Moving object detection using Markov Random Field and Distributed Differential Evolution

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Applied Soft Computing 15 (2014) 121–135

Contents lists available at ScienceDirect

Applied Soft Computing

j ourna l h o mepage: www.elsev ier .com/ locate /asoc

oving object detection using Markov Random Field and Distributedifferential Evolution

shish Ghosha,∗, Ajoy Mondala, Susmita Ghoshb

Machine Intelligence Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700108, IndiaDepartment of Computer Science and Engineering, Jadavpur University, Kolkata 700032, India

r t i c l e i n f o

rticle history:eceived 16 March 2012eceived in revised form 22 July 2013ccepted 25 October 2013vailable online 9 November 2013

eywords:arkov Random FieldAP estimationifferential Evolutionistributed Differential Evolution

a b s t r a c t

In this article, we present an algorithm for detecting moving objects from a given video sequence. Here,spatial and temporal segmentations are combined together to detect moving objects. In spatial segmen-tation, a multi-layer compound Markov Random Field (MRF) is used which models spatial, temporal, andedge attributes of image frames of a given video. Segmentation is viewed as a pixel labeling problemand is solved using the maximum a posteriori (MAP) probability estimation principle; i.e., segmenta-tion is done by searching a labeled configuration that maximizes this probability. We have proposedusing a Differential Evolution (DE) algorithm with neighborhood-based mutation (termed as DistributedDifferential Evolution (DDE) algorithm) for estimating the MAP of the MRF model. A window is consid-ered over the entire image lattice for mutation of each target vector of the DDE; thereby enhancing thespeed of convergence. In case of temporal segmentation, the Change Detection Mask (CDM) is obtained

bject detection by thresholding the absolute differences of the two consecutive spatially segmented image frames. Theintensity/color values of the original pixels of the considered current frame are superimposed in thechanged regions of the modified CDM to extract the Video Object Planes (VOPs). To test the effective-ness of the proposed algorithm, five reference and one real life video sequences are considered. Resultsof the proposed method are compared with four state of the art techniques and provide better spatialsegmentation and better identification of the location of moving objects.

. Introduction

Detection and tracking of moving objects from a given videoequence are challenging tasks in video processing and have beenn active research area for the last few decades [1,2]. It has widepplicability in video surveillance, event detection, anomaly detec-ion, dynamic scene analysis, activity recognition, activity baseduman recognition [1,2] etc. To detect moving objects for a givenideo sequence, various object regions which are moving withespect to their background are identified [2]. It can be performedsing (i) change/motion detection and (ii) motion estimation [2]nd the detected objects, in turn, can be tracked. Tracking provideshe velocity, acceleration and position of moving objects at differentime instants.

Literature on detection of moving objects using different
tochastic models is quite rich. Markov Random Field (MRF) models one such approach which represents spatial continuity amongdjacent pixels and is robust to degradation. Since the last few
∗ Corresponding author. Tel.: +91 33 2575 3110/3100; fax: +91 33 2578 3357.E-mail addresses: [email protected] (A. Ghosh), [email protected]

A. Mondal), [email protected] (S. Ghosh).

568-4946/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.asoc.2013.10.021

© 2013 Elsevier B.V. All rights reserved.

decades, MRF models [3–7] and Hidden MRF models [8] are usedfor segmenting images and these models are quite popular forsegmenting video sequences [9–20]. In [9,21], to detect movingobjects, MRF model was considered in the spatial direction only.Whereas, in a video, two image frames are not independent ofeach other. Hence, temporal coherence can be explored to obtainbetter segmented output. Considering this temporal coherence, amulti-layer MRF modeling is adhered to in [10–16] (one frame intemporal direction). Kim and Park [11] showed that a combinationof spatial segmentation and temporal segmentation provides betterresults for detecting moving objects. To preserve the boundary ofthe objects, Sududhi et al. [12] proposed a multi-layer compoundMRF model which takes care of the spatial distribution of color,temporal color coherence, and edge map/line-field in the tempo-ral frames (two frames in temporal direction) to obtain a spatialsegmentation. Temporal coherence helps in preserving the regioninformation in segmentation. The use of edge map/line-field canpreserve the accurate object boundary in segmentation.

To the best of our knowledge, in the literature no method is
available which exploits the merits of Differential Evolution (DE)scheme with MRF model. In the present article, the applicability ofDE has been explored with MRF model for moving object detec-tion. A preliminary experiment of this work was reported in [17].
dx.doi.org/10.1016/j.asoc.2013.10.021

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dx.doi.org/10.1016/j.asoc.2013.10.021

