Phương pháp đếm giấy xếp chồng dựa trên sự kết hợp độ cong cực tiểu và phát hiện đỉnh

value is dark overall, resulting in a 
change in the gray profile curve. The curvature 
values are all greater than zero. There is no local 
minimum value, and the point will be missed, so it 
needs to be corrected.
Since the thickness of the paper is constant, the 
distance between two adjacent sheets should 
also be within a range. As shown in Figure 3, 
the center points Z2 and Z6, the center distance 
d1 (d2) is much smaller than (greater than) the 
distance between two adjacent center points 
under normal conditions. To prevent multiple or 
missing inspections, the paper for the previous 
step is detected. Further judgment is made at 
the center point: ideally, the distance d between 
the center points of two adjacent paper sheets 
is a sheet thickness Wr plus the width dr of the 
slit, but since the detected ridge diagram is not 
an absolute straight line, the actual above, the 
distance d between two adjacent paper center 
points should be plus or minus three pixels on the 
basis of a sheet thickness Wr and a slit width dr, 
namely:
 (4)
If the detected actual distance ds of two adjacent 
center points is in the range of d to 2d in the 
equation (4), and the gray values in the middle 
2/32)(
2
)(
2
})(1{
)(
dz
dP
dz
Pd
zk
zf
zf
+
=
3±+= drWrd
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LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
Tạp chí Nghiên cứu khoa học - Đại học Sao Đỏ, ISSN 1859-4190 Số 1(64).2019
position of the two adjacent center points and one 
pixel in the left and right if it is greater than 70, it is 
considered that a piece of paper has been missed 
between the detected two center points; similarly, 
if the ds of two adjacent center points detected 
are within the range of 2d to 3d in the formula 
(4), and in the one-third and two-thirds positions 
of the two adjacent center points and the gray 
value in the left and right pixels are greater than 
70, it is considered that two sheets of paper have 
been missed between the detected two center 
points. And so on to judge the situation of missed 
detection. 
Fig.3.The relationship of the original profile, 
filtered profile and curvature
If the detected actual distance ds of two adjacent 
center points is smaller than d in the equation 
(4), the distance between the point and another 
adjacent center point is further determined, if the 
point is adjacent to the two center points. If the 
sum of the distances is less than d, the point is 
considered to be the center point of the multi-
check and is removed. 
When it is determined that two adjacent center 
points have missed a piece of paper, the curvature 
values of the intermediate positions of the two 
adjacent center points are reversed; when it 
is determined that two adjacent center points 
have been detected, two sheets are missed. For 
paper, the curvature values of the one-third and 
two-thirds of the two adjacent center points are 
reversed; and so on. The curvature value of the 
missed inspection is treated as in equation (5):
The relationship of the original profile Pf(z), filtered 
profile Pf1(z) and curvature k(z) (Z1, Z2’ (multi-
detection), Z2, Z3, Z4, Z5, Z6 (less-detection), Z7 
represent the paper center respectively. dr, ds(d1, 
d2), Wr is the width of the gap, the distance of the 
two adjacent centers and the width of the paper 
respectively).







+−=+
+−=+
+−=+
)1()1(
....
)1()1(
)1()1(
22
n
k
n
k
n
k
n
k
n
k
n
k
ss
ss
ss
dndn
dd
dd
 (5)
Experiments have shown that after calibration, the 
missing or multi-checked paper can be detected 
very well.
2.5. Count the paper with peak detection
In [14], the detected ridge line results are 
counted one by one by pixel, which is not only 
time-consuming, computationally intensive, but 
also cannot be correctly counted for non-absolute 
straight lines. In order to prevent inaccurate 
counting, the ridge line count is used in the peak 
detection method [15-16].
Fig 4. (a) The acquired ridge line result;
 (b) Result of the peak detection
It can be seen from Figure 3 Pf(z) that the original 
paper has large fluctuations in the grayscale 
(b)
(a)
Z1 Z2 Z3 Z4 Z5 Z6 Z7
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Tạp chí Nghiên cứu khoa học - Đại học Sao Đỏ, ISSN 1859-4190 Số 1(64).2019
profile due to some external disturbances such 
as noise. If the peak value is directly detected, 
it is easy to cause false detection and multiple 
inspections. The result of the paper ridge obtained 
by the minimum curvature method is as shown in 
Figure 4.(b), and the cross-sectional view is neat 
and regular, and there is no fluctuation. When the 
detected ridge diagram appears broken.
When cracking or non-absolute straight line, 
in order to reduce its influence on the detection 
result, calculate the average value of each ridge 
line as the value of the ridge line, and then perform 
peak search on the processed paper ridge line, as 
shown in Figure 4. For the processed paper ridge 
diagram, the peak position is the center point of 
the paper, and the peak number is the stack paper 
count result. Experiments show that this method 
can effectively reduce the interference of external 
noise such as noise, and when the ridge line breaks 
or the ridge line is non-absolute straight line, it can 
also reduce its influence on the counting result.
