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Accepted Manuscript
A new Wronskian change detection model based codebook background subtraction for visual surveillance applications
Deepak Kumar Panda, Sukadev Meher
PII:
DOI:
Reference:
S1047-3203(18)30186-X
https://doi.org/10.1016/j.jvcir.2018.07.014
YJVCI 2248
To appear in:
J. Vis. Commun. Image R.
Received Date:
Revised Date:
Accepted Date:
9 May 2017
29 November 2017
27 July 2018
Please cite this article as: D.K. Panda, S. Meher, A new Wronskian change detection model based codebook
background subtraction for visual surveillance applications, J. Vis. Commun. Image R. (2018), doi: https://doi.org/
10.1016/j.jvcir.2018.07.014
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A new Wronskian change detection model based codebook background subtraction for
visual surveillance applications
Deepak Kumar Panda, Sukadev Meher
National Institute of Technology Rourkela, 769008, Odisha, INDIA
Abstract
Background subtraction (BS) is a popular approach for detecting moving objects in video sequences for visual surveillance applications. In this paper, a new multi-channel and multi-resolution Wronskian change detection model (MCMRWM) based codebook
background subtraction is proposed for moving object detection in the presence of dynamic background conditions. In the proposed
MCMRWM, the multi-channel information helps to reduce the false negative of the foreground object; and the multi-resolution data
suppresses the background noise resulting in reduced false positives. The proposed algorithm considers the ratio between feature
vectors of current frame to the background model or its reciprocal in an adaptive manner, depending on the l2 norm of the feature
vector, which helps to detect the foreground object completely without any false negatives. Extensive experiments are carried out
with challenging video sequences to show the efficacy of the proposed algorithm against state-of-the-art BS techniques.
Keywords: Visual surveillance, Moving object detection, Background subtraction, Dynamic backgrounds, Wronskian change
detection model, Codebook model.
1. Introduction
5
10
15
20
Detection of moving objects in video sequences has numerous applications such as: visual surveillance, traffic control and 30
surveillance, machine vision applications, optical motion capture, object-based video coding, multimedia applications, face
and gait recognition and activity recognition. Moving object
detection is the first step; and hence, accurate classification of
pixels with lowest false error is very crucial for the overall suc- 35
cess of these applications. The most widely used technique
in the presence of a static camera is background subtraction
(BS), which detects moving object by comparing every incoming frame with the up-to-date (learnt) statistical background
model and classifies moving object which appreciably deviates 40
from the model. However, the job is not so easy as it seems to
be. This is because backgrounds are changing and are usually
multi-modal in nature. Some examples of such changing background are: waving trees or bushes, flag fluttering in the wind,
ripples in water bodies, ocean waves and spouting fountain. Be- 45
sides, there is illumination variation, relocation of background
object and initialization of background model with moving objects. Foreground objects moving with different velocity and
shadows cast by them are some of the other canonical challenges.
50
2. Related works
25
Several researchers have studied and published different BS
algorithms for tackling many background challenges as sur55
Email address: deepakkumar.panda@gmail.com (Deepak Kumar
Panda, Sukadev Meher)
Preprint submitted to Journal of Visual Communication and Image Representation
veyed in [1–4]. BS techniques can be classified into basic background modelling [5], statistical background modelling [6–10],
fuzzy background modelling [11–16] and histogram modelling
[11, 12, 17–19], depending on the methodology used to represent the background model. Some of the researchers have categorized BS techniques into pixel-based or region-based techniques, depending on whether the feature used for background
modelling is calculated at the pixel-level [5–8, 13, 20] or regionlevel [11, 12, 14, 17–19]. Depending on the number of features used in background modelling, BS techniques can also be
classified into single-feature [6] or multi-feature. Further, BS
techniques can be divided into single [5–8, 13, 14, 20] or multimodal [17–19, 21–29] techniques, depending on the number of
background distributions used for background modelling. Multimodal BS techniques can handle dynamic environment such
as swaying of leaves, spouting fountain and ripples in water
surface better than single modal BS schemes. First, uni-modal
BS techniques are described followed by multi-modal BS techniques.
Wren et al. [6] have modelled each pixel using single Gaussian distribution. The parameters of Gaussian (i.e. mean and
variance) are learnt from temporal history. The background at
each pixel is modelled by fitting a Gaussian probability distribution function (PDF). A pixel will be labelled as foreground if
it does not belong to the PDF. It is well suited for indoor environments but fails in outdoor scenes. Σ − ∆ estimation (SDE)
[5] proposed by Manzanera and Richefeu increments or decrements the background model by one if the incoming pixel is
greater or less than the corresponding background pixel. The
model is simple to implement and easy to execute. However,
it fails in the presence of dynamic scenes. The W 4 system [7]
November 29, 2017
60
65
70
75
80
85
90
95
100
105
110
proposed by Haritaoglu et al. models the background using the115
minimum and maximum gray values. Like the previous background models, this also fails in the presence of non-stationary
background, as the threshold for change detection is decided
by the median of maximum absolute difference between pixels of consecutive frames. Julio [20] et al. have improved the120
W 4 technique by modelling the background using the intensity
range calculated from the minimum and maximum intensity
values. The technique was further modified by Hati et al. [8].
However, all these techniques fail in the presence of dynamic
background as there is no regular background update scheme125
involved.
Durucan and Ebrahimi [9] detected moving object using
Wronskian change detection model (WM). It yields an accurate
result in the presence of noise and illumination variation. However, the background model is chosen from the first frame of130
the video, and there is no background updating scheme and no
adaptive threshold is employed. Robust BS under Wronskian
framework with an adaptive threshold is proposed by Badri et
al. [30]. However, WM considers only the ratio of pixels of the
current frame to the background frame and not its reciprocal.135
Panda and Meher [31] have proposed a simple BS technique by
integrating WM in a single Gaussian distribution. The model
parameters are updated using a Gaussian weighted learning rate
for every linearly dependent pixel.
Visual background extractor (ViBe) [10] is a non-parametric140
pixel-based classification technique. The algorithm is a computationally efficient and can be initialized from the first frame.
The algorithm considers the spatial redundancy and builds the
background from the centre pixel or pixels in the neighbourhood. The background update is different from the conventional145
first-in-first-out strategy and uses random sampling values. Baf
et al. have proposed fuzzy-based BS using colour similarity
measure [13]. Also, authors have integrated both colour and
texture feature [14]. Here, instead of giving equal weight to
features, fuzzy aggregation of features is done using Choquet150
integral. Zhang and Xu have combined both colour and texture using Sugeno integral [32]. The use of correlogram in BS
is reported in [33]. Correlogram captures the pixel-relation of
the two pixels at a specified distance. The authors have further
proposed multi-channel correlogram [15] using inter-channel155
and intra-channel correlogram to exploit inter-relation of pixels on the same and across the colour channels. To reduce the
dimension of correlogram feature vector, fuzzy correlogram is
proposed. Mason and Duric [34] modelled background using
colour and edge histograms. Foreground detection is done by160
comparing colour and edge histograms computed in a local region between the background model and the current image using histogram intersection and chi-squared distance. Kim and
Kim [11] explored the use of fuzzy colour histograms in BS.
Panda and Meher [12] have proposed dynamic texture BS us-165
ing fuzzy colour difference histogram. It is a region-based approach, where the colour difference between pixels is measured
in a local neighbourhood. The variation of pixel intensity due
to illumination and non-stationary background is made minimal
by modelling the background using the difference of intensity170
values. A new fuzzy texture feature is proposed in [35] which
2
is calculated from gray-level co-occurrence matrix. To reduce
the dimension of the feature, Chiranjeevi and Sengupta have
calculated features from fuzzy co-occurrence matrix. The features are intensity, energy, local homogeneity and x-directional
mean.
Multi-modal BS techniques are well suited for the dynamic
environment as each background corresponds to a changing environment. However, this comes at the cost of an increase in
computational complexity, memory requirement and a decrease
in processing speed. Stauffer and Grimson [21] have proposed
multi-modal BS where each pixel is modelled using Gaussian
mixture model (GMM). It has remained popular and widely