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22 A. Ghosh et al. / Applied Sof

robust analysis of the results with application in different com-lex video sequences is reported in the present article. Comparisonith recent state-of-the-art techniques along with its quantitative

nalysis has also been made in the present version.The present work considers, a spatial segmentation scheme

here multi-layer compound MRF model [12] has been used foretecting moving objects in a given video sequence. Spatial seg-entation as well as temporal segmentation are combined for

etecting moving objects. The assumed MRF model takes care ofpatial distribution of color, temporal color coherence, and edgeap/line-field in temporal direction (two frames in the temporal

irection) of a given video frame. The considered MRF model isound to preserve accurate object boundary. The spatial segmen-ation using the considered multi-layer compound MRF model isquivalent to a pixel labeling problem and is solved using the MAPstimation principle. A Distributed Differential Evolution (DDE)lgorithm is proposed for searching the maximum a posterior prob-bility of MRF modeled frame. In the proposed search technique, aopulation represents a segmented output of the considered videorame and size of the population is equal to the dimension of theideo frame. A population consists of a set of target vectors. Here,ach target vector encodes the red (R), green (G), and blue (B) com-onents of the segmented output and a set of such target vectorsonstitutes each population. The population is initialized randomly.t is to be noted that the segmentation of the MRF modeled frameorresponds to the MAP estimation and the proposed DDE algo-ithm maximizes this probability. This maximization process haseen done iteratively by evolving the target vectors (i.e., possibleolutions) of the population using the following three operations:utation, crossover, and selection. The algorithm continues until

ome stopping criterion is reached. At the end of the evolutionaryrocess, a stable labeled configuration is obtained. Such a configu-ation is considered as the required segmented output of the givennput video frame.

In the proposed DDE, to mutate each target vector, instead ofonsidering the whole population, a small window centered at thearget vector is considered thereby reducing computational times compared to the conventional Differential Evolution algorithm.t also provides a better spatial segmentation as the considered

indow maintains the spatial regularity of the lattice in MRF.In temporal segmentation, the difference images of each of the

, G, and B channels are obtained by taking absolute differencef the respective R, G, and B components of the two consecutivepatially segmented image frames. Thereafter, Change Detectionasks (CDMs) of each of the R, G, and B channels are obtained

y thresholding the corresponding difference images. The changednd the unchanged regions in the current frame are obtained byonsidering the union of CDMs of these three channels. To obtainhe exact location of the moving objects in the current frame, we

odify the obtained CDM by considering the information of pixelselonging to the moving objects in the previous frame and resultf the corresponding current spatial segmentation. Video Objectlane (VOP) is extracted by superimposing the intensity/color val-es of original pixels of the current frame on the changed regionsf the modified CDM.

To test the effectiveness of the proposed algorithm investigationas carried out on five reference and one real life video sequences.esults obtained by the proposed method are compared with thosef MRF with DGA scheme [10,11], MRF with DGA scheme withulti-layer compound MRF model as used in the proposed method

henceforth, called as modified MRF with DGA scheme), MRF withraph Cut scheme [7,22], and MRF with SA and ICM scheme [12].

Organization of the article is as follows. Section 2 describes theelated work. In Section 3, the proposed methodology for mov-ng object detection where spatial segmentation (spatio-temporal

RF based image modeling, MAP estimation framework for MRF

puting 15 (2014) 121–135

modeling), DE algorithm, DE algorithm with neighborhood-basedmutation, the proposed DDE algorithm for MAP estimation, seg-mentation of subsequent frames based on change information, andtemporal segmentation are described. Experimental results anddiscussion are given in Section 4 and conclusive remarks are putin Section 5.

2. Related work

For change/motion detection initially a reference frame is con-sidered where no objects are present [2]. Detection of movingobjects becomes very difficult using temporal segmentation if thereference frame is absent or movement of objects is either veryslow, or very fast, or they halt for some time and then move again[1,2].

In order to solve these problems a region based robust videoframe segmentation algorithm is needed [1,2]. Salember and Mar-ques [23] had proposed a computationally efficient watershedbased spatial segmentation scheme. To detect the object’s bound-ary, they have used both spatial and temporal segmentations. Butthis scheme sometimes produces over-segmented results.

Image segmentation using MRF model can be achieved by esti-mating maximum a posteriori (MAP) probability of the concernedmodel [3,10,11,24]. For a given observed image or a video frameY, segmentation is obtained by searching a configuration X whichmaximizes this probability. This maximization process is quitecomplex owing to the large search space. Hence, efficient andeffective optimization algorithms are required to maximize theposterior probability.

The MAP of the MRF model has been estimated using var-ious optimization algorithms such as Simulated Annealing (SA)[4,24,25], Iterated Conditional Mode (ICM) [3,24], and Genetic Algo-rithm (GA) [5,24]. Though the convergence speed of SA is less butit has the capability of finding better solutions [5,24]. On the otherhand, ICM consumes less time as compared to other optimizationtechniques; but sometimes it may get stuck to local optima [5,24].In [12], Subudhi et al. has proposed an MRF model based spatialsegmentation scheme by combining both SA and ICM to estimatethe MAP of the corresponding model. It has the ability to providecomparable results quickly. In [12], the SA was initially executedfor a few iterations to get a suboptimal solution and thereafter ICM(with suboptimal solution as initialization) was used to obtain theoptimal solution. As SA is executed for a few iterations, the sub-optimal solutions obtained using SA sometimes correspond to thelocal optima or nearer to the local optima and thereafter ICM mayget stuck to the same and may not reach the global optimum ornear to the global optimum. Hence, segmentation using the samealgorithm may not be a good choice. Moreover, the setting of thenumber of iterations in SA, is not easier.

