
rotating platform or the circular calibration block is 
placed, and the line laser is passed through the center of 
the rotating platform; 
(2) Rotate the rotating platform at an angle (15 
degrees) and start collecting data; 
(3) Extracting the center coordinates of the laser 
stripe in the data as pixel coordinates; 
(4) Calculating the world coordinates corresponding 
to the pixel coordinate system and storing the sample 
set; 
(5) After rotating 180 degrees, the sample set is 
derived for calculation of the rotation parameters. 
C. Plane fitting 
In the three-dimensional reconstruction of the 
rotating scanning mode, the obtained rotating point 
cloud is plane-fitted to fit the rotation center of the 
rotating platform [13]. The line laser emitter emits a 
laser beam that intersects the surface of the calibration 
block. As shown in the figure below, point A emits a 
line laser, and BC is the line of intersection between the 
laser and the calibration block. The plane formed 
between points A, B, and C is a light plane. The points 
in the light plane (ΔABC) conform to the plane 
equation (11). 
In online laser scanning, the acquired point clouds 
are all in the light plane, so all point clouds conform to 
the plane equation (11): 
 0a  dczbyx  
The n point cloud data obtained by the rotation scan 
are sequentially brought into the upper equation of the 
light plane. 
 
 
 










0
0
0
222
111
dczbyax
dczbyax
dczbyax
nnn

 

Line laser transmitter
Right 
camera
Left 
camera
Space laser plane
P
P P
A
B
C  
Figure 4.  Light plane equation 
There are 4 unknown n equations, and the values of 
four unknowns a, b, c, d can be solved by least squares 
method. The center of rotation of the rotating platform 
can be expressed as: 

)
1
,
1
,
1
(
11 1
 
 

n
i
i
n
i
n
i
ii
z
n
y
n
x
n
O
 
In general, by gradually increasing the height of the 
rotating platform, a series of center points can be fitted 
in a straight line, so that the rotation axis can be 
calibrated. Then through the Rodrigo rotation formula 
[14], we can complete the coordinate transformation 
and so on. 
The comparison between the calibration methods of 
the center of rotation is shown in Table 1 below. 
 
 
 
 
 
 
 
International Journal of Advanced Network, Monitoring and Controls          Volume 04, No.01, 2019 
52 
TABLE I.  COMPARISON BETWEEN ROTATION CENTER CALIBRATION METHODS 
calibration 
method 
Advantage Disadvantage Applicable situation 
Ellipse fitting 
method 
It can reduce the error in 
the measurement process 
with high precision. 
During the fitting 
process, the number of 
iterations is variable and 
it takes a lot of time. 
Due to interference of factors such 
as position and angle, the extracted 
edge contour is elliptical. Or the 
calibration block is elliptical. 
Symmetry 
method 
The principle is simple 
and easy to understand, 
and the accuracy is high. 
It is necessary to select 
multiple locations for 
testing, and to obtain an 
average value, which 
takes a lot of time. 
Suitable for circular rotating 
platforms. Or a circular calibration 
block. The point cloud obtained by 
scanning has higher precision. 
Plane fitting 
The operation is simple, 
no need to manually paste 
the mark points, and the 
speed is fast. 
The accuracy is low. 
Suitable for circular rotating 
platforms. Or a circular calibration 
block. 
 
V. CONCLUSION 
This paper introduces the basic process of linear 
laser rotation scanning. The measured object starts 
from a fixed angle and starts to rotate 360 degrees 
around the rotation axis or rotation center to obtain the 
three-dimensional contour of the rotating object. The 
basic knowledge of the rotating center of the rotating 
platform parameters during the rotating scanning 
process is introduced, and the calibration methods of 
the three rotating centers are summarized. The 
principles and steps of these three calibration methods 
are analyzed in detail. The advantages and 
disadvantages of the three methods and their 
application are summarized. It lays a theoretical 
foundation for the study of the calibration method of 
the rotating center. 
ACKNOWLEDGMENT 
This work is partially supported by Science & 
Technology Program of Weiyang District of Xi'an City 
with project “201836". 
 
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