used algorithm for the last two decades. However, challenges
such as heavy cluttered environment, shadow cast by object and
foreground objects moving with different velocities make the
algorithm inefficient. Further, the assumption that backgrounds
are Gaussian may not always hold. Many researchers have improved and extended the GMM algorithm [2]. The number of
Gaussians in GMM is automatically decided by Zivkovic and
Heijden [22] algorithm.
To overcome limitations of GMM, a non-parametric BS using kernelized GMM is proposed in [23]. It models PDFs at
each pixel from temporal samples using kernel density estimation. However, the algorithm is computationally intensive and
requires large memory. The bandwidth of kernel estimation is
also fixed. An improved kernel density estimation with variable
kernel bandwidth is proposed in [25]. A non-parametric codebook BS is proposed in [24]. It is efficient in memory and has
high processing speed. Temporal pixel values are represented
as a codebook, which consists of one or more codewords depending on the pixel variation. Foreground detection is done by
comparing current pixel’s codeword with the codeword stored
in the codebook using pixel-level detection scheme. The algorithm can cope up with slow changes in the background but
fails in fast changing backgrounds. In a similar approach to
codebook BS, Yao and Odobez [36] have proposed multi-layer
BS based on colour and texture. RGB vector is used as colour
feature and texture is represented by local binary pattern (LBP).
Dynamic background subtraction based on invariant moments
(Hu set) is proposed in [26]. Here, each pixel is modelled as a
set of moments which are calculated in a local region and are
clustered into the codebook.
Hierarchical codebook model is proposed in [27] which uses
12 intensity values to represent a block. The multi-feature concept used here extends the concept of block truncation coding. First, the block removes most of the background and gives
coarse detection of the foreground object. To get the fine silhouette of foreground object, a pixel-level detection is performed.
It is very hard to get the proper block size for coarse detection. To overcome this limitation, multilayer codebook model
for moving object detection is proposed in [28] with three adaptive block sizes. Instead of using 12 intensity values, the authors
have represented block using 3 features i.e mean of each channel of the colour image.
Heikkila and Pietikainen [17] have proposed multi-modal
BS using LBP histogram which is computed in a circular region. The foreground detection is done by comparing the back-
Table 1: Description of different Wronskian change detecton model based BS
175
180
185
190
195
200
205
210
Authors
Title
E.
Durucan and T.
Ebrahimi [9]
Change detection and background
extraction by linear algebra.
B. N. Subudhi,
S.
Ghosh and A.
Ghosh [30]
Change detection for moving object segmentation with robust background construction under Wronskian framework.
D. Panda and
S. Meher [31]
Video object segmentation based
on adaptive background and Wronskian change detection model.
Remarks
It is a simple background subtraction technique where each current frame is compared with the reference background frame
using Wronskian model. Here, background frame is not updated rather the first
frame is chosen as reference frame.
Robust background construction under Wronskian framework with adaptive
threshold. Here, the background is updated
and an adaptive threshold is proposed.
A simple BS technique by integrating
Wronskian change detection model in a
single Gaussian distribution. The model
parameters are updated using a Gaussian
weighted learning rate for every linearly
dependent pixel.
ground model with the LBP histogram of the current frame using histogram intersection. Zhang et al. [18] have extended
the spatial LBP to temporal-domain for background modelling.
The basic LBP operator produces large histogram bins for similarity comparison and is very sensitive to noise; even a small
215
change in and around the central pixel changes the LBP code.
Zhang et al. [19] have proposed dynamic BS where each pixel
is modelled as a weighted local dependency histogram (LDH)
which explores spatial dependencies between the centre pixel
and the neighbouring pixels.
Zhang et al. [29] have integrated both pixel-level and region-220
level feature using covariance matrix descriptor. Each pixel is
modelled as a group of weighted adaptive covariance matrices.
Chiranjeevi and Sengupta [37] have proposed covariance-based
dynamic background subtraction using multiple features calculated from the gray level co-occurrence matrix. Each pixel is225
modelled with a mean feature vector and covariance matrix descriptor. Mahalanobis distance measure is used to calculate the
distance between the current frame and the background model.
An improved local Hu moment based GMM BS is proposed
in [38] where the moment is calculated in a weighted manner230
to reduce the effects of background moving pixels. A neighbourhood supported model level fuzzy aggregation based BS is
proposed in [16]. The multiple features consist of both intensity and spatial textural features. The spatial textural features
are calculated from gray-level co-occurrence matrix which con-235
sists of local homogeneity, energy, and the x-directional mean.
The fuzzy aggregation of features is done using both Choquet
and Sugeno integral. Authors have demonstrated the better performance of Choquet over Sugeno. The model of the algorithm
is initialized from the neighbourhood pixels for faster convergence.
The review of the literature reveals that most of the tech-240
niques fail to handle illumination variation and multi-modal
backgrounds like swaying vegetation and ripples in water surface. The original Wronskian change detection model (WM) is
computed from a single (gray-scale) image and does not use the
multi-channel and multi-resolution properties of an image. WM
uses either the ratio between feature vectors of current frame to245
the background model or its reciprocal; due to which, it fails
to detect foreground object accurately and results in false negative. A comparative study of different WM based BS is reported
in Table 1. The traditional codebook BS algorithm is a pixel3
Figure 1: Region of support at pixel location (x, y).
based foreground detection algorithm; and as a result, it reports
an increase in false positives for the multi-modal backgrounds.
The proposed algorithm addresses these challenges. It is
a statistical, region-based, multi-feature and multi-modal BS
technique. The contribution made in this paper are:
1. A new multi-channel and multi-resolution Wronskian change
detection model (MCMRWM) based codebook (CB) BS
technique is proposed for effective detection of moving
objects in the presence of dynamic environment.
2. Multi-channel information is employed to reduce the false
negative of the foreground object; while multi-resolution
information is utilized to suppresses background noise to
reduce false positives.
3. To determine Wronskian, either the ratio between feature
vectors of current frame to the background model or its
reciprocal is applied in an adaptive manner, depending on
the l2 norm of the feature vector, to detect the foreground
object completely without any false negatives.
The rest of the paper is organized as follows. In Section 3,
the proposed MCMRWM and its integration with CB framework are reported in detail. The qualitative and quantitative
results and its discussion are reported in Section 4 and finally,
Section 5 concludes the work done and presents future research
directions.
3. Proposed method
First, the basic Wronskian change detection model (WM) is
presented in Section 3.1. Then, the proposed multi-channel and
multi-resolution Wronskian change detection model (MCMRWM)
is illustrated in Section 3.2. In Section 3.3 the proposed MCMRWM is used for foreground detection using the CB technique.
3.1. Wronskian change detection model (WM)
Durucan and Ebrahimi [9] have proposed Wronskian change
detection model (WM) for detecting change between two pixels. In this model, each pixel is associated with spatial neighbourhood known as region of support. The region of support
Figure 2: Block diagram of the proposed multi-channel and multi-resolution feature vector calculation for WM.
250
255
260
265
270
can have various dimensions (e.g. 3 × 3, 5 × 5, 7 × 7). Figure 1 shows a 3 × 3 region of support for a pixel located at
(x, y). Therefore, each pixel is related to a vector which consists of central pixel and neighbouring pixel and is generated by
a row-major ordering of a region of support. To detect change
between two pixels, a linear independence test is carried out by275
the vectors of corresponding pixels. If a pixel is found to be linearly independent, then the pixel is considered to be foreground
or else background.
To check linear dependence or independence of vectors, the
simple test is to calculate the Wronskian function. If the vector
is linearly dependent, then the determinant of the Wronskian
matrix, W will reduce to zero; else it is linearly independent
[9].
280
The Wronskian is a determinant of two differentiable functions B(E) and I(E) given by:
B I W(B, I) = 0 0 (1)
B I where B(E) and I(E) represent the reference background and
the current frame of a video sequence, respectively. B(E) and285
I(E) are functions of illuminance E and their derivatives are
given by B0 = dB/dE and I 0 = dI/dE.
W(B, I) = BI 0 − IB0
(2)
4
On solving, Wronskian matrix reduces to the form [9]:
!
B 2
B
W(B, I) =
−
I
I
(3)
If the region of support for every pixel is incorporated in (3),
then the WM can be represented in terms of vector image model:



n
~ j) 2
~ j) 
B(
1 X  B(



 −
(4)
W =
n j=1  ~It ( j)
~It ( j) 
where n represents the number of elements in the vector image,
j refers to the element or the component of the vector image and
t denotes the time instant or the frame number. The factor 1/n is
incorporated to normalize the results to the vector dimensions
so that the same threshold can be applied for different vector
dimensions.
The WM can also be expressed by the ratio of current pixel
to the background pixel, i.e


2
n
~It ( j) 
1 X  ~It ( j) 


 −
W =
(5)
n j=1  B(
~ j)
~ j) 
B(
(a)
(b)
(c)
(d)
(e)
Figure 3: Illustration of multi-resolution in Wronskian change detection scheme: (a) Original, (b) Ground truth, (c) WM using Gaussian filtered image at σ =
[0.5, 1, 1.5], (d) WM using Gaussian filtered image at σ = [0.75, 1.5, 2.25], (e) WM using Gaussian filtered image at σ = [1, 2, 3].
3.2. Multi-channel and multi-resolution Wronskian change detection model (MCMRWM)
290
295
300
WM [9] uses single channel (gray-scale) information for de-315
tecting the change between the vectors of two pixels. It uses the
concept of linear dependence or independence of vectors to test
whether the pixel has undergone any change or not. However, it
fails to utilise the multi-channel information of an image due to
which it loses colour information in change detection. The pro-320
posed algorithm uses multi-channel information of an image,
which helps to detect the moving object, when there is colour
similarity between the foreground and the background pixels.
This helps to reduce the total false negative detections.
To extend the conventional WM to MCMRWM, the input
image is segregated into three colour channels. From each chan-325
nel, three levels of multi-resolution images are generated using
a 2D circular symmetric Gaussian filter bank which is expressed
as follows:
g(x, y, σ) =
305
310
1 −( x2 +y2 )/2σ2
e
2πσ2
(6)
330
where (x, y) is the spatial coordinate, σ represents the spread
(standard deviation) of the filter kernel that controls the low
pass cut-off frequency which in turn, controls the blur. This results in different resolution outputs of a given image by varying
335
σ.
The Gaussian filtered images of a given input image are calculated as follows:
GF (σ) = g(x, y, σ) ∗ I(x, y)
(7)
340
where ∗ indicates the convolution operation.
5
After calculating three multi-resolution planes at σ1 , σ2 and
σ3 for each of the channels in the Gaussian filtered image, every
frame of the video will produce nine 2-dimensional planes. For
each pixel in the nine planes, mean is computed in a 3×3 spatial
neighbourhood. This is done to remove small amount of noise
associated with the pixel and removes false errors in the final
segmented result. Thus, the feature vector at each pixel can be
represented as follows:
n
o
~x = R̄σ1 , R̄σ2 , R̄σ3 , Ḡσ1 , Ḡσ2 , Ḡσ3 , B̄σ1 , B̄σ2 , B̄σ3
(8)
where R̄σ , Ḡσ and B̄σ are the means of a pixel calculated in a
3 × 3 spatial neighbourhood for R, G, and B channels of the
Gaussian filtered colour image at three different resolutions of
σ1 , σ2 and σ3 , respectively. The proposed scheme of getting
multi-channel and multi-resolution feature vector is presented
in Figure 2.
The human visual system (HVS) works similar to the Gaussian filter bank. The eyes see the distant object with background
blur, and the focus is on the foreground object, i.e., the Gaussian filter is blurred with higher σ. As the observer goes near
to it, the foreground object and the background are seen clearly,
i.e., Gaussian blur filter with lower value of σ is employed.
This multi-resolution capability of HVS is implemented in our
proposed algorithm by employing three different standard deviations.
The three multi-resolution output images of a Gaussian filter correspond to the variation of background pixel in the dynamic environment. At lower σ, the output of the Gaussian
filter contains rich information about the image. But as σ increases, the Gaussian filter blurs the background more and makes
(a)
(b)
(c)
(d)
(e)
Figure 4: Illustration of the proposed multi-channel and multi-resolution Wronskian change detection scheme: (a) Original, (b) Ground truth, (c) WM using (9), (d)
WM using (10), (e) Proposed WM using (11).
345
350
355
360
the image insensitive to noise and insignificant movement in a
dynamic background environment. The proposed algorithm is
tested on three different sets of σ, and their segmented results
on “WavingTrees” (WT) [39] and “Canoe” [40] sequence are
shown in Figure 3.
To detect the change between the feature vectors of background model and the current frame, a linear independence test
is conducted using the Wronskian function given in (4). Here,365
the proposed MCMRWM algorithm can be computed at a given
pixel by:


!2
n
~xtB ( j) 
1 X  ~xtB ( j)

W =
−
(9)

n j=1  ~xt ( j)
~xt ( j) 
370
where ~xtB and ~xt are the features of the background model and
current frame respectively, t represents the frame number and
n represents the number of features in the vector image. The
factor (1/n) is incorporated to normalize
375
the results.
Hoever, problem may arise if ~xtB ≥ ~xt i.e. feature
vector of current frame contains higher intensity values than
the feature vector of background models. Under such circumstances, the above equation is modified as:


380
!2
n
~xt ( j) 
1 X  ~xt ( j)
W =
− B 
(10)
 B
n i=1 ~xt ( j)
~xt ( j)
6
In order to avoid ambiguity, a generalized MCMRWM rule
can combine the above two cases, in the following way.
!

n B 2

~xt ( j)
~xtB ( j)

1 P

~xtB ≥ ~xt 
−
,

~xt ( j)
 n i=1 ~xt ( j)

!
W= 
(11)
2
n 

~x( j)
~xt ( j)