3. EXPERIMENT
Paper will inevitably have some abnormal 
conditions, such as uneven end faces, wide 
gaps, adhesions and foreign matter, as shown in 
Figure 5.
For the papers of the four anomalies in Figure 4, 
the fast linear growth algorithm (LSD) [9] and the 
frequency domain are used in the literature.
(a) (b) (c) (d)
Fig 5. Abnormal papers ((a), (b), (c) and (d) are the 
irregular papers, wide-gap papers, sticky papers 
and impure papers respectively)
For the papers of the four anomalies in Figure 
5, the fast linear growth algorithm (LSD) [9] in 
the literature and the combination of frequency 
domain analysis and correlation metrics [10] and 
the uncorrected algorithm and the algorithm in this 
paper are used. 
Detection, the test results are shown in Figure 6. 
As can be seen from Fig. 6, for the LSD algorithm 
in (a), since it is based on the gradient field of the 
paper image, some of the papers in (a1), (a2), and 
(a3) are dark, or paper. The change from the gap 
is not obvious. In the paper (a4), there is foreign 
matter on the paper to make the gradient change 
abnormally, so the algorithm will cause some 
 Fig 6. ((a1)-(a4), (b1)-(b4), (c1)-(c4) and (d1)-(d4) are the detectingresult of four kinds of abnormal 
paper using LSD algorithm, frequency domain analysis and correlation measurement algorithm, 
our uncorrected algorithm and our algorithm respectively represent the paper that is missed or extra)
(a1) (a2) (a3) (a4)
(b1) (b2) (b3) (b4)
(c1) (c2) (c3) (c4)
(d1) (d2) (d3) (d4)
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LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
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papers (a1), (a2) and (a3) to be missed. (a4) For 
the case of multiple detection; for the frequency 
domain analysis and correlation metric algorithm 
in (b), the comb filter used is easy to cause 
misdetection for paper with local periodic anomaly, 
and the correlation metric is for weak implicit modal 
signals. It is easy to cause missed detection, 
so the algorithm will lead to (b1), (b2), (b3) and 
(b4) miss detection and multiple detection; (c) in 
this paper uncorrected algorithm, for paper with 
abnormal grayscale changes. The paper area may 
have no minimum value of curvature, such as A in 
(c1), (c2), (c3), and (c4), which makes it easy to 
miss the paper. Or a sheet of paper with multiple 
curvature minimum values, such as B in (c2), which 
makes it easier to check the paper. The correction 
algorithm in (d), on the basis of (c), combines the 
grayscale characteristics of the paper with the 
information of the distance of the adjacent paper 
to further judge the detected paper, and fills the 
missing paper, and the paper that is checked 
more. Removed, which improves the accuracy 
of paper detection. At the same time, in order 
to further verify the accuracy of the algorithm, 
different types of paper with thickness between 
0.05 mm and 0.2 mm are counted. The minimum 
curvature method combined with peak detection is 
combined. The method can be effectively counts 
of different types of paper, wherein, before the 
correction accuracy is not reached 99.9%, after 
subsequent counting error rate after correction is 
less than 0.01%.
4. CONCLUSION 
Aiming at the problem of stacking paper detection 
and counting, this paper proposes a method of 
detecting and counting laminated paper using the 
combination of minimum curvature method and 
peak detection. The basic principle is to first obtain 
the gray cross-section of the stacked paper, pre-
process and calculate the curvature; then detect 
the center point of the paper, and then correct the 
detected center point by judging the spacing and 
gray value between the adjacent two center points. 
Thereby the ridge line results of the stacked paper 
are obtained, and finally the peak detection is used 
to count the ridge line results. Experiments show 
that the algorithm of this paper can significantly 
reduce the situation of multiple inspection and 
missed detection of paper, can count many 
different types of paper, and has high accuracy. 
The algorithm in this paper has been applied to 
paper testing instruments.
REFERENCES
[1]. Hui, Jiang Jin (2015), Study on paper counting 
based on texture segmentation. pp.135-148. 
[2]. Wang Xinxin, Xu Jiangwei, Zou Weijin, Liu 
Yongfeng, Wang Xiuli (2014), Study on TFT-LCD 
defect detection system[J], Journal of Electronic 
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[3]. Wu C Z, Wang Y N (2015), Research on foreign 
insoluble particulate detection method for medicinal 
solution based on machine vision[J], Chinese 
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[4]. Hou Weiyan,Zhang Liwei et al (2015), Design and 
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and system for touchless counting of stac-ked 
substrates, especially bundled banknotes [P], 
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[6]. Harba Rachid. Ferte La, Saint Aubin (fr) et al, 
(2010). Card-counting device[P], United States: 
US 2010/0226576A1.