GA was used as an alternative optimizer to SA and ICM in [5] dueto suitable values of the parameter, its ability to explore and exploitthe search space quickly using the concept of natural evolutionand selection [26]. It is robust for identifying solutions to combi-natorial optimization problems. In [5,26,27], it is mentioned thatthe GA sometimes converges to a premature solution and has lowsearching speed. To overcome these problems, GA has been modi-fied in [28,29]. In [28], a deterministic hill-climbing procedure wasembedded into GA. Although the computational cost was low, itstill landed up to a suboptimal solution. Zhang et al. developed evo-lutionary algorithm based on a combination of GA and SA [30,31].These algorithms produce better segmentation than those obtained
using GA alone, but had a lower convergence speed. A combinationof ICM and GA was proposed by Lai and co-worker [5]. For quickconvergence and to obtain better segmentation, a new version ofGA called, Distributed Genetic Algorithm (DGA) has been proposed

A. Ghosh et al. / Applied Soft Computing 15 (2014) 121–135 123

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edges/line-fields of the (t − 1)th frame xt−1 and the (t − 2)th framext−2) is considered to preserve the accurate object boundary in seg-

Fig. 1. Block diagram

or segmenting textured images in [32] and video sequences in10,11]. In DGA [11], the chromosome with the highest fitness valuemong its neighborhood was selected. During crossover, a neigh-oring chromosome within the window was randomly picked upnd a component of the feature vector was chosen and replaced byhe corresponding value of the feature vector of the selected chro-

osome. For this reason, DGA merges smaller regions to a largeegion and produces over-segmented results at the boundary of anbject.

Unlike evolutionary approaches, some deterministic methodsuch as Belief Propagation (BP) and Graph Cuts (GC) have beensed for MAP estimation. In [14], Yin and Collins had presentedP approach for moving object detection using a 3D MRF model. Inhis method, each hidden state in the 3D MRF model represented aixel’s motion likelihood and was estimated using message passing

n a 6-connected spatio-temporal neighborhood. Huang et al. [15]ad proposed a framework for segmenting moving objects using

new spatio-temporal MRF model and Loopy Belief PropagationLBP) was used to estimate MAP of MRF model. In [22], Szeliski et al.tudied different energy minimization methods such as ICM, swap-ove, expansion-move, max-product LBP, and Tree-Reweighedessage passing (TRW) for stereo, image stitching, interactive seg-entation, and denoising. The authors mentioned that the TRW

nd expansion-move GC algorithms achieve minimum energy.eng and Jian-ya [7] had proposed a novel MRF based imageegmentation scheme where MAP of MRF model was estimatedsing expansion-move algorithm in GC. However, these approaches7,14,15,22] are found to provide over-segmented results.

. Proposed method for moving object detection

Fig. 1 represents the block diagram of the proposed method.s mentioned earlier, in the present article spatial and temporalegmentations are integrated together to detect moving objects.patial segmentation accurately provides the boundary of theegions in a given scene, whereas temporal segmentation deter-ines the changed and the unchanged regions. MRF model with

patio-temporal framework is used for spatial segmentation as itas used in [12]. Color features, both in spatial and temporal direc-

ions, and edge map/line-field in temporal direction are taken intoonsideration while modeling the image frame. The edge map haseen obtained using a 3 × 3 Laplacian mask. Segmentation using theRF model is usually done through the MAP estimation principle.sing a local mutation based DE termed as Distributed Differential
volution (DDE) is proposed to estimate the MAP of such a model. InDE unlike conventional DE algorithm, a small window is consid-red over the image lattice for mutating each of the target vectors.andom initialization is done for segmenting the initial frame. A
e proposed method.

change information based initialization is utilized for segmentingthe subsequent frames.

In temporal segmentation, the difference images for each ofthe R, G, and B channels are obtained by computing the absolutedifferences of the corresponding R, G, and B components of two con-secutive spatially segmented image frames. Then, the CDMs of eachof the R, G, and B channels are obtained by thresholding the cor-responding difference images. These CDMs represent the changedand the unchanged regions in the respective channel. Union ofCDMs of these three channels is taken to obtain the changed andthe unchanged regions in the current frame. The changed regionscorrespond to moving objects whereas the unchanged regions cor-respond to stationary objects and background. To obtain the exactlocations of the moving objects, the CDM is modified. Informationof the pixels belonging to the moving objects in the previous frameand output of the current spatial segmentation are considered tomodify it. The intensity/color values of the original pixels of thecurrent frame are then superimposed on the changed regions ofthe modified CDM to extract the VOP.

3.1. Spatial segmentation

Spatial segmentation can be done by combining the spatial andtemporal features of a given video image frame in a single frame-work [11,33]. In the present article, MRF (with both spatial andtemporal features) based image modeling is considered for spatialsegmentation.

