Journal of Beijing Institute of Technology, 2016, Vol. 25, No. 1
Adaptive learning rate GMM for moving object
detection in outdoor surveillance for sudden
illumination changes
HOCINE Labidi 苣 ,摇 CAO Wei( 曹伟) ,摇 DING Yong( 丁庸) ,摇 ZHANG Ji( 张笈) ,摇
LUO Sen鄄lin ( 罗森林)
( School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China)
Abstract: A dynamic learning rate Gaussian mixture model ( GMM) algorithm is proposed to deal
with the problem of slow adaption of GMM in the case of moving object detection in the outdoor sur鄄
veillance, especially in the presence of sudden illumination changes. The GMM is mostly used for de鄄
tecting objects in complex scenes for intelligent monitoring systems. To solve this problem, a mix鄄
ture Gaussian model has been built for each pixel in the video frame, and according to the scene
change from the frame difference, the learning rate of GMM can be dynamically adjusted. The exper鄄
iments show that the proposed method gives good results with an adaptive GMM learning rate when
we compare it with GMM method with a fixed learning rate. The method was tested on a certain
dataset, and tests in the case of sudden natural light changes show that our method has a better ac鄄
curacy and lower false alarm rate.
Key words: object detection; background modeling; Gaussian mixture model ( GMM ) ; learning
rate; frame difference
CLC number: TP 391郾 41摇 摇 Document code: A摇 摇 Article ID: 1004鄄 0579(2016)01鄄 0145鄄 07
摇
摇
In surveillance systems, the detection of
moving objects is known to be a primary research
problem. Many methods can be used to detect a
target. One of them is background subtraction.
The key problem is to construct an efficient back鄄
ground models in order to remove undesirable
subtraction results due to sudden scene changes.
though it is effective to remove periodic noise
such as moving sea waves, waving trees, etc. ,
the learning rate is still slow in the case of back鄄
grounds with high dynamics. Many researchers
studied GMM further and proposed a few im鄄
proved methods.
Sheng and Cui [2] presented a novel adaptive
To build such a model, Ref. [1] proposed a clas鄄
method to adjust the learning rate of the GMM in
to deal with complex background variations
number adaptive method to decrease the amount
sical method to create a robust background model
(light, wind effects, etc. ) . This model assumes
that every pixel of a complex background can be
described with K (3 to 5) Gaussian distribution.
This technique became later well known for mod鄄
eling a dynamic background.
However, even
Received摇 2014鄄 09鄄 04
苣 Author for correspondence
E鄄mail: lab. hoc@ gmail. com
DOI: 10. 15918 / j. jbit1004鄄0579. 201625. 0121
Hilbert Space. Suo and Wang [3] used a model
of computation in the GMM and proposed an up鄄
dating method with an adaptive learning rate to
accurately segment a slow moving object. In
Refs. [4 - 8] , several techniques were presented
to enhance the performance of the GMM. Jiao et
al. [9] added a virtual Gaussian component into the
GMM, and the optimization of the updating
process parameters is done in order to increase
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Journal of Beijing Institute of Technology, 2016, Vol. 25, No. 1
the convergence time of the GMM. Subra and Ka鄄
ren
[10]
presented an adaptive GMM approach for
the background subtraction to be applied in real
time surveillance. Their model is robust and a鄄
daptable to a dynamic background. Li, Tian and
P( X) =
the mean value and the covariance matrix of the ith
Gaussian in the mixture model at time t, and
浊( X,滋,撞) =
eling approach for moving object detection, in
gion N 伊 M in the scene, where the area is chosen
anywhere in the frame as long as it doesn蒺t con鄄
od, because the selection of the moving object re鄄
gion needs to be updated at each sampling time.
In this paper, we present a technique that al鄄
lows to maximize the N 伊 M size region as defined
in Ref. [11] . Here, we take the whole frame and
exclude the moving object area based on the
frame difference. This allows for the determina鄄
tion of susceptible changes in the supervised
scene. Moreover, the learning rate of the GMM is
dynamically adjusted.
In the outdoor surveil鄄
lance, where the environment presents complex
details and sudden illumination changes can be
frequent, this method has a good adaptability,
and it also can be used to effectively detect the
presence of a moving object.
Stauffer and Grimson
K Gaussian distributions ( K is a small number
from 3 to 7) in order to model the intensity distri鄄
bution for each pixel.
1
- 2 ( X - 滋 t) T 撞 - 1 ( X - 滋 t)
(3)
three parts: 淤 Mixture model construction. 于
Forground Object extraction. 盂 Parameters up鄄
date.
Mixture models construction: 淤 Initializa鄄
tion: First weights 棕 i,t to be initialized as 1 and
others as 0; the mean value 滋 i,0 is also initialized
to 0. The covariance matrix is initialized as a
large value V0 . 于 Matching: A new coming pixel
value is checked against the existing K Gaussian
distributions until a match is found, and a match
is defined as a pixel value within 2郾 5 standard de鄄
viation of a distribution.