[7]. Wang Fuzhi,Huang Dagui (2009), A paper grain 
segmentation algorithm based on peak-valley 
morphology[J], Journal of Electronic Measurement 
and Instrument, 2009, 23(6): 103-107.
[8]. ZHENG Guang, CHEN You-ping, YU Wen-
yong, AI Wu (2007), Study on Paper Counting 
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[9]. Yang Shuo, Peng Shuang, Xiao Changyan (2015), 
Fast linear growth algorithm for image analysis 
and counting of laminated papers[J], Computer 
Applications & Software, 2015,32(9): 188-191.
[10]. Dai Wei,Xiao Changyan (2016), Detection of 
laminated paper quantity based on image frequency 
domain analysis and correlation measurement[J], 
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1651. 
[11]. Chen Xuwen, Liu Guixiong, Huang Jian (2015), 
Image acquisition and surface curvature 
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NGHIÊN CỨU KHOA HỌC
Tạp chí Nghiên cứu khoa học - Đại học Sao Đỏ, ISSN 1859-4190 Số 1(64).2019
Pham Thi Dieu Thuy
- Pham Thi Dieu Thuy received the B.S. degree in automation from Thai Nguyen University 
of technology, Thai Nguyen, Vietnam, in 2006 and the M.S. degree in Measurement and 
Control systems from Ha Noi University of Science and Technology, Ha Noi, Vietnam, in 
2010. Her current research interests include medical image processing, machine vision 
and machine learning. 
- Email: dieuthuy303@gmail.com
- Telephone No: 0986468005
Ha Minh Tuan
- Ha Minh Tuan received the B.S degree in automation from Vietnam Maritime University, 
Hai Phong, Vietnam, in 2005 and the M.S. degree in Measurement and Control systems 
from Ha Noi University of Science and Technology, Ha Noi, Vietnam, in 2010. His current 
research interests include medical image processing, machine vision and machine 
learning.
- Email: minhtuanha031@gmail.com
THÔNG TIN VỀ TÁC GIẢ
[12]. Tao Q, Liu L (2016), Double regional evolution 
based on level set for image segmentation[J], 
Electronic Measurement Technology, 2016, 39 (9): 
91-95.
[13]. Zhang M Y, Chen Z Y, Wang X (2013), Paper 
counting algorithm based on image texture[J], 
Optical Technique, 2013, 39(2): 151-156.
[14]. Chao Yang, Zengyou He and Weichuan Yu (2009), 
Comparison of public peak detection algorithms for 
MALDI mass spectrometry data analysis[J], BMC 
bioinformatics, 2009, 10(1): 4.
[15]. ZHANG Z M, LIANG Y Z, et al (2012), Multiscale 
peak alignment for chromatographic data 
sets[J], Journal of chromatography A, 2012, 
12(23): 93-106.
Nguyen Thi Viet Huong
- Nguyen Thi Viet Huong received the B.S. degree in Electrical Engineering Technology 
from Hung Yen University of Technology and Education, Vietnam, in 2009 and the M.S. 
degree in Control Engineering and Automation from Hung Yen University of Technology and 
Education,Vietnam, in 2014. Her current research interests include Control Engineering 
and Automation. Summary of current work: Lecturer, Faculty of Electrical Engineering, 
Sao Do University.
- Email: nguyenthiviethuong1986@gmail.com
- Telephone No: 0989505045
Pham Thi Thao
- Pham Thi Thao received the B.S. degree in Electrification and power supply of enterprises 
from Thai Nguyen university of Technology, Thai Nguyen, in 2002 and the M.S. degree in 
Automation from Ha Noi University of Science and Technology, Ha Noi, Vietnam, in 2004. 
Her current research interests include Control Engineering and Automation. Summary of 
current work: Lecturer, Faculty of Electrical Engineering, Sao Do University.
- Email: phamhathao@gmail.com
- Telephone No: 0905006188
29
LIÊN NGÀNH ĐIỆN - ĐIỆN TỬ - TỰ ĐỘNG HÓA
Tạp chí Nghiên cứu khoa học - Đại học Sao Đỏ, ISSN 1859-4190 Số 1(64).2019
Luong Thi Thanh Xuan
- Luong Thi Thanh Xuan received the B.S. degree in Technology Education from Thai 
Nguyen University of Technology, Thai Nguyen, in 2003 and the M.S. degree in Automation 
from Thai Nguyen University of Technology, Thai Nguyen, Vietnam, in 2011. Her current 
research interests include Control Engineering and Automation. Summary of current work: 
Lecturer, Faculty of Electrical Engineering, Sao Do University.
- Email: thanhxuan7980@gmail.com
- Telephone No: 0982791980