image. This approach, called further Frame Difference, works with
some background changes but fails if the moving object stops sud-
denly. In [27], the authors suggest the initialization and mainte-
nance of the background model by the arithmetic mean (or
weighted mean) of the pixels between successive images. So, given
a video V with length l containing gray scale images defined by
V ¼fZ
1
; ...; Z
l
g, the background model B can be defined by:
B ¼
1
l
X
l
t¼1
Z
t
: ð1Þ
Typically Eq. (1) is used to initialize the background model.
1
How-
ever, after the initialization, to perform the background model main-
tenance, it is also common to use Eq. (1) recursively by:
B
t
¼ð1
a
ÞB
t1
þ
a
Z
t
; ð2Þ
where B
t
is the background model at time t 2f1; lgZ and
a 2½0; 1R is the learning rate. The main advantage of this meth-
od is the adaptive maintenance of the background model while
changes occur in the scene (see Fig. 1). Afterwards, [34] clarify that
some foreground pixels are included in the background model up-
date. To solve this issue, an adaptive-selective method is proposed.
In this approach, only the regions with no moving object are
updated.
After building the background model, the next step is the fore-
ground detection. The first and most common way is to compute
the absolute difference between the current frame and the back-
ground model, similarly to Static Frame Difference method. How-
ever, in this case the background model is continuously adapted
instead of a static image. The foreground detection can be per-
formed in other ways. More recent methods, such as
[1,24,23,26,46] suggest the use of color, texture and edges features
to improve the foreground detection. In [46], the authors present a
Table 2
Possible combinations of synthetic data generated for BMC, and their respective number.
Parameter Value Description Number
Scenes 1 Rotary 10
2 Street 10
Event types 1 Cloudy, without acquisition noise, as normal mode 4
2 Cloudy, with salt and pepper noise during the whole sequence 4
3 Sunny, with noise, which generates moving cast shadows 4
4 Foggy, with noise, making both background and foreground hard to analyze 4
5 Wind, with noise, to produce a moving background 4
Use cases 1 10 s without objects, then moving objects during 50 s 10
2 20 s without event, then event (e.g. sun uprising or fog) during 20 s, finally 20 s without event 10
Fig. 3. Examples of synthetic (top) and real (bottom) videos and their associated ground truth in the BMC benchmark.
Table 3
Parameter settings of each BS algorithm.
Method ID Settings
Basic methods, mean and variance over time
StaticFrameDifferenceBGS T ¼ 15
FrameDifferenceBGS T ¼ 15
WeightedMovingMeanBGS T ¼ 10
WeightedMovingVarianceBGS T ¼ 15
AdaptiveBackgroundLearning T ¼ 15;
a ¼ 0:5
DPMeanBGS
T ¼ 2700;
a ¼ 10
7
; LF ¼ 30
DPAdaptiveMedianBGS T ¼ 20; LF ¼ 30; SR ¼ 10
DPPratiMediodBGS T ¼ 30; SR ¼ 5; HS ¼ 16;
c ¼ 5
Fuzzy based methods
FuzzySugenoIntegral T ¼ 0:67; LF ¼ 10;
a
learn
¼ 0:5;
a
update
¼ 0:05; RGB þ LBP
FuzzyChoquetIntegral T ¼ 0:67; LF ¼ 10;
a
learn
¼ 0:5;
a
update
¼ 0:05; RGB þ LBP
LBFuzzyGaussian T ¼ 160; LR ¼ 150;
q ¼ 100;
r
¼ 195
Statistical methods using one Gaussian
DPWrenGABGS T ¼ 12:15; LF ¼ 30;
a ¼ 0:05
LBSimpleGaussian LR ¼ 50;
q ¼ 255;
r
¼ 150
Statistical methods using multiple gaussians
DPGrimsonGMMBGS T ¼ 9;
a ¼ 0:05; n ¼ 3
MixtureOfGaussianV1BGS T ¼ 10;
a ¼ 0:01
MixtureOfGaussianV2BGS T ¼ 5;
a ¼ 0:01
DPZivkovicAGMMBGS T ¼ 20;
a ¼ 0:01; n ¼ 3
LBMixtureOfGaussians T ¼ 80;
a ¼ 60; q ¼ 120;
r
¼ 210
Type-2 Fuzzy based methods
T2FGMM_UM T ¼ 1; K
m
¼ 2:5; n ¼ 3; a ¼ 0:01
T2FGMM_UV T ¼ 1; K
v
¼ 0:6; n ¼ 3; a ¼ 0:01
T2FMRF_UM T ¼ 1; K
m
¼ 2:0; n ¼ 3; a ¼ 0:01
T2FMRF_UV T ¼ 1; K
v
¼ 0:9; n ¼ 3; a ¼ 0:01
Statistical methods using color and texture features
MultiLayerBGS Original default parameters from [45]
Non-parametric methods
PixelBasedAdaptiveSegmenter Original default parameters from [22]
GMG T ¼ 0: 7; LF ¼ 20
1
Other authors such as McFarlane and Schofield [31], Prati et al. [33] and Calderara
et al. [9] suggests to use the median filter instead of the mean or average filter.
6 A. Sobral, A. Vacavant / Computer Vision and Image Understanding 122 (2014) 4–21
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