Extraction of the foreground object: All
Gaussian components are ordered by the value of
棕 i,t
, then the first B distributions are chosen as
滓 i,t
the background model which have the most sup鄄
porting evidence and the least variance [12] :
B = argmin b
b
(移棕
i =1
i,t
>H
)
(4)
ground.
Parameters update: Whether the current pix鄄
el value x i,t satisfies or not the following condi鄄
tion:
The history of a particular pixel { x0 , y0 } at
{ X1 ,…,X t } = { I( x0 ,y0 ,i) 颐 1臆i臆t}
e
probability that the pixel appears to the back鄄
propose a mixture of
any time t be given by
(2仔) | 撞 |
1
2
where H is a threshold (0郾 5臆T臆1) which is the
1摇 Gaussian mixture model
[1]
n
2
To apply the GMM, the algorithm consists of
tain any moving objects. This condition of selec鄄
tion is considered to be a weak point in this meth鄄
1
撞 i,t = 滓2i I
which the learning rate can be adjusted dynami鄄
culating inter鄄frame difference for a selected re鄄
(2)
where 棕i,t is the weight and 滋i,t , 撞i,t are respectively
Zhang [11] proposed an adaptive background mod鄄
cally according to the scene change based on cal鄄
K
棕 i,t 浊( X,滋 i,t ,撞 i,t )
移
i =1
(1)
| x i,t - 滋 i,t | 臆2郾 5滓 i,t
(5)
There are two cases for the update method:
淤 x i,t matches at least one of the K Gaussian
where I is the image sequence. { X1 , …, X t } is
models, for the matched Gaussian distribution 滋 i,t
tions, and the probability of the observed pixel
滋 i,t = (1 - 籽) 滋 i,t - 1 + 籽X t
modeled by a mixture of K Guassian distribu鄄
and 撞 i,t will be updated as
with value X at time t is estimated as
— 146 —
撞 i,t = (1 - 籽) 撞 i,t - 1 +
(6)
HOCINE Labidi et al. / Adaptive learning rate GMM for moving object detection in outdoor surveillance . . .
籽diag[ ( X t - 滋 i,t ) T ( X t - 滋 i,t ) ]
(7)
rates are used to adjust 琢 value. The weakness of
And for the other unmatched Gaussian mod鄄
gion while moving object does not enter the area.
where 籽 = 琢G i ( X t | 滋 i,t - 1 撞 i,t - 1 )
els 滋 i,t and 撞 i,t will remain unchanged.
于 x i,t is unmatched to any of the distribu鄄
tions and the last probable distribution G j parame鄄
tres are replaced as
where we calculate the inter鄄frame difference on
the new frames I忆n I忆n - 1 I忆n - 2 , which is I n I n - 1 I n - 2
with a value 0 given to the object area pixels,
0, as shown in Fig. 1. In this way we maximize
棕 j,i - 1 = 棕0
the selected area without objects. The proposed
滋 j,t = x i,t
撞 j,t = 滓 I
In this paper, we proposed another method,
therefore the difference value in this area will be
j = argmin i { 棕 i,t - 1 } ,i = 1,…,k
2
0
this method is that one must choose a specific re鄄
method flow in shown in Fig. 2.
(8)
棕0 is a small positive constant. At last, up鄄
date the weights 棕 i,t of all the Gaussian distribu鄄
tions as
棕 i,t = (1 - 琢) 棕 i,t - 1 + 琢M
where M equals 1 for the matched distributions,
otherwise M is 0.
2摇 Proposed method
The real number 琢 is the learning rate of the
parameter estimates. It also reflects the weight
value of the current pixel. If 琢 is chosen as a
Fig. 1摇 Object area in the three frames
small number, the algorithm爷 s ability to adapt to
scene changes will be weaker. Thus more time is
required to track the environment dynamics. If 琢
is fixed to larger values, it will yield faster param鄄
eter change and background updating speed. In
this case the ability to adapt to environmental
change is strong, but at the same time it is easy
to bring noise.
Since the inter鄄frame difference reflects the
light conditions change quickly, Li and Zhang [11]
presented a method to adjust the learning rate in
real time according to the ratio of the light chan鄄
ges from the frame difference. First, we select a
monitoring area in a specific region ( moving ob鄄
ject does not enter the area) , with the number of
pixels M 伊 N, then we find the rates of inter鄄
frame pixels value which change significantly to
determine the light conditions change, and the
— 147 —
Fig. 2摇 Proposed method flow chart
Journal of Beijing Institute of Technology, 2016, Vol. 25, No. 1
1
WD - 撞 移
i =1
W
D1 =
D2 =
{
{
1,
D
( D1 夷D2 ) > 姿
移
j
| I忆n ( i,j) - I忆n - 1 ( i,j) | > H
0,
other
1,
| I忆n ( i,j) - I忆n - 2 ( i,j) | > H
0,
other
(9)
(10)
(11)
den change in illumination. When the light chan鄄
ges suddenly in the second column, we can see
that it has a slow convergence rate and a long
learning rate. A better result can be obtained with
a dynamic learning rate and the moving object can
be detected effectively.
where 夷 is And operator; H is the threshold of
two frame difference; 姿 reflects the ratio of the
successive three pixels values changed significant鄄
ly in his paper to 0郾 4; 撞 is the sum of the object
surface present in the image; W and D are the
width and the high of the frames.