3.1.1. Spatio-temporal MRF based image modelingHere, the observed video sequence y is assumed to be a 3D vol-

ume, consisting of spatio-temporal image frames. The tth frame ofthe video sequence y is represented as yt. Each pixel of yt is a spa-tial site s, denoted by yst, q is a temporal site, and e is an edge site.Let, S be the set of all the sites. Thus S = {s} ∪ {q} ∪ {e}. Let Yt rep-resent a random field and yt be a realization of it at time t. Thus,yst denotes a pixel at site s at time t. Let x denote the segmenta-tion of video sequence y and xt the segmented version of yt. Let Xt

be the MRF and xt represents one of its realization. In the presentinvestigation, the second order MRF modeling in spatial as well as intemporal directions are considered to take care of the spatial distri-bution of color and temporal color coherence, respectively. AnotherMRF model (with the edge/line-field of the current frame xt and the

mentation. As Xt is an MRF, it satisfies the following Markovianproperty:

P(Xst =xst |Xqt =xqt, ∀q ∈ S, s /= q)=P(Xst =xst |Xqt =xqt, (q, t) ∈ �st),

124 A. Ghosh et al. / Applied Soft Computing 15 (2014) 121–135

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here �st denotes the neighborhood of site s at time t. For temporalRF, the following Markovian property is also satisfied:

(Xst = xst |Xqr = xqr, s /= q, t /= r, ∀(s, t), (q, r) ∈ V)

= P(Xst = xst |Xqr = xqr, s /= q, t /= r, (q, r) ∈ �sr).

ere V represents the 3D volume of the video sequence and �sr

enotes the neighborhood of (s, t) in temporal direction.The novelty of the MRF model lies in the fact that it takes into

ccount the spatial and temporal characteristics of a region [24].he regions are assumed to have uniform intensities. The consid-red image frame is assumed to come from an imperfect imagingodality. It is also assumed that some noise has corrupted the

ctual image to produce the observed image yt. Given this observedmage yt our aim is to find out the image xt, which maximizes theosterior probability. An estimate of xt is denoted by xt . Hence, it

s assumed that due to the presence of noise xt cannot be observedroperly. But a noisy version of xt (i.e., yt) is observed. Noise isssumed to be white (additive i.i.d., i.e., independent and identicallyistributed). Hence Yt can be expressed as [24]

2

Vcpt(xst, xqr) =

Vcept(xst, xer) =

t = xt + N(0, � ), (1)

here N(0, �2) is the i.i.d. noise with zero mean and �2 variance.Fig. 2 represents the 2nd order MRF modeling. In Fig. 2(a), the

i, j)th pixel with its spatial neighbors are used to construct the

irection, and (c) MRF model with line-field in temporal direction.

second order clique function in spatial direction. Fig. 2(b) showsthe considered MRF model in temporal direction. Here, each site sat location (i, j) in the tth frame is modeled with neighbors of thecorresponding pixels in the temporal direction i.e., in the (t − 1)thand the (t − 2)th frames. Similarly, Fig. 2(c) diagrammatically rep-resents the considered MRF model with edge/line-field of the tthframe with the neighbors of the corresponding pixels in the (t − 1)thand the (t − 2)th frames.

The prior probability of the MRF framework can be representedby Gibb’s distribution with P(Xt) = (1/z)e−U(Xt)/T, where z representsthe partition function and it is expressed as z =

∑xt

e−U(Xt )/T , andU(Xt) denotes the energy function (a function of clique potentials).The parameter T is the temperature constant and is set to 1 as in[24]. The following clique potential functions have been consideredfor spatial and temporal directions:

For spatial direction,

Vcps(xst, xqt) ={

+ if xst /= xqt, (s, t), (q, t) ∈ S,

− if xst = xqt, (s, t), (q, t) ∈ S.

Similarly, in temporal direction

if xst /= xqr, (s, t), (q, r) ∈ S, t /= r, and r ∈ {(t − 1), (t − 2)} if xst = xqr, (s, t), (q, r) ∈ S, t /= r, and r ∈ {(t − 1), (t − 2)}

and for edge map in temporal direction,

� if xst /= xer, (s, t), (e, r) ∈ S, t /= r, and r ∈ {(t − 1), (t − 2)}� if xst = xer, (s, t), (e, r) ∈ S, t /= r, and r ∈ {(t − 1), (t − 2)} ,

where, Vcps(xst, xqt) denotes the clique potential for spatial direc-
tion at time t. Vcpt(xst, xqr) represents the temporal clique potential,and the edge potential in temporal direction is denoted by Vcept(xst,xer). Here, the parameters ˛, ˇ, and � are positive constant and areassociated with the clique potential function. They are empirically

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etermined during execution. Hence, in the priori image model, thelique potential function is a combination of the above mentionedhree terms and the energy function takes the form

(Xt) =∑c∈C

Vcps(xst, xqt) +∑c∈C

Vcpt(xst, xqr) +∑c∈C

Vcept(xst, xer). (2)

n Eq. (2), C is the set of cliques (here, 2nd order cliques are consid-red). Three clique potentials Vcps(xst, xqt), Vcpt(xst, xqr), and Vcept(xst,er) over all possible cliques are added to obtain the energy function(Xt).

.1.2. MAP estimation framework for MRF modelingIn MRF modeling, the observed image sequence y is considered

s a degraded version of the actual image sequence x. For example,t tth instant of time, the observed image frame yt is considered as

degraded version of the true labeled xt. It is already mentionedhat the spatial segmentation using MRF model considers the prin-iple of MAP estimation and it is done by maximizing the posteriorrobability given in Eq. (3).