1 P

−
,
otherwise

B
B
 n
~x ( j)
~x ( j)
i=1
t
t
To realize the limitations of the WM rules given in (9) and
(10) and therefore to understand the significance of the proposed rule given in (11) a simulation study is carried out with
four different video sequences: “WavingTrees” [39], “Fountain
with swaying leaves” [41], “WavingLeaves” [41] , “Campus”
[42] and “Lobby” [42]. The results are shown in Figure 4.
Original sequence and ground truth are shown in the Figure
4(a) and Figure 4(b) respectively. The proposed MCMRWM
algorithm’s detection result using (9) and (10) are shown in the
Figure 4(c) and Figure 4(d) respectively. Interestingly, the WM
using (9) detects light coloured pixel of the background to the
dark coloured pixel of the current frame whereas the WM using
(10) detects light coloured pixel of the current frame to the dark
coloured pixel of the background. The foreground segmentation result using the proposed WM given in (11) is adaptive
and takes both the situations into consideration and hence performs equally well in both the conditions which is evident from
the foreground segmented result shown in Figure 4(e). This
420
425
430
experiment demonstrates the superior performance of the proposed modified WM rule compared to the conventional WM
rule. Hence, this modified rule will be employed in subsequent
development of BS algorithm in this paper.
The proposed codebook based BS consists of following three
sub steps as shown in Figure 5.
1. Background modelling,
2. Foreground detection,
3. Background maintenance.
405
410
415
(13)
3.3.1. Background modelling
The first step in BS is background modelling, and its performance totally depends on the choice of feature used for background construction. This is an important step for the robust
detection of foreground objects.
445
In this paper, background modelling is done using codebook
model which is a collection of codewords : C = {c1 , c2 , ..., cL }.
Here, C is the codebook, c is the codeword and L is the number of codewords present in the codebook. Each codeword
ci , i = 1, ..., L, consists of feature vector vi = (x) and a 4-tuple
auxi = h fi , λi , pi , qi i. The feature vector consists of nine mean
intensity values calculated in a 3 × 3 spatial neighbourhood for450
each channels of the Gaussian filtered colour image at three
different resolutions σ1 , σ2 and σ3 , Frequency, f is the number
of occurrences of the codeword. The maximum interval during
which the codeword has not repeated is represented by λ, which
is also known as maximum negative run-length. p and q denote455
time instants when the codeword has been accessed first time
and last time, respectively.
Let {x1 , x2 , ..., xN } be the N training samples used for background modelling. For every feature vector present in the training sample, a linear independence test is carried out with all the460
codewords present in the codebook using (11).
A feature vector is said to be linearly dependent if the multichannel Wronskian change detection model is less than or equal
7
(14)
Codewords, whose maximum negative run-length are higher
than T M are deleted from the codebook. Here, T M is a predefined constant and is set to N/2. Then, the final, refined codebook, M is formed by:
M = {ci |ci ∈ C ∧ λi ≥ T M }
440
400
v L = xt
auxL = h1, t − 1, t, ti
λi = max {λi , (N − qi + pi − 1)} .
435
395
(12)
The maximum negative run-length, λ of all the codewords
are updated after the completion of the background training as
3.3. Background subtraction (BS)
390
vi = (1 − α)vi + αxt
auxi = h fi + 1, max {λi , t − qi } , pi , ti
If the codebook is empty i.e. C = φ and L = 0 or the
feature vector is linearly independent, then a new codeword will
be added to the codebook and length of the codebook will be
incremented.
Figure 5: Block diagram of the proposed multi-channel and multi-resolution
Wronskian change detection model based codebook background subtraction
scheme.
385
to some constant threshold (th1 ). Otherwise, it is linearly independent. If the feature vector is found to be linearly dependent, then the corresponding codeword is updated. Instead of
finding the linearly independence test with all the codewords in
the codebook, the first linearly dependent codeword from the
codebook is selected and its value is updated according to the
following rule.
(15)
In busy railway station, public offices, or in the marketplace it is
very hard to train the background model in the presence of foreground object because clean background image is not available.
The last step of the background modelling i.e. codebook filtering ensures that even if the foreground object is present in the
initial codebook training, its codeword will be discarded from
the codebook and the background model can be made free of
moving foreground object.
3.3.2. Foreground detection
In this step, detection of moving object is done using the
multi-channel Wronskian change detection model. This step is
done after the completion of N training frames i.e. after background modelling. Here, sensitivity of the moving object detection is very crucial. The feature vector of the current frame
is used to test whether it is linearly dependent or independent
with the codewords in the codebook using (11).
If the value of multi-channel Wronskian change function is
less than some constant threshold (th2 ), feature vector is linearly dependent; else linearly independent. Here, th2 is chosen
less than th1 for refinement of foreground pixel. If the feature is
found to be linearly dependent with the codeword in the codebook, then the first linearly dependent codeword is chosen for
updation using (12) and the pixel is labelled as “background”.
If the feature vector is found to be linearly independent with all
the codewords, then the pixel is classified as “foreground”.
(a)
(b)
Figure 6: Flow chart of the proposed multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction scheme: (a)
training stage, (b) testing stage.
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470
475
480
485
3.3.3. Background maintenance
To make the detection of foreground object possible in all
seasons and day and night using the BS technique, the maintenance of the background is important for keeping abreast to
the changes in the environment. A foreground object which has490
been moving and has recently become stationary should be detected as background. Similarly, the background object which
has been stationary during codebook training but has recently
started moving should be classified as foreground. These are
some of the examples where updation of background becomes
an essential and mandatory step. To develop such a robust tech-495
nique, the current pixels should be compared with the up-todate background model for correct detection of a moving object.
A new model cache similar to the codebook is created for
storing codewords of foreground pixel. The feature vector of
the current frame is compared with the codewords in cache us-500
ing multi-channel Wronskian function given in (11). If feature
vector is found to be linearly dependent then the codeword is
updated using (12). If the feature vector is found to be linearly
independent with all the codewords or the codebook is empty,
then a new codeword is added to the cache using (13).
8
Alike background training of codebook, refinement of cache
is done by deleting codewords with higher maximum negative
run-length. This step is done to remove foreground codeword
which has become stationary or to remove occasionally codewords which were classified as “foreground”.
H = H − {hi |hi ∈ H ∧ λi ≥ T H }
(16)
where H represents the final cache after refinement of codewords with higher maximum negative run-length and after deletion.
If the codewords from cache are frequently reoccurring, then
the codewords are added to the codebook.
M = M ∪ {hi |hi ∈ H ∧ fi ≥ T add }
(17)
The length of the codebook and cache are updated accordingly.
At last, codewords from codebook, whose maximum negative run length (λi ) is high are deleted. The codeword with large
λi have every chance to be foreground codeword.
