Adaptive threshold for moving objects detection using gaussian mixture model

TELKOMNIKA Telecommunication, Computing, Electronics and Control
Vol. 18, No. 2, April 2020, pp. 1122~1129
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v18i2.14878  1122
Journal homepage: http://journal.uad.ac.id/index.php/TELKOMNIKA
Adaptive threshold for moving objects detection
using gaussian mixture model
Moch Arief Soeleman, Aris Nurhindarto, Muslih, Karis W., Muljono,
Farikh Al Zami, R. Anggi Pramunendar
Faculty of Computer Science Dian Nuswantoro University, Indonesia
Article Info ABSTRACT
Article history:
Received Aug 14, 2019
Revised Dec 30, 2019
Accepted Feb 20, 2020
Moving object detection becomes the important task in the video surveilance
system. Defining the threshold automatically is challenging to differentiate
the moving object from the background within a video. This study proposes
gaussian mixture model (GMM) as a threshold strategy in moving object
detection. The performance of the proposed method is compared to the Otsu
algorithm and gray threshold as the baseline method using mean square error
(MSE) and Peak Signal Noise Ratio (PSNR). The performance comparison of
the methods is evaluated on human video dataset. The average result of MSE
value GMM is 257.18, Otsu is 595.36 and Gray is 645.39, so the MSE value
is lower than Otsu and Gray threshold. The average result of PSNR value
GMM is 24.71, Otsu is 20.66 and Gray is 19.35, so the PSNR value is higher
than Otsu and Gray threshold. The performance of the proposed method
outperforms the baseline method in term of error detection.
Keywords:
Detection
Gaussian mixture model
Moving object
Otsu
Threshold
This is an open access article under the CC BY-SA license.
Corresponding Author:
Moch Arief Soeleman,
Faculty of Computer Science,
Dian Nuswantoro University,
207 Imam Bonjol St., Indonesia,
Email: arief22208@gmail.com
1. INTRODUCTION
Research in video processing has become one of the exciting fields in computer vision research,
as the use of methods continues to be developed to produce quality results in the field of computer vision,
especially detection of moving objects based on surveillance cameras. The increasing CTTV technology,
especially in the use of surveillance cameras in monitoring human activities or activities in daily life both
at home, offices, and in open spaces. In the central part of monitoring activities of moving objects,
especially humans, the process of detection of moving objects is an essential step carried out at an early stage
to be able to carry out more specific operations in object analysis such as extraction, classification, and
identification. Moving object detection has some basic formation, mathematically the exposure of moving
objects results from modeling the background and foreground [1, 2]. This modeling aims to get pixels that will
become foreground-background.
Some approaches in modeling this static background include using statistical component methods
such as running average [3, 4], and histogram analysis [5]. Otsu thresholding [6] is a threshold method in
segmentation techniques, the application of the Otsu method makes it easier to do homogeneous division of
parts based on similarity criteria to recognize objects. Before observing the segmented image, the process must
first go through the image input process so that it is easy to proceed to the next process.

TELKOMNIKA Telecommun Comput El Control 
Adaptive threshold for moving objects detection using gaussian mixture model (Moch Arief Soeleman)
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The next process is to add brightness to the image to improve image quality. After that, the image
segmentation process is done with the Otsu thresholding method and through discriminant analysis approach
so that it can maximize these variables so that objects with a background can separate automatically.
In a previous study, Soeleman, Mauridhi Hery, Hariadi in [7] used the adaptive threshold approach to get
the background of moving objects using fuzzy c-means clustering, and the fuzzy method produced better
performance than the Otsu threshold. In another study, Zeng, Jia and Chen in [5] used fuzzy to obtain
foreground objects with a histogram approach to partition the foreground from the background video sequence.