ˆt = arg maxxt

P(Xt = xt |Yt = yt), (3)

here, xt is an estimated label. Using Bayes’ theorem, Eq. (3) cane written as

ˆt = arg maxxt

P(Yt = yt |Xt = xt)P(Xt = xt)P(Yt = yt)

. (4)

ince the prior probability P(Yt = yt) is constant, Eq. (4) can beeduced to

ˆt = arg maxxt

P(Yt = yt |Xt = xt, �)P(Xt = xt, �), (5)

here � is the parameter vector associated with xt. According toammersley Clifford theorem [24], the prior probability followsibb’s distribution as follows

P(Xt = xt) ∝ e−U(xt )

= e−

{∑c∈C

Vcps(xst ,xqt )+∑c∈C

Vcpt (xst ,xqr )+∑c∈C

Vcept (xst ,xer )

}. (6)

his model is an edge based MRF model as used in [12]. The corre-ponding likelihood function P(Yt = yt|Xt = xt) is as follows:

(Yt = yt |Xt = xt) = P(yt = xt + n|Xt = xt, �)

= P(N = yt − xt |Xt = xt, �). (7)

ere, n is the realization of the Gaussian noise N(0, �2). Assumingecorrelation among the three RGB planes for the color image andhe variance to be the same among each plane [34], Eq. (7) can bexpressed as

(N = yt − xt |Xt = xt, �) = 1√(2�)3�3

e−(1/2�2)‖yt−xt‖2. (8)

sing Eqs. (6)–(8), Eq. (5) can be rewritten as

ˆt = arg maxxt

1√(2�)3�3

[e−[‖yt−xt‖2/2�2]e−[∑c∈C

Vcps(xst ,xqt )+Vcpt (xst ,xqr )+

his is equivalent to{[‖yt − xt‖2

] ∑
ˆt = arg min
xt 2�2+ [

c∈C

{Vcps(xst, xqt) + Vcpt(xst, xqr) + Vcept(x

here xt is the MAP estimate. The MAP of MRF model is estimatedy the proposed Distributed Differential Evolution algorithm. In

puting 15 (2014) 121–135 125

xst ,xer )]]. (9)

the following sections, Differential Evolution, Differential Evolutionwith neighborhood-based mutation, and the proposed DistributedDifferential Evolution are briefly described.

3.2. Differential Evolution (DE) algorithm

Differential Evolution (DE) [35,36] is a parallel stochastic searchmethod which uses a number of parameter vectors, called the targetvectors, as a population in each generation. The parameter vec-tors of initial population are chosen randomly. DE generates newparameter vectors (called, mutant vectors) by adding the weighteddifference of the two parameter vectors to a third vector. This oper-ation is called mutation. With this operation, DE explores the searchspace. Thereafter, crossover operation is applied to increase thediversity of the mutated vectors. In crossover operation, param-eters of the mutated vector and those of the target vector (apredetermined one) are swapped, based on crossover probability,to yield a trial vector. During selection process, if the trial vec-tor yields better objective function than the target vector, thenthe trial vector replaces the target vector for the next genera-tion.

DE searches for a global optimum solution in a d-dimensionalreal parameter space IRd. It begins with a randomly initiated pop-ulation consisting of N numbers of d-dimensional real valuedparameter vectors at a generation. Each parameter vector formsa candidate solution to the multidimensional optimization prob-lem. Let at generation G, the population consists of N numbers ofd-dimensional parameter vectors

�xi, G = (xi,1, G, xi,2, G, . . ., xi,d, G), (11)

where i = 1, 2, . . ., N. The initial parameter vectors of thepopulation (at G = 0) is chosen randomly and should coverthe entire parameter space constrained by minimum andmaximum bounds: �xmin = (xmin,1, xmin,2, . . ., xmin,d) and �xmax =(xmax,1, xmax,2, . . ., xmax,d). Hence we may initialize the jth compo-nent of the ith vector as:

xi,j, 0 = xmin,j + randi,j(xmax,j − xmin,j), (12)

where j = 1, 2, . . ., d and randi,j is a uniformly distributed randomnumber lying between 0 and 1.

3.2.1. MutationIn DE, parameter vector at the current generation is called target

vector. For each target vector �xi, at generation G, for i = 1, 2, . . ., N, amutant vector is generated as

�vi, (G + 1) = �xr1, G + F × (�xr2, G − �xr3, G). (13)

The indices r1, r2, and r3 are mutually exclusive integers andrandomly chosen from the range [1, N]. The chosen indices r1,r2, and r3 are different from the index i. The difference of twotarget vectors (�xr2, G − �xr3,G) is amplified by the scaled factorF ∈ [0, 2].

st, xer)}] , (10)

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.2.2. CrossoverIt is used to increase the diversity of the population. The mutated

ector generated through the mutation operation exchanges itsarameters (components) with the target vector to obtain trialector. The trial vector at generation (G + 1) is formed as:

� i, (G + 1) = (ui,1, (G + 1), ui,2, (G + 1), . . ., ui,d, (G + 1)), (14)

here

i,j, (G + 1) =

⎧⎪⎨⎪⎩

vi,j, (G + 1) if randi,j ≤ CR or j = jrand,

xi,j, G otherwise (15)

here j = 1, 2, . . ., d and jrand ∈ [1, d] is a randomly chosen index,hich ensures that ui,j, (G + 1) gets at least one component from theutant vector �ui, (G + 1). CR ∈ [0, 1] is the crossover probability.