M = M − {ci |ci ∈ M ∧ λi ≥ T delete }
(18)
The proposed algorithm is summarised in Algorithm 1 and
flow chart is shown in Figure 6.
505
Algorithm 1 Algorithm for the proposed multi-channel and
multi-resolution Wronskian change detection model based
510
codebook background subtraction.
for each training sample do
for each codeword in the codebook do
Calculate multi-channel and multi-resolution Wronskian change detection model
if multi-channel and multi-resolution Wronskian is515
less than threshold then
Update the codeword
end if
end for
520
if no match is found or codeword is empty then
Add a new codeword
end if
end for
Delete codeword from codebook whose maximum-negativerun-length is high
525
for each testing pixel do
for each codeword in the codeebook do
Calculate multi-channel and multi-resolution Wronskian change detection model
if multi-channel and multi-resolution Wronskian is
less than threshold then
Label pixel as background
Update the codeword
530
end if
end for
if no match is found then
Label pixel as foreground
for each codeword in the cache do
Calculate multi-channel and multi-resolution
Wronskian change detection model
535
if multi-channel and multi-resolution Wronskian
is less than threshold then
Update the codeword in the cache
end if
end for
if no match is found or cache is empty then
Add a new codeword to the cache
end if
end if
Delete codeword from cache whose maximum-negative-540
run-length is high
Move the frequently reoccurring codeword in the cache
to codebook
Delete codeword from codebook whose maximumnegative-run-length is high
end for
545
9
4. Results and discussions
The proposed technique is implemented in MATLABR , running on a 32-bit Windows7TM platform with IntelR CoreTM i52400 CPU @3.10 GHz, 3.10 GHz and 4 GB RAM. The multiresolution feature is calculated by varying the values of σ in
the Gaussian filter bank. The choice of σ depends on the extent of background clutter as shown in Figure 3. The number
of training frames (N) has been taken as 100 whereas the BS
parameters are assigned different values i.e. T M = 50, T H = 50,
T add = 200, T delete = 200 [27, 28]. All the parameters are
kept constant during the experiment except th, which is chosen
empirically. The performance of the proposed BS algorithm is
evaluated on publicly available video sequences to show its efficacy in the different challenging environments, and the results
are compared with state-of-the-art BS schemes.
To evaluate the proposed algorithm in an objective way, accuracy metrics like Recall, Precision, F1 , Similarity, Matthew’s
correlation coefficient (MCC), and Percentage of correct classification (PCC) are employed. They are defined in the following
subsection.
4.1. Accuracy metrics
Precision, also known as the positive prediction, which is
the ratio of detected true positives to the total number of foreground pixels detected by the algorithm. It is defined as:
Precision =
tp
tp + fp
(19)
Recall, also known as detection rate. It is the ratio of detected
true positives to the total number of foreground pixels present
in the ground truth.
Recall =
tp
t p + fn
(20)
F1 metric, also known as Figure of Merit or F-measure. is the
weighted harmonic mean of Precision and Recall.
F1 =
2 ∗ Recall ∗ Precision
Recall + Precision
(21)
Similarity measure is defined as:
S imilarity =
tp
t p + fn + f p
(22)
Matthew’s correlation coefficient (MCC) is defined as:
(tp × tn) − ( f p × f n)
MCC = p
(23)
(tp + f p) × (tp + f n) × (tn + f p) × (tn + f n)
Percentage of correct classification (PCC), given by:
PCC =
t p + tn
× 100.
t p + tn + f p + fn
(24)
where t p (true positive) represents the number of pixels classified correctly as foreground, tn (true negative) counts the number of background pixel classified correctly, f p (false positive)
is the number of pixels that are incorrectly classified as foreground, and fn (false negatives) represent the number of pixels
Table 2: Description of video sequences
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Video
Resolution
NoOfFrames
Environment
Camouflalge (CF)
160 × 120
353
Indoor
Curtain (CU)
160 × 128
2965
Indoor
Fountain (FO)
160 × 128
523
Outdoor
OceanWaves (OW)
720 × 480
903
Outdoor
PETS2006 (PE)
720 × 526
3021
Indoor
WaterSurface (WS)
160 × 128
633
Outdoor
WavingTrees (WT)
160 × 120
287
Outdoor
Boats (BO)
320 × 240
7999
Outdoor
Canoe (CN)
320 × 240
1189
Outdoor
Fountain02 (FO2)
432 × 288
1499
Outdoor
Highway (HI)
320 × 240
1700
Outdoor
Office (OF)
360 × 240
2050
Outdoor
which are wrongly labeled as background but should have been
classified as foreground. The confusion matrix for the background subtraction is shown in Table 3. All of the above metric
uses manually segmented ground-truth images of foreground
objects.
Table 4: Video sequence and associated challenges.
Associated background challenges
Colour similarity
Swaying vegetation
Moving of Venetian blinds
Spouting fountain
Ripples in water surface
Illumination variation
Crowded public place
Highway
Foreground is static for a while
Table 3: Confusion matrix for background subtraction
Algorithm result
Foreground
Background
Ground truth
Foreground
Background
TP (True Positive)
FP (False Positive)
FN (False Negative) TN (True Negative)
4.2. Dataset
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560
565
Description
A person is seen coming in front of flickering monitor.
Persons are seen walking past the Venetian
blinds.
People are walking at the backdrop of
spouting fountain.
A person is seen walking in the sea shore.
People are walking in the platform of a railway station.
A person is seen moving on the bank of
water surface.
A person is walking in the backdrop of
waving tree.
Boats are sailing on the river and vehicles
are passing by.
Canoe is sailing in the midst of ripples in
water surface and swaying of vegetation.
Spouting fountain and vehicles are seen
passing by behind the fountain.
Vehicles are moving on the road and there
is small swaying of leaves.
A person comes to office and takes out a
book and read it for a while.
The proposed algorithm is evaluated on video sequences
which are publicly available for research purposes. The test sequence “Camouflage” (CF) and “WavingTress” (WT) are taken
570
from Wallflower dataset [39]. The frames of “Curtain” (CU),
“Fountain” (FO) and “WaterSurface” (WS) are downloaded from
I2R database[42]. The test sequence “OceanWaves” (OW) has
been taken from [41]. The PETS2006 sequence has been taken
from PETS dataset [43]. The video sequence “Boats” (BO),
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“Canoe” (CN), “Fountain02” (FO2), “Highway” (HI) and “Office” (OF) are downloaded from CDNET [40, 44]. The description of the video sequences is reported in the Table 2. The challenges associated with each of the video sequences used in the
experimental study has been summarised in Table 4.
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10
Video sequence
CF
WT
CU
FO, FO2
OW, WS,BO, CN
LO
PE
HI
OF
4.3. Performance comparison between MCMRWM and different WM based BS methods
The proposed algorithm has been evaluated with Wronskian
function based BS schemes such as Wronskian change detection model (WM) [9] and robust background construction under
Wronskian framework (RBCWM) [30]. The video sequences
used for the evaluation are “Camouflage”, “Curtain”, “Fountain”, “OceanWaves”, “PETS2006”, “WaterSurface” and “WavingTrees”.
The qualitative comparison of the proposed MCMRWM algorithm with WM and RBCWM is shown in Figure 7. The
WM scheme works well with CF, CU, FO, OW, PE, WS and
WR sequences. However, it fails to detect the foreground object
in case of WT sequence. The results obtained from RBCWM
technique fails to segment foreground object in each of the test
sequences. The performance of the proposed algorithm is shown
in Figure 7(e). It clearly shows better-segmented results than
(a)
(b)
(c)
(d)
(e)
Figure 7: Illustratin of the proposed multi-channel and multi-resolution Wronskian change detection scheme with different WM based BS schemes: (a) Original,
(b) Ground truth, (c) WM, (d) RBCWM, (e) Proposed.