In another study, Yesong, Xiaoping Li, Na Fu and Qiongxin Liu in [8] used the gaussian mixture
model approach to detect moving objects based on background subtraction. Vivek Maik, Hyungtae Kim,
Daedhee Kim, Eunjung Chae and Joonki Paik in [9] modified the gaussian mixture model to overcome sudden
changes in the object's background. The same method in the gaussian mixture model is also used in [10-12].
From some of these studies it can be concluded that detecting moving objects is a difficult challenge in
the detection method. Kittipop Peuwnuan, Kuntpong Woraratpanya and Kitsuc in [13] using integral image for
thresholding adaptive in image, authors proposed two stage for process in low and high intensity for
thresholding and segmentation. Senthilkumaran and Vaithegi in [14] using thresholding technique for
segmentation medical image, the proposed method have fast performance to extract foreground from
background. In different method many researcher using background modelling [15-17] to detect moving
objects in video, but background modelling have a problem when it suddenly occurs an intensity change
and dynamic background, so the method have disadvantage to detect moving object. In other method Nur
Ayuni Mohamed and Mohd Asyraf Zulkifley in [18] using optical flow to detect the motion of human fall-
dawn, that evaluation using intersection over union for measuring.
In this paper, the gaussian mixture model method is proposed to detect moving objects with adaptive
threshold approach to obtain the foreground from the dynamic background of a frame sequence. As threshold
strategic gaussian mixture model were compared against gray threshold and Otsu algorithm to evaluate
the achievement. The rest of paper is arranged as follows. Passage 2 discussed our research method in detection
moving objects. Passage 3 shows the results and analysis of the experimental our proposed and discussion.
Finally, conclusion are given in passage 4.
2. RESEARCH METHOD
The proposed method be composed of several steps to threshold strategic in the moving object
detection, as illustrated in Figure 1. In the initial stage, the frame breakdown begins in the video dataset,
then adaptive threshold using gaussian mixture model, Otsu and gray threshold in parallel process to get
the foreground from video dataset, the next step the binary moving objects in the frame is continued
by the morphology operation until the moving object is detected, finally we evaluate all performance of
adaptive threshold method.
Figure 1. Flow method in threshold for object detection
2.1. Gaussian mixture model
Stauffer et.al in [19] proposed the gaussian mixture model (GMM) method as a type density model
consisting of gaussian function components. The component of this function consists of different weights to

 ISSN: 1693-6930
TELKOMNIKA Telecommun Comput El Control, Vol. 18, No. 2, April 2020: 1122 - 1129
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produce multi-model density. The gaussian mixture model method proposed by Grimson is very efficient in
separating the foreground and background from the input frame sequence
The number of GMM in [8, 17] used affects the number of background models. The greater
the number of GMM models used, the more background models a pixel has. There are several stages of
the process for this method, namely the stage of matching input to the distribution and the stage of selecting
the distribution that reflects the background. In GMM each pixel In the matching stage, there is a parameter
update stage. The GMM equation model [8] is as (1).
𝑃(𝑋𝑡) = ∑ 𝜔𝑖𝑡 𝜂(𝑋𝑡, 𝜇𝑖,𝑡, ∑𝑖,𝑡)𝐾
𝑖=1 (1)
The parameter K in (1) is the numeral of distributions, while µ is the average value of gaussian at term unit t,
and ∑ is the covariance matrix at I threshold on gaussian and ꞷ is the weight. The following equation is
a gaussian probability density function.
𝜂(𝑋𝑡, 𝜇𝑖,𝑡, 𝛴𝑖,𝑡) =
1
(2𝜋)
𝑛
2 𝛴1/2
𝑒𝑥𝑝
1
2
(𝑥 𝑡− 𝜇 𝑡) 𝑇
𝛴−1(𝑥 𝑡−𝜇 𝑡)
(2)
𝜔𝑖,𝑡 = (1 − 𝛼)𝜔𝑖,𝑡−1 + 𝛼𝑀(𝑖,𝑡) (3)
The parameter n is the gaussian distribution dimension, the value of n = 1 when the background model
is a gray image, ∑I,t is a color image, and the amount of n = 3 is an RGB image. When the parameter M is 1,
then it matches, and vice versa, the parameter M is 0. The parameter values µ and α are updated with
the following equation.