.2.3. SelectionThe selection operation is used to decide whether the target or

he trial vector survives for the next generation (G + 1). The trialector �ui, (G + 1) is compared to the target vector �xi, G using somebjective function. If the vector �ui, (G + 1) yields better (objective)unctional value than �xi, G, then the vector �ui, (G + 1) goes to theext generation (G + 1) as a member of the population; otherwise

�i, G. The selection operation is describe as:

�i, (G + 1) =

⎧⎪⎨⎪⎩

�ui, (G + 1) if f (�ui) ≤ f (�xi),

�xi, G otherwise (16)

here f (�xi) is the objective function to be minimized.

.3. Differential Evolution (DE) algorithm witheighborhood-based mutation

The efficiency of most of the Evolutionary Algorithms (EAs)epends on their exploration and exploitation ability duringearching. Using exploitation, the searching algorithm exploitsnformation and moves toward better solutions; whereas explo-ation allows to introduce new information into the population andelps to search new regions [36]. In DE, three vectors are randomlyhosen from the whole search space to mutate each target vector.ometime, such mutation mechanism delays the convergence anday get stuck to local optima. In literature, some modifications ofE have been done to increase the convergence speed and to getetter solutions. In such a context, Tasoulis et al. [37] proposed

topological index based neighborhood DE where each popula-ion is divided into different sub-populations. Each sub-populationvolves independently toward a solution. The best individual ofach sub-population is moved to other sub-populations accord-ng to ring topology. The best individuals of each sub-populationre allowed to migrate to the next sub-population of the ring. Onhe other hand Das et al. [38] proposed DE with neighborhood-ased mutation to achieve better balancing of both exploration andxploitation ability of DE. The authors have proposed two kinds ofeighborhood model for mutation of DE. The first one is the localeighborhood model where each vector is mutated using the bestosition found so far in a small neighborhood of it. For every tar-et vector, a neighborhood of radius k is defined. They assumedhat the vectors within the neighborhood can be organized on aing topology with respect to their indices. For each target vector,
he mutant vector is generated using combination of the best vec-or in the neighborhood and two other vectors chosen from theame neighborhood. On the other hand, the second one is referredo as the global mutation model where the globally best vector of
puting 15 (2014) 121–135

the entire population is used to generate the mutant vector. Theycombined local and global mutant vectors using scalar weight togenerate actual mutant vector. Instead of index based neighbor-hoods, few works using distance based neighborhood have alsobeen proposed for single global optimization. Epitropakis et al. [39]proposed a proximity based mutation operator which selects thevectors to perform mutation operation based on distance relatedprobability.

All the above discussed methods are for finding solutions ofsingle objective functions. To solve multi-modal optimization prob-lems, Qu et al. [40] proposed a neighborhood mutation strategyand integrated it with various niching DE algorithm. For eachtarget vector, mutation is performed within its Euclidean neigh-borhood. The proposed method is able to maintain the multipleoptima found during the evolution and evolve toward global/localoptimum. Decomposition based multi-objective evolutionary algo-rithm decomposes the approximation of the Pareto front intoa number of single objective optimization sub-problems. Eachsub-problem is optimized using information from its neighboringsub-problems. In such cases, the neighborhood size (NS) plays amajor role. In this regard, Zhao et al. [41] proposed an ensemble ofdifferent NSs and dynamically adjust their selection probabilitiesbased on their previous performance.

From the above discussion we may conclude that in DEalgorithms, each parameter (target) vector of the population is con-sidered to be a solution. It also may be noted that all the localneighborhood based DE algorithms have defined the neighborhoodeither depending on the index of target vectors (ring topology) orEuclidean distances among them. However use of such an approachdirectly for image/video frame segmentation rarely gives satis-factory results. It may produce a segmentation result with manynumber of isolated pixels in a region. Hence, it is found not toprovide a context based segmentation result that maintain the spa-tial regularity. In an image/video frame, belongingness of pixels toa particular class is more likely to be the same as that of its neigh-boring pixels. Hence, this motivated us to include the neighboringpixels (defined by a window or mask) at a particular pixel locationof an image for mutation in DE. Please note that the target vectorspresent inside a window may not be topologically close. Hence,we modified the use of DE algorithm with neighborhood-basedmutation for image/video frame segmentation and have termedit Distributed Differential Evolution (DDE) algorithm.

3.4. Proposed Distributed Differential Evolution (DDE) algorithmfor the MAP estimation

In conventional DE algorithm, to mutate each target vector,three vectors are randomly selected from the whole population(total search space). Using the mutation operation, it explores newsearch regions. DE needs large computational time for convergence.Since the mutated vector may not lie within its neighborhood, thesolution might not have spatial regularity. Hence, its use for videoimage segmentation might not carry proper contextual informa-tion.