WM and RBCWM on each of the video sequences.
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590
595
600
Figure 8: Average quantitative metrics for the proposed MCMRWM with different WM based BS schemes.
11
The quantitative comparison of MCMRWM with WM and
RBCWM algorithms are reported in Table 5. The WM scheme
reports higher recall for PE frames whereas the proposed MCMRWM algorithm exhibits higher values for each of the accuracy metrics across all the video sequence. The RBCWM algorithm shows lesser performance as compared to WM and
MCMRWM.
The average quantitative metrics for MCMRWM with WMbased BS algorithms across each of the dataset (CF, CU, FO,
OW, PE, WS and WT) are shown in Figure 8. The values of
PCC metric are normalised for fair comparison with other metrics. The values clearly indicate that performance of MCMRWM is better than WM and RBCWM schemes.
The proposed MCMRWM scheme performs better than WM
and RBCWM due to the adaptive nature of the proposed adaptive Wronskian rule given by (11). In addition to this, the multichannel and multi-resolution features of the image give an accurate silhouette of the foreground object. The multi-channel
information helps to reduce the false negative of the foreground
object, and the multi-resolution data suppresses the background
Table 5: Performance evaluation of MCMRWM with different WM based BS
schemes.
Videos Algorithm Precision Recall F1
Similarity MCC PCC
CF
CU
FO
WM
0.878
0.932 0.896 0.841
0.830 91.500
RBCWM
0.460
0.132 0.196 0.110
-0.029 48.989
MCMRWM 0.937
0.995 0.965 0.932
0.930 96.563
WM
0.824
0.788 0.794 0.681
0.784 96.907
RBCWM
0.176
0.502 0.259 0.154
0.180 74.834
MCMRWM 0.857
0.924 0.886 0.805
0.878 98.138
WM
0.499
0.704 0.576 0.413
0.571 96.444
RBCWM
0.030
0.382 0.055 0.028
-0.029 53.374
MCMRWM 0.796
0.991 0.883 0.790
0.879 98.060
WM
0.594
0.624 0.549 0.425
0.548 97.850
0.274
0.438 0.266 0.083
0.127 85.290
MCMRWM 0.646
0.730 0.627 0.525
0.629 98.377
OW RBCWM
PE
WS
WT
605
WM
0.605
0.854 0.700 0.552
0.701 97.333
RBCWM
0.045
0.244 0.070 0.037
0.002 76.191
MCMRWM 0.987
0.717 0.831 0.710
0.829 97.461
WM
0.838
0.931 0.881 0.788
0.873 98.097
RBCWM
0.066
0.205 0.100 0.053
-0.023 71.617
MCMRWM 0.848
0.975 0.907 0.830
0.902 98.501
WM
0.634
0.627 0.608 0.455
0.497 81.341
RBCWM
0.248
0.385 0.290 0.171
-0.010 54.861
MCMRWM 0.864
0.958 0.901 0.840
0.839 92.599
Table 6: Comparative results of state-of-the-art BS techniques on
flage” (CF) sequence.
Algorithm
Precision Recall F1
Similarity MCC
CB
0.885
0.996
0.936 0.882
0.881
CM
0.795
0.797
0.793 0.663
0.607
FBS
0.918
0.945
0.931 0.871
0.859
GMM
0.533
0.800
0.632 0.465
0.132
HCB
0.656
0.992
0.785 0.653
0.547
HGMM
0.916
0.842
0.874 0.782
0.753
MCB
0.856
0.971
0.909 0.835
0.822
FMCC
0.851
0.867
0.857 0.750
0.714
AFABS(C)
0.930
0.971
0.949 0.905
0.905
SCBS
0.910
0.738
0.814 0.688
0.686
ADMGMM 0.792
0.807
0.789 0.663
0.610
WavGMM
0.712
0.965
0.817 0.694
0.585
MCMRWM 0.937
0.995
0.965 0.932
0.930
Table 7: Comparative results of state-of-the-art BS techniques on
(CU) sequence.
Algorithm
Precision Recall F1
Similarity MCC
CB
0.587
0.937
0.718 0.564
0.711
CM
0.366
0.891
0.516 0.351
0.513
FBS
0.805
0.644
0.699 0.567
0.691
GMM
0.460
0.865
0.543 0.407
0.532
HCB
0.535
0.967
0.678 0.522
0.680
HGMM
0.881
0.842
0.855 0.753
0.846
MCB
0.832
0.794
0.806 0.679
0.793
FMCC
0.941
0.557
0.670 0.542
0.688
AFABS(C)
0.857
0.549
0.650 0.506
0.656
SCBS
0.945
0.269
0.408 0.264
0.475
ADMGMM 0.785
0.639
0.690 0.549
0.679
WavGMM
0.537
0.904
0.649 0.512
0.640
MCMRWM 0.857
0.924
0.886 0.805
0.878
noise resulting in reduce false positives.
4.4. Performance comparison of MCMRWM with the state-ofthe-art BS schemes
610
615
620
625
In addition to this, the proposed MCMRWM algorithm has
also been evaluated against state-of-the-art BS techniques such
as Codebook (CB) [24], Covariance based methods (CM) [29],
Fuzzy background subtraction (FBS) [13], Gaussian mixture
model (GMM) [45], Hierarchical codebook (HCB) [27], Hierarchical Gaussian mixture model (HGMM) [41], Moments
based codebook (MCB) [26], Fuzzy multi-channel correlogram
(FMCC) [15], Advanced fuzzy aggregation based BS using Choquet integral (AFABS(C)) [16], Spatial correlated BS (SCBS)
[38], Advance distance measure using support weight and histogram of gradients in Gaussian mixture model (ADMGMM)
[46], Wavelet based Gaussian mixture model (WavGMM) [47].630
The results yielded by these techniques are analysed in the following sub-sections.
4.4.1. Qualitative results
For the subjective evaluation of the proposed MCMRWM635
algorithm against state-of-the-art BS schemes, the segmented
foregrounds are shown in Figures 9–20.
The performance of CB algorithm works better with CF,
PE, CN and OF sequences. However, it fails for FO, OW and
WT sequences. CB is a pixel based BS and does not take care640
12
“CamouPCC
94.112
81.113
93.164
56.317
74.925
87.565
91.300
86.027
95.463
84.217
80.300
78.471
96.563
“Curtain”
PCC
93.753
85.881
95.883
81.175
91.773
97.693
96.879
96.121
95.507
93.757
95.604
89.134
98.138
Table 8: Comparative results of state-of-the-art BS techniques on “Fountain”
(FO) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.269
0.851
0.398 0.256
0.440 90.398
CM
0.374
0.832
0.514 0.348
0.535 94.563
FBS
0.427
0.639
0.504 0.342
0.497 95.674
GMM
0.165
0.832
0.272 0.160
0.321 83.499
HCB
0.452
0.882
0.594 0.426
0.611 95.474
HGMM
0.501
0.506
0.501 0.346
0.485 96.668
MCB
0.458
0.823
0.582 0.420
0.593 95.885
FMCC
0.901
0.482
0.619 0.456
0.645 97.982
AFABS(C)
0.540
0.423
0.471 0.311
0.459 96.629
SCBS
0.790
0.398
0.523 0.364
0.547 97.559
ADMGMM 0.719
0.776
0.740 0.591
0.734 98.154
WavGMM
0.148
0.860
0.248 0.144
0.304 80.846
MCMRWM 0.796
0.991
0.883 0.790
0.879 98.060
of its neighboring pixels in foreground classification. The subjective results of CM is good for FO sequence. But, it fails for
most of the sequence. The feature vector used in CM includes
coordinates, gradients and LBP. This is not sufficient to handle
dynamic background. The qualitative results for FBS is better
only for PE videos. However, it fails for CU, WT, BO, CN,
FO2, HI and OF sequences. It uses multi-channel pixel values
with Choquet integral for foreground detection which is insufficient to handle variation due to swaying vegetation and ripples in water surface. The same is true for GMM, which fails
in most of the test sequences. HCB, MCB, HGMM, FMCC,
AFABS(C), SCBS, ADMGMM and WavGMM are block level
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 9: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Camouflage” (CF) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS,
(m) ADMGMM, (n) WavGMM, (o) Proposed.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 10: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Curtain” (CU) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
ADMGMM, (n) WavGMM, (o) Proposed.
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650
background subtraction technique. HCB technique performance655
is better for CU, FO, OW, WS, WT and HI videos but their
performance degrades for CF, BO, CN and FO2 sequences.
HGMM algorithm works for CF, CU, OW, PE, WS, BO, FO2,
HI and OF sequence. MCB algorithm qualitative results shows
the detection is better in case of FO, WS and FO2 sequence.660
FMCC performance is better than AFABS(C) and SCBS BS
technique. The algorithm works better for OW, PE and FO2
sequences. The segmentation result of AFABS(C) I s good for
CF and OW sequences. ADMGMM and WavGMM are multimodal GMM based BS technique. ADMGMM works better
with CU, FO, FO2 and HI sequences. The performance of665
ADMGMM is better than WavGMM in most of the video sequences. This is due to the fact that ADMGMM uses region13
level classification. The distance measure is a weighted average
of supported weights and histogram of oriented gradients.
The performance of the MCMRWM is better than state-ofthe-art BS algorithms in most of the video sequences used for
the evaluation. This is due to the fact that it uses multi-channel
and multi-resolution information in background modelling and
as well in foreground classification.