𝜇𝑖,𝑡 = (1 − 𝜌)𝜇𝑖,𝑡−1 + 𝜌𝑋𝑖,𝑡 (4)
𝜎𝑖,𝑡
2
= (1 − 𝜌)𝜎𝑖,𝑡−1
2
+ 𝜌(𝑋𝑡 − 𝜇𝑖,𝑡)2
(5)
𝜌 = 𝛼𝜂(𝑋𝑡, 𝜇𝑖,𝑡, 𝜎𝑖,𝑡) (6)
𝐵 = arg 𝑚𝑖𝑛 𝑏(Σ 𝑘=1
𝑏
𝑤 𝑘 > 𝑐𝑓) (7)
Using (3) in the parameter update stage, the values of GMM parameters are used to process the next input.
Updated values consist of weights, averages, and variants. The weight value is updated every time.
After the weight values have been normalized, the total weight of all distributions is not more than 1. Then the
mean value of a distribution is updated every time there is a pixel value that matches the distribution value.
Using (5) and (6) the standard deviation value of a distribution is updated every time there is a pixel value that
matches that distribution. The next step by (7) the pixels which are probabilistic matches the gaussian model,
if they are against the background, they will be classified as background pixels and their opponents as the
foreground.
2.2. Otsu algorithm
The Otsu method [6] aims to split the grey image histogram upon two different regions automatically
without any help from the user to enter the threshold value. Otsu as the threshold method is set to the mark
using z. The scope value of z is in the midst of 1 and R, wherever 𝑅 = 255. The likelihood of every pixel in
the th
i degree could be resolved by employed (8).
𝑝𝑖 = 𝑛𝑖/𝑁 (8)
Where in in is the amount of pixel in the th
i degree and N is the unqualified of amount of pixels. The mean
grey degree of an image frame use (9).
𝜇 𝑇 = ∑ 𝑖 × 𝑝𝑖
𝑅−1
𝑖=1 (9)
Towards single threshold, Otsu split the pixels inside two group 𝐶1 = {0,1, . . . , 𝑧}
and 𝐶2 = {𝑧 + 1, 𝑧 + 2, . . . , 𝑅 − 1}. The likelihood of group can be calculated by applying (10).

1125
𝜔1(𝑧) = ∑ 𝑝𝑖
𝑧
𝑖=1
𝜔2(𝑧) = ∑ 𝑝𝑖
𝑅−1
𝑖=1
(10)
𝜇1(𝑧) = ∑
𝑖 × 𝑝𝑖
𝜔1(𝑧)
𝑧
𝑖=1
𝜇2(𝑧) = ∑
𝑖 × 𝑝𝑖
𝜔2(𝑧)
𝑅−1
𝑖=1
(11)
The amount of z can be calculated applying (12) and (13).
𝑧′ = 𝑚𝑎𝑥
1≤𝑘<𝐿
𝛼 𝐵
2
(𝑧) (12)
𝛼 𝐵
2(𝑧) = 𝜔1(𝑧)(𝜇1(𝑧) − 𝜇 𝑇)2
+ 𝜔2(𝑧)(𝜇2(𝑧) − 𝜇 𝑇)2
(13)
2.3. Gray threshold
A binary image [20] construct by thresholding through a grey scale or color image by surrounding
pixel grade to 1 or 0 rely on whether they are above or below the threshold value. This frequently usual
to distinct or portion a section object within the image based upon the pixel values. The basic operation
thresholding operates on an image as follows:
For pixel 𝑍 (𝑟, 𝑠) scope the image Z
𝑖𝑓 𝑍(𝑟, 𝑠) > 𝑡ℎ𝑟𝑒𝑠ℎ𝑜𝑙𝑑
𝑍(𝑟, 𝑠) = 1
𝑒𝑙𝑠𝑒
𝑍(𝑟, 𝑠) = 0
𝑒𝑛𝑑
Towards scale of gray image frame, that pixels have substance a single intensity value, a single threshold must
be picked, and for colour image, a detached threshold can be specified for each narrow.