In this article, we have proposed using a DE algorithm withneighborhood-based mutation and called it Distributed DifferentialEvolution (DDE) algorithm. In the proposed DDE, each populationis divided into a number of sub-populations (overlapping w × wwindows). To mutate each target vector, a small window (sub-population) centered at the target vector is considered instead ofconsidering the whole population. This mechanism accelerates thesearching speed of the DE algorithm. As the considered window
maintains the spatial regularity of the MRF model, the proposedDDE algorithm is expected to provide better segmentation.
In the proposed DDE based search procedure a population cor-responds to a segmented output of the considered video frame and

t Com

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E

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3

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ize of the population is equal to the dimension of the video frame.ach population (same as that of conventional DE) consists of aet of target vectors. Here, each target vector �xst (xR

st , xGst , and xB

st)ncodes the R, G, and B channels of a pixel of the segmented out-ut. Initial population is chosen randomly. Here, it is also noted thathe segmentation of the MRF modeled frame is achieved by esti-

ating the MAP of the said model. The proposed DDE algorithmaximizes this probability by iteratively evolving the target vec-

ors (a possible solution) of the population using three operations:utation, crossover, and selection until some stopping criterion is

atisfied. At the end of this evolutionary process, a stable labeledonfiguration is obtained. Such a configuration is considered as theequired segmented output of the given input video frame. Fitnessf the target vector is inversely proportional to the cost function.he cost function of a target vector is defined in terms of its localnergy and formulated as

st =[

‖�yst − �xst‖2

2�2

]+ [

∑c∈C

{Vcps(�xst, �xqt) + Vcpt(�xst, �xqr)

+ Vcept(�xst, �xer)}]. (17)

he energy values of all the target vectors are summed up to obtainhe energy value of the population. The population having a lowernergy value is considered as a better solution. Each target vec-or is then evolved by mutation, crossover, and selection (therebyielding new target vectors) operations through a number of gen-rations/iterations. Mutation, crossover, and selection operatorsf the proposed DDE model and its stopping criterion are brieflyescribed in the following sections.

.4.1. MutationUsing mutation operation, a mutant vector is generated by

dding the weighted difference between the two vectors to a thirdector. The search space is explored quickly using this operation.

mutant vector corresponding to sth target vector �xst(G) (where = 1, 2, . . ., (M × N)) of the population at generation G is generatedccording to the following equation

st(G + 1) = �xpt(G) + F × (�xqt(G) − �xrt(G)), (18)

here �xpt , �xqt , and �xrt are the three randomly chosen vectors fromhe w × w neighborhood centered around the target vector �xst; and

is a random number drawn from a Gaussian distribution withean � and variance �2.

.4.2. CrossoverCrossover operation is needed to increase the diversity of the

utated vector. The parameters of the mutated vector (�vst(G + 1))nd the target vector (�xst(G)) are swapped, depending on therossover probability (say, CR), to yield a trial vector �ust(G + 1) ateneration (G + 1). The trial vector at generation (G + 1) (denoted as

�st(G + 1)) consists of three components uRst(G + 1), uG

st(G + 1), andBst(G + 1); and is obtained by

jst(G + 1) =

⎧⎪⎪⎨⎪⎪⎩

vjst(G + 1) if (Rj ≤ CR)or j = Rs

xjst(G) if (Rj > CR)and j /= Rs. (19)

ere, Rj (with j = 1, 2, and 3) is a random number in [0, 1] and Rs is annteger which denotes randomly chosen index in [1, 3]. It ensureshat the trial vector �ust(G + 1) will contain at least one parameterrom the mutated vector �vst(G + 1).

puting 15 (2014) 121–135 127

3.4.3. SelectionThe selection operation helps the better fitted vectors to survive

for the next generation. If the cost function of the trial vector �ust(G +1) is less than that of the target vector �xst(G), then �xst(G + 1) isreplaced by �ust(G + 1), otherwise the old value of �xst(G) is retained.

3.4.4. Stopping criterionAs mentioned earlier, the target vectors of the population are

evolved using three DDE operators (namely, mutation, crossover,and selection) through a number of generations until the termi-nation criterion is satisfied. In the present work, execution of thealgorithm is terminated when the class labels of 90% target vectorsof the population remain unchanged between the two consecutivegenerations.

In the proposed DDE, the population corresponds to segmenta-tion of the considered video image frame. The population consistsof target vectors which encode red, green, and blue componentsof each pixel of the segmented image frame. Here, size of the pop-ulation is equal to the dimension of the segmented image frame.Instead of considering the whole search space for mutation, in theproposed DDE we have considered a sub-set of it. A window isdefined at each pixel location and the pixels from its neighbor areused for mutation to obtain the estimated label of correspondingpixel. Since this mechanism uses a small subspace for mutation ithelps in saving the large computational time of the DE and alsomaintain the spatial regularity as mutation is obtained from theneighboring pixels. This is also expected to provide better seg-mented result.

In the proposed search technique, each population is dividedinto a number of overlapping w × w windows. Here, each w ×w window corresponds to a sub-population. Three (mutation,crossover, and selection) operations of conventional DE algo-rithm are applied within each window centering the target vector,yielding new sub-populations. They are merged to generate animproved population. This is similar to a distributed evolutionaryalgorithm where the whole population is divided into a numberof sub-populations and several sub-populations evolve indepen-dently. Afterwards, migration operation is performed to generatean improved population. The proposed algorithm is termed as dis-tributed differential evolution algorithm.