4.4.2. Quantitative results
The objective evaluation of the proposed MCMRWM algorithm against state-of-the-art BS schemes are presented in Tables 6–17. The best performance value obtained for each of the
metric is highlighted in bold for clear representation.
From the quantitative results, it can be inferred that the per-
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 11: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Fountain” (FO) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
ADMGMM, (n) WavGMM, (o) Proposed.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 12: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “OceanWaves” (OW) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS,
(m) ADMGMM, (n) WavGMM, (o) Proposed.
670
675
680
formance of state-of-the-art BS techniques varies for different
videos sequences and hence it is difficult to find out which algorithm works better in most of the test sequences. To overcome
this issue, an overall ranking of different BS techniques based685
on the accuracy metrics is given in Table 18.
The rank has been calculated for 13 BS techniques using
12 video sequences. Ranking of BS algorithms is based on
their performance in terms of accuracy metrics. To adopt a rank
based score system, for evaluating the overall performance, the690
competitors are sorted in ascending order of their performance
(say, Precsion values) and are assigned scores of 1, 2, 3, ...,
13, for each test sequence. A cumulative score is obtained by
considering all test video sequences. Then the total score for a
competitor (algorithm) is determined by adding its cumulative695
14
scores across all metrics (Precision, Recall, etc.). Finally, the
competitors are assigned overall ranks: 13, 12, ..., 1 (13 for the
best and 1 for the worst) based on their total score.
The overall performance evaluation schemes are presented
in Table 18. In the evaluation processes, the proposed scheme:
MCMRWM comes out as the winner while HGMM [41] is the
second best player. From the Table 18, it can be observed
that the over all score for MCMRWM is 874 whereas that of
HGMM is only 592 which is 47% less than 874. This indicates
the high performance of the proposed scheme.
The average quantitative results for state-of-the-art and the
proposed MCMRWM techniques tested over 12 test sequences
are demonstrated in Figure 21.
The values of Precision for different BS techniques are shown
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 13: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over
“PETS2006” (PE) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C),
(l) SCBS, (m) ADMGMM, (n) WavGMM, (o) Proposed.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 14: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “WaterSurface” (WS) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l)
SCBS, (m) ADMGMM, (n) WavGMM, (o) Proposed.
700
705
in Figure 21(a). The CM algorithm is 0.79 whereas the pro-710
posed MCMRWM scheme yields 0.65. This is followed by
FMCC algorithm which exhibits 0.58. The next best result is
shown by SCBS scheme which yields 0.56. The average Recall
values are presented in Figure 21(b). CB algorithm has the
highest average Recall value, i.e. 0.81. The next best algo-715
rithm is HCB which yields 0.81 and the third best is MCMRWM scheme, which exhibits 0.80. The proposed algorithm
yields just 1.24% less than the highest reported scheme. The average values of F1 measure are shown in Figure 21(c). It clearly
shows that the proposed scheme yields the highest value which720
is 0.67 while HGMM algorithm shows 0.53 followed by FMCC
and HCB scheme at 0.50. MCMRWM algorithm reports 26%
increase from the next best scheme. The MCMRWM algorithm
15
has the highest average S imilarity among all the state-of-theart techniques as shown in Figure 21(d). It reports 0.58 while
HGMM scheme comes second with 0.44 followed by FMCC
which yields 0.39. MCMRWM scheme shows 31% increase
in their result from the HGMM technique. The average values
of MCC are shown in Figure 21(e). MCMRWM scheme exhibits 0.66 which is the maximum value among the compared
BS algorithms and HGMM technique records the second best
value with 0.51 while FMCC scheme comes third which gives
0.49. MCMRWM records 29% increase from the second best
algorithm. In term of PCC shown in Figure 21(f), MCMRWM
scheme exhibits 97.70% which is the highest among all the
BS schemes. The second best result, reported by AFABS(C)
scheme, is 95.93% followed by HGMM algorithm with 94.67%.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 15: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “WavingTrees” (WT) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS,
(m) ADMGMM, (n) WavGMM, (o) Proposed.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 16: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “boats”
(BO) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
ADMGMM, (n) WavGMM, (o) Proposed.
725
730
It can be seen from the figure that MCMRWM scheme reports higher average values for Precision, F1 , S imilarity, MCC
and for PCC as well. However, it reports third best result for735
Recall value. This is manageable as the harmonic mean between Precision and Recall i.e. F1 is highest for the proposed
scheme. Thus, it is observed that the proposed scheme performs much better than the state-of-the-art algorithms in terms
740
of average quantitative results.
This demonstrates quite a superior performance of the proposed BS scheme compared to the state-of-the-art techniques.
745
16
5. Conclusion
In this paper, a new multi-channel and multi-resolution Wronskian change detection model (MCMRWM) based codebook
BS is proposed for foreground detection in the presence of dynamic environment for visual surveillance applications. The
proposed MCMRWM scheme calculates the ratio between feature vectors of current frame to the background model or its reciprocal in an adaptive manner, depending on the l2 norm of the
feature vector, which helps to detect the foreground object completely without any false negatives. In addition, MCMRWM
takes advantage of multi-channel, multi-resolution and spatial
information of an image for foreground detection. The multichannel information exploits the colour relation in segmentation which helps to detect the foreground object with less num-
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 17: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Canoe”
(CN) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
ADMGMM, (n) WavGMM, (o) Proposed.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
Figure 18: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Fountain02” (FO2) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS,
(m) ADMGMM, (n) WavGMM, (o) Proposed.
750
755
760
ber of false negatives. The multi-resolution image is determined
by passing each channel of the colour image through the Gaussian filter bank. Small variations in the background and low
power additive noise is pixel values are suppressed effectively765
with different Gaussian blurs. As a result, multi-resolution image nullifies the pixel variation in the changing background
such as swaying vegetation, ripples in water surface, spouting
fountain, etc. which, in turn, reduces false positive detections.
The spatial relation helps to overcome small noise in the foreground detection. However, MCMRWM scheme fails to detect
shadow cast by the object. Moreover, presence of a foreground770
object during the initialization of background for modelling creates ghost effect. Further, fixed learning rate does not eliminate
this effect.
775
17
Experiments are conducted with state-of-the-art BS techniques on publicly available video sequences to show the effectiveness of the proposed algorithm in different challenging
environments. It is observed that the proposed scheme outperforms all state-of-the-art techniques. The qualitative and quantitative results show that the proposed BS technique can be used
efficiently in wide variety of visual surveillance applications.