2.4. Binary frame moving object
The result of the thresholding process with the adaptive threshold with gaussian mixture model, Otsu
and gray threshold that produces binary images [21] zero and one where the value 1 represents as the object or
foreground and the amount 0 as the background.
2.5. Morphology
Morphological filter results to noise from a foreground distribution by using an erosion filter which
aims to reduce the dimensions of the vehicle's dimensions to be close to the actual size, while reducing small
movements if it does not need to be segmented. Although the results do not look completely clean, this
condition is good enough for the detection of moving objects.
Morphology operations in the form of erosion and dilation were done to get better object results based
on the shape of the object [22]. Dilation is the process of adding pixels to the boundary of an object in a digital
input image, while erosion is the process of moving/reducing pixels at the border of an object Morphological
operations include erosion 𝐹′
= 𝑓 ⊝ 𝑠 where 𝐹′
is new binary image from image 𝑓 have structuring element
s, the dilation notation of image f with structuring element s is 𝐹′
= 𝑓 ⊕ 𝑠, opening, and closing [23]. At this
stage, the disposal process is carried out [24] imperfect pixel objects from the detection result.
3. RESULTS AND ANALYSIS
In this section, the results of the experimental algorithm that have been applied to the threshold
of moving objects for object detection are presented in Figure 2. The dataset used consists of 200 frame
sequences. In order to judgement our adaptive threshold practice, we use a dataset in realistic with permission
to Le2i “Laboratorie Eletronique, Informatique et Image” video surveillance state by using an unaccompanied
camera [25]. The video has frame rate is 25 per second, and with resolution on 320 x 240 pixels. The video
data explained with principal adversity of reasonable frame sequences which can come across at a human as
well as in a straightforward office room. The frame sequences comprise fluctuating of illumination,
and distinctive hardship as though occlusions or confound and textured background. The actors bring about
certain normal habitual activities. The dataset comprises number of frames. For judgement goal, with extra
information representing the ground-truth of the detection position in the image sequence. Then, each frame of
each video is labelled: the localization of the body is automatic assigned with bounding boxes. The experiment
uses MATLAB 2016b and runs on a CPU with an i5-8265U processor with RAM LPDDR3 8 GB.

 ISSN: 1693-6930
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For the detailed explanation, we applied our approach in Figure 2, whereas we compared gaussian
mixture model with Otsu and gray threshold. For sake the simplicity, we take example as follows:
in the frame number 90, the subject arrived at room, thus the bounding box start to detect the subject, then
followed by frame number 102 and frame number 168. In the frame number 168 and 179, we can see that
gaussian mixture model able to maintain the bounding box to the subject, where the other method is not
successful. Thus, from visual evaluation, we can conclude that the gaussian mixture model is robust than other
methods. The following were shown the resulting frame of the experiment:
Frame 90 102 168 179
Method
Original
Frame
Gaussian
Mixture
Model
Otsu
Gray
Threshol
d
Figure 2. Result of the threshold and detection by gaussian mixture model, Otsu and gray threshold

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3.1. Evaluation
In the experiments carried out to measure the performance of each adaptive threshold method that has
been applied for the detection of moving objects, including the gaussian mixture model, the Otsu algorithm
and the gray threshold, MSE and PSNR are used. Evaluation of the threshold results in the detection method
is used peak signal to noise ratio (PSNR) [26] which is a method of comparing the maximal value of the stated
signal with the quantity of noise intensity on the signal. Before determining the PSNR value, first, calculate
the value [27]. Whereas mean square error (MSE) [28] is the average square error value between the original
image and the improved image, which is formulated in the (14) dan (15).