If the pixels changing satisfies the formula
(9) , then the learning rate 琢 can be adjusted as
ruler 玉, if not, then as ruler 域.
Ruler 玉: when 琢 臆0郾 1 then 琢 is expanded
twice, otherwise 琢 keeps unchanged.
Ruler 域: when 琢逸0郾 05 then 琢 is reduced to
half, otherwise 琢 keeps unchanged.
3摇 Experiment and analyzes
3郾 1摇 Experiment
In order to verify the efficiency of this meth鄄
od, we have applied the algorithm to the dataset
3DPeS [13] ( It contains numerous video sequences
taken from a real surveillance setup, composed
by 8 different surveillance cameras, monitoring a
section of the campus of the University of Modena
and Reggio Emilia. ) . Frame size is 704 伊 576.
The test is performed on MATLAB. The Gaussian
distributions number is 5. First weights 棕 i,t are
initialized as 1, others as 0. The mean value
滋 i,0 = 0, The covariance matrix is initialized as a
Fig. 3摇 Moving object detection with sudden illumination
changes in camera 08
In comparison with the method given by Li
large value V0 = 50.
Y, Tian H, Zhang Y [11] , the proposed technique
above in Fig. 3. The first column is a raw video
nitoring region in a specific area. However, with
The results of the first test series are shown
frame, and the second column is the foreground
object with a fixed learning rate. At last, the
foreground with a dynamic learning rate is shown
in column 3. The frames were taken from the
camera number 7 in the dataset. It contains sud鄄
gives a good result without a need to select a mo鄄
the change in the value of 琢, the noise changes
too, thus requiring a filter to adapt to this noise.
In Fig. 4, we obtained a better result dealing
with noise, which was achieved by using a dy鄄
namic learning rate.
摇 摇 摇
— 148 —
Column 3 presents the
HOCINE Labidi et al. / Adaptive learning rate GMM for moving object detection in outdoor surveillance . . .
alarm rate ( FAR) . We also calculate the accuracy
results of the foreground with a fixed learning
rate. The frames was taken from the camera
of the methods.
FAR = FP / ( TP + FP)
number 3 from the same dataset.
TRDR = TP / ( TP + FN)
Accuracy = ( TP + TN) / ( TP + TN + FP + FN)
where TP is true positive, FP is false positive, FN
is false negative, and TN is true negative.
In order to obtaine more results, we per鄄
formed a third test series shown in Fig. 5. The
FAR, TRDR and the Accuracy were calculated for
each frame, and are shown in Tab. 1.
Fig. 4摇 Moving object detection with a presence of noise
3郾 2摇 Performance analysis
The improved background modeling method
is evaluated using the measures proposed by
Black, Ellis and Rosin [14] . Since we are only
comparing performance of detection in the case of
sudden illumination changes, we utilize just a
subset of the performance measures, namely
Fig. 5摇 Calculate alpha flow chart
tracker detection rate ( TRDR ) and the false
摇 摇 摇 摇
Tab. 1摇 FAR, TRDR and the accuracy for different frames
Frame
Accuracy
TRDR
Precision (1鄄FAR)
18
19
20
21
23
28
46
49
Fix
72郾 19
73郾 67
76郾 21
76郾 81
71郾 18
82郾 02
99郾 69
99郾 82
Changing
73郾 60
98郾 86
98郾 44
97郾 86
96郾 40
98郾 92
99郾 43
99郾 62
Fix
87郾 71
87郾 30
92郾 38
89郾 23
92郾 88
84郾 99
79郾 05
83郾 53
Changing
87郾 67
54郾 76
67郾 70
71郾 50
68郾 56
64郾 80
74郾 67
81郾 09
Fix
02郾 01
02郾 01
02郾 33
02郾 26
02郾 05
02郾 77
66郾 64
83郾 64
Changing
02郾 11
29郾 69
23郾 43
17郾 85
11郾 58
30郾 82
67郾 29
80郾 13
摇 摇 We tested our method in case of natural sud鄄
den change of illumination ( Fig. 6) . The first col鄄
umn is the frame number. The second one is the
original frame, and it is clear that we have a sud鄄
that we achieved a fast adaptation with the light鄄
ing change since the 19th frame, which is con鄄
firmed by the accuracy ( Fig. 7) , where we have
a fast adaptation, compared to the background
den change in illumination from the frame 15 to
detection with the GMM with fixed alpha. Final鄄
the frame 37. The third column is the background
ly, in Fig. 8 we see that the proposed method had
detection with fixed alpha, and the last column
ameliorated the false alarm rate.
shows results of the proposed method. It is clear
摇 摇
— 149 —
Journal of Beijing Institute of Technology, 2016, Vol. 25, No. 1
Fig. 7摇 Accuracy for the method with fixed alpha and the
method with adaptive alpha
Fig. 8摇 FAR for the method with fixed alpha and the
Fig. 6摇 Moving object detection in case of
method with adaptive alpha
natural sudden light changes
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4摇 Conclusion
We have presented an improved mixture
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( Edited by Cai Jianying)