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Figure 19: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Highway” (HI) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
ADMGMM, (n) WavGMM, (o) Proposed.
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Figure 20: Performance comparison of multi-channel and multi-resolution Wronskian change detection model based codebook background subtraction over “Office”
(OF) sequence: (a) Original, (b) Ground truth, (c) CB, (d) CM, (e) FBS, (f) GMM, (g) HCB, (h) HGMM, (i) MCB, (j) FMCC, (k) AFABS(C), (l) SCBS, (m)
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Figure 21: Average Quantitative metrics for state-of-the-art techniques across all the video sequences used. (a) Precision, (b) Recall, (c) F1 , (d) Similarity, (e) MCC,
(f) PCC.
Table 9: Comparative results of state-of-the-art BS techniques on “OceanWaves” (OW) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.445
0.858
0.553 0.430
0.566 96.561
CM
0.297
0.818
0.324 0.121
0.245 77.410
FBS
0.608
0.535
0.502 0.372
0.506 97.611
GMM
0.201
0.793
0.305 0.192
0.334 88.592
HCB
0.438
0.883
0.551 0.429
0.568 96.467
HGMM
0.605
0.648
0.570 0.448
0.568 97.874
MCB
0.006
0.062
0.011 0.005
0.014 98.100
FMCC
0.721
0.588
0.587 0.461
0.594 98.256
AFABS(C)
0.738
0.518
0.541 0.410
0.559 98.127
SCBS
0.640
0.396
0.409 0.276
0.432 97.299
ADMGMM 0.580
0.644
0.550 0.427
0.550 97.644
WavGMM
0.413
0.787
0.458 0.225
0.366 89.719
MCMRWM 0.646
0.730
0.627 0.525
0.629 98.377
Table 10: Comparative
“PETS2006” (PE) sequence
Algorithm
Precision
CB
0.429
CM
0.429
FBS
0.800
GMM
0.278
HCB
0.489
HGMM
0.798
MCB
0.273
FMCC
0.792
AFABS(C)
0.660
SCBS
0.277
ADMGMM 0.666
WavGMM
0.519
MCMRWM 0.987
19
results of state-of-the-art BS techniques on
Recall
0.868
0.868
0.744
0.621
0.954
0.811
0.103
0.650
0.766
0.046
0.783
0.907
0.717
F1
0.564
0.564
0.768
0.332
0.642
0.800
0.037
0.690
0.704
0.034
0.711
0.650
0.831
Similarity
0.402
0.402
0.633
0.216
0.478
0.671
0.019
0.547
0.553
0.017
0.556
0.492
0.710
MCC
0.581
0.581
0.761
0.350
0.660
0.794
-0.051
0.692
0.694
-0.021
0.703
0.662
0.829
PCC
94.594
94.594
98.246
90.745
94.952
98.321
74.238
97.762
97.261
88.626
97.054
95.958
97.461
Table 11: Comparative results of state-of-the-art BS techniques on “WaterSurface” (WS) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.608
0.943
0.735 0.585
0.731 94.662
CM
0.561
0.900
0.690 0.528
0.682 93.915
FBS
0.894
0.805
0.845 0.732
0.835 97.740
GMM
0.282
0.939
0.425 0.275
0.443 79.660
HCB
0.741
0.924
0.819 0.695
0.810 96.861
HGMM
0.965
0.818
0.884 0.794
0.880 98.391
MCB
0.886
0.927
0.905 0.830
0.899 98.575
FMCC
0.969
0.763
0.852 0.744
0.849 98.008
AFABS(C)
0.974
0.775
0.863 0.759
0.860 98.126
SCBS
0.936
0.576
0.712 0.555
0.719 96.511
ADMGMM 0.848
0.488
0.597 0.442
0.611 95.354
WavGMM
0.333
0.931
0.488 0.324
0.501 85.039
MCMRWM 0.848
0.975
0.907 0.830
0.902 98.501
Table 14: Comparative results of state-of-the-art BS techniques on “Canoe”
(CN) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.098
0.599
0.129 0.095
0.147 96.973
CM
0.104
0.632
0.178 0.098
0.205 82.969
FBS
0.055
0.416
0.028 0.015
0.040 96.979
GMM
0.168
0.549
0.245 0.144
0.224 83.855
HCB
0.055
0.601
0.085 0.055
0.102 91.788
HGMM
0.044
0.462
0.049 0.028
0.047 90.379
MCB
0.079
0.561
0.103 0.067
0.115 94.638
FMCC
0.059
0.593
0.088 0.058
0.103 92.333
AFABS(C)
0.131
0.512
0.118 0.084
0.134 98.240
SCBS
0.152
0.459
0.102 0.063
0.145 98.967
ADMGMM 0.043
0.510
0.059 0.035
0.060 88.558
WavGMM
0.026
0.591
0.044 0.025
0.051 61.642
MCMRWM 0.335
0.569
0.369 0.268
0.398 99.610
Table 12: Comparative results of state-of-the-art BS techniques
ingTrees” (WT) sequence
Algorithm
Precision Recall F1
Similarity MCC
CB
0.546
0.996
0.699 0.545
0.621
CM
0.759
0.895
0.817 0.695
0.757
FBS
0.463
0.269
0.328 0.199
0.191
GMM
0.692
0.598
0.636 0.470
0.530
HCB
0.703
0.965
0.807 0.687
0.715
HGMM
0.631
0.679
0.639 0.483
0.496
MCB
0.887
0.862
0.873 0.775
0.831
FMCC
0.962
0.589
0.723 0.576
0.694
AFABS(C)
0.684
0.608
0.640 0.480
0.536
SCBS
0.854
0.406
0.548 0.384
0.511
ADMGMM 0.665
0.917
0.761 0.625
0.662
WavGMM
0.481
0.827
0.597 0.438
0.422
MCMRWM 0.864
0.958
0.901 0.840
0.839
Table 15: Comparative results of state-of-the-art BS techniques on “Fountain02” (FO2) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.041
0.554
0.059 0.039
0.080 98.098
CM
0.010
0.541
0.017 0.009
0.032 87.931
FBS
0.055
0.462
0.041 0.024
0.071 99.571
GMM
0.039
0.597
0.067 0.038
0.099 94.597
HCB
0.042
0.563
0.062 0.041
0.086 98.004
HGMM
0.047
0.526
0.061 0.041
0.081 98.761
MCB
0.103
0.537
0.118 0.083
0.147 99.656
FMCC
0.045
0.549
0.064 0.043
0.085 98.271
AFABS(C)
0.061
0.476
0.051 0.031
0.079 99.526
SCBS
0.056
0.469
0.055 0.032
0.083 99.500
ADMGMM 0.056
0.539
0.072 0.049
0.096 99.212
WavGMM
0.014
0.547
0.024 0.013
0.038 81.665
MCMRWM 0.136
0.533
0.159 0.112
0.208 99.893
on “WavPCC
79.178
90.330
72.585
82.778
86.413
79.247
93.691
89.329
83.534
83.547
84.197
70.701
92.599
Table 13: Comparative results of state-of-the-art BS techniques on “Boats”
(BO) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.022
0.549
0.036 0.021
0.057 95.245
CM
0.021
0.559
0.039 0.023
0.058 96.256
FBS
0.023
0.468
0.029 0.016
0.044 98.092
GMM
0.011
0.506
0.021 0.011
0.055 98.295
HCB
0.014
0.570
0.025 0.014
0.046 91.214
HGMM
0.021
0.477
0.029 0.017
0.044 97.315
MCB
0.022
0.486
0.031 0.018
0.049 97.619
FMCC
0.017
0.557
0.029 0.017
0.051 93.528
AFABS(C)
0.017
0.468
0.023 0.012
0.039 97.772
SCBS
0.044
0.467
0.047 0.027
0.079 99.288
ADMGMM 0.014
0.505
0.024 0.013
0.036 92.324
WavGMM
0.008
0.554
0.016 0.008
0.028 73.138
MCMRWM 0.056
0.590
0.103 0.024
0.057 98.641
[16]
815
[17]
820
[18]
[19]
825
[20]
Table 16: Comparative results of state-of-the-art BS techniques on “Highway”
(HI) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
CB
0.206
0.810
0.301 0.201
0.331 88.222
CM
0.232
0.818
0.332 0.228
0.359 87.730
FBS
0.356
0.511
0.347 0.234
0.338 94.832
GMM
0.144
0.557
0.199 0.118
0.181 76.010
HCB
0.365
0.808
0.464 0.351
0.475 92.541
HGMM
0.450
0.756
0.514 0.408
0.516 96.202
MCB
0.274
0.582
0.338 0.230
0.330 91.959
FMCC
0.301
0.832
0.414 0.296
0.433 91.687
AFABS(C)
0.340
0.501
0.331 0.220
0.323 94.670
SCBS
0.446
0.472
0.377 0.259
0.372 95.808
ADMGMM 0.468
0.668
0.492 0.376
0.486 96.246
WavGMM
0.179
0.786
0.262 0.172
0.285 84.445
MCMRWM 0.554
0.773
0.645 0.483
0.638 96.658
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Table 17: Comparative results of state-of-the-art BS techniques on “Office”
(OF) sequence
Algorithm
Precision Recall F1
Similarity MCC PCC
880
CB
0.438
0.834
0.540 0.429
0.559 96.712
CM
0.118
0.631
0.188 0.110
0.174 75.577
FBS
0.478
0.376
0.312 0.200
0.332 95.865
GMM
0.139
0.679
0.163 0.092
0.175 69.237
HCB
0.482
0.678
0.525 0.371
0.526 94.606 885
HGMM
0.657
0.755
0.699 0.553
0.690 97.727
MCB
0.214
0.808
0.319 0.203
0.347 86.818
FMCC
0.434
0.539
0.427 0.282
0.425 94.072
AFABS(C)
0.501
0.565
0.444 0.331
0.442 96.339
SCBS
0.715
0.436
0.527 0.360
0.537 96.678 890
ADMGMM 0.568
0.357
0.386 0.253
0.398 95.476
WavGMM
0.322
0.807
0.415 0.309
0.422 86.152
MCMRWM 0.785
0.785
0.785 0.785
0.785 0.785
895
Table 18: Overall performance evaluation
Algorithm
CB [24]
CM [29]
FBS [13]
GMM [45]
HCB [27]
HGMM [41]
MCB [26]
FMCC [15]
AFABS(C) [16]
SCBS [38]
ADMGMM [46]
WavGMM [47]
MCMRWM
845
850
855
860
865
870
875
Precision
64
52
93
38
64
103
80
107
112
111
85
33
141
Cummulative Score
Recall F1 Similarity MCC
135
92
92
92
107
65
63
67
43
71
71
69
86
42
39
53
135
88
89
92
71 105
108
97
76
95
95
89
74 100
101
102
50
81
79
80
18
63
64
72
63
88
89
83
113
41
42
37
120 156
155
153
PCC
69
46
102
34
62
108
102
97
110
91
88
28
149
Total
Score
544
400
449
292
530
592
537
581
512
419
496
294
874
Rank
10
3
5
1
8
12
9
11
7
4
6
2
13
900
905
910
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HIGHLIGHTS

A multi-channel and multi-resolution Wronskian model is employed for background
subtraction.

It detects moving objects efficiently in the presence of dynamic backgrounds.

Multi-channel information reduces the false negative detections.

Multi-resolution information reduces false positive detections.
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