𝑀𝑆𝐸(𝐹, 𝑋) =
1
𝐾𝑄
∑ ∑ [𝐹(𝑎, 𝑏) − 𝑋(𝑎, 𝑏)]𝑄
𝑏=1
𝐾
𝑎=1 (14)
𝑆𝑁𝑅(𝐹, 𝑋) = 10. 𝑙𝑜𝑔10 (
𝑚𝑎𝑥2
𝑀𝑆𝐸(𝐹,𝑋)
) (15)
The variable F indicates that the frame ground truth, while the parameter X is a frame sequence that has
a size of K x Q, the max value indicates the maximum amount of the pixel frame. The results of the mean
square error and PSNR values of the gaussian mixture model and the Otsu technique can be seen in
Table 1. From Table 1 shows that the MSE GMM value is lower than Otsu and gray, and the PSNR GMM
shows higher than the Otsu and Gray Algorithm.
Table 1. Average performance evaluation adaptive threshold with MSE and PSNR (dB)
Evaluation GMM Threshold Otsu Threshold Gray Threshold
MSE 257.18 595.36 645.39
PSNR 24.71 20.66 19.35
3.2. Experimental results
The result of thresholding in human moving in video dataset, Figure 3 and Figure 4 show the MSE
and PSNR of adaptive threshold in human detection, successively. The diagram of result show the best
accomplishment of GMM (MSE = 89.11, PSNR = 28.63) at frame 33. Averagely, MSE of GMM is 257.18,
Otsu is 595.36 and gray threshold is 645,38. Also, PSNR of GMM is 24.71, Otsu is 20.66 and gray threshold
is 19.36.
Figure 3. Performance MSE (dB) of adaptive threshold
Figure 4. Performance PSNR (dB) of adaptive threshold

 ISSN: 1693-6930
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Based on the test results that the lower the value of mean square error (MSE), the thresholding process
of finding objects in moving on the video frame the better the results or have a low error rate, whereas if
the mark of the peak signal to noise ratio (PSNR) is higher the better the quality threshold moving objects in
the video frame. Then it can be shown in Figure 3 graph that shows the success rate of the moving object
threshold process.
3.3. Discussion
The possible reason Otsu threshold method is underperformed compared with GMM are the Otsu does
not use spatial coherence and any object structure. Also, the Otsu threshold still use assumption in using binary
class, which partition the grayscale histogram value into binary class. Due to dataset which can be seen at
Figure 3, it shows that the video contains more than two segment class. Thus, in frame number 179, the Otsu
threshold segment the bed and person into one due to color of bed and color of clothes have same gray color.
The possible reason gray threshold is underperformed compared with GMM are the Gray threshold
failed to detect non-edge pixels. As we can see at Figure 3, the Gray only segment the pants due to it contains
more value than the clothes which more same like the foreground. Although GMM possess same characteristic
like Otsu threshold, which uses histogram-based techniques, but the GMM itself assumes the histogram
distribution is represented by two gaussian curves, which able to finding a threshold and describe the two
regions obtained.
4. CONCLUSION
This paper provided an adaptive threshold technology on assign the threshold of object moving for
especially in human detection. The outcome showed that the achievement of an object moving in video
detection using a gaussian mixture model is better than with standard otsu algorithm and gray threshold.
The average of MSE values is 257.18 dB smaller than the other and the PSNR value is 24.71 dB higher than
Otsu and gray threshold. Future work is an arrangement to evaluate other threshold techniques, to improve
performance in threshold strategy.
ACKNOWLEDGEMENTS
This research was funded by a PDUPT Research Grant number 026/L6/AK/SP2H/RESEARCH/2019,
from the Ministry of Research, Technology, and Higher Education, Republic of Indonesia.
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