For existing DE algorithms, the population consist of a numberof target vectors. Each target vector is considered to be a solution.For DE with neighborhood based mutation algorithms, neighbor-hood is defined either depending on the index of the target vectorsor the Euclidean distances among them. On the other hand, in theproposed DDE, the whole population is considered to be a solution(segmented output of the considered video frame). Each target vec-tor of the population represents one pixel of the segmented frame.Here, neighborhood is defined based on the spatial regularity of thetarget vector (pixel).

3.5. Segmentation of subsequent frames based on changeinformation

It is already mentioned that the spatial segmentation usingmulti-layer compound MRF model is obtained by estimating theMAP of that model. To segment the initial frame, random initializa-tion was made in [11]. Due to random initialization, segmentationusing MRF model becomes computation intensive. Though in caseof video sequences, random initialization is highly redundant inthe temporal direction as most of the information in the currentframe is already present in the previous frame and only some parts
of any frame changes over time. Accordingly, it can be inferred thatthe current segmentation results will basically be the same as thosefor the previous frame, except for the changed parts. Therefore,based on this assumption, Subudhi et al. [12] proposed a change


Fig. 3. Results on 7th and 15th frames of Claire video sequence: (a) Original frames. Spatial segmentations obtained using (b) MRF with DGA scheme [10,11], (c) modifiedMRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM scheme [12], (f) the proposed method. Temporal segmentations obtained using (g)M raph CV A sche(

iqierf

osf

1

2

RF with DGA scheme [10,11], (h) modified MRF with DGA scheme, (i) MRF with GOPs obtained using (l) MRF with DGA scheme [10,11], (m) modified MRF with DG

p) the proposed method.

nformation based heuristic initialization for segmenting the subse-uent frames. In [12], initialization is done by combining the change

nformation between the current frame and the previously consid-red frame with the previously segmented one. This mechanismeduces the computational cost for segmenting the subsequentrames. The complete procedure is now described in detail.

Let xt be the spatial segmentation of the frame yt at tth instantf time. At time (t + d), yt+d represents the input frame and xt+d is itsegmented version. Let x(t+d)i be its initialization and is obtained asollows:

. Obtain the changes corresponding to the frame yt+d by thresh-olding the absolute difference of the intensities between yt+d andyt frames. The original pixel values of yt+d frame correspondingto the changed pixels at yt+d frame is denoted by y(t+d)|yt+d−yt | .

. The pixels in the previously segmented frame corresponding tothe changed pixels at (t + d)th frame can be found as

xti = xt − xt‖yt+d−yt ‖ . (20)

These regions in xti are replaced by original intensities of yt+d
frame for initializing the segmentation of (t + d)th frame and canbe written as
x(t+d)i = xti + y(t+d)‖yt+d−yt ‖ . (21)

ut scheme [7,22], (j) MRF with SA and ICM scheme [12], (k) the proposed method.me, (n) MRF with Graph Cut scheme [7,22], (o) MRF with SA and ICM scheme [12],

To obtain xt+d (segmentation of the yt+d frame), DDE algorithm withx(t+d)i (i.e., change information based) as an initialization is used tosegment yt+d frame.

3.6. Temporal segmentation

In case of temporal segmentation, Change Detection Mask(CDM) is obtained by thresholding the absolute differences of thetwo consecutive spatially segmented image frames. The obtainedCDM represents the changed regions and the unchanged regions inthe current frame. The changed regions correspond to the movingobjects whereas the unchanged regions correspond to stationaryobjects and background. In order to obtain the locations of themoving objects in the absence of any reference frame, some infor-mation from previous frame is used to update the obtained CDM.This information is represented as:

Q ={

qi,j|0 ≤ i ≤ (M − 1), 0 ≤ j ≤ (N − 1)}

, (22)

where Q is a matrix having the same size of the video frame. Eachelement qi,j of the matrix Q represents the value of the VOP at loca-tion (i, j). If qi,j = 1, then the pixel belongs to the moving object in theprevious frame; otherwise to the background or to the still object
in the previous frame. Based on this information, the obtained CDMis modified. If the pixel (in CDM) belongs to a moving object in theprevious frame and its label is the same as that of the correspond-ing pixel in the previous frame, then the said pixel belongs to the

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oving objects in the current frame. Subsequently, the modifiedDM represents the final temporal segmentation.

With the help of temporal segmentation, the given videorames are divided into two regions: changed (moving objects)nd unchanged (stationary objects and background). The changedegions and the unchanged regions of the CDMt at tth instant ofime, are represented as CRt and URt, respectively. The changedegions in the modified CDM are identified as moving objects inhe current frame. As mentioned, the Video Object Planes (VOPs)re extracted by superimposing the intensity/color values of origi-al pixels of the considered current frame yt in the changed regionsRt of the modified CDM, thereby detecting the moving objects inhe current frame yt.

. Experimental results and discussion

To test the effectiveness of the proposed algorithm, five refer-nce video sequences (Claire, Grandma, Container, Deadline [42], andarlsruhe-taxi [43]) and one real life video sequence (Rahul) are con-idered. These are well known benchmark video sequences. Claire,randma, Deadline, and Rahul video sequences have only one mov-

ng object, whereas Container and Karlsruhe-taxi video sequencesave multiple moving objects.

Since the main objective of the present work is to handle thehallenges for detection of moving objects from video sequences

ig. 4. Results on 12th and 87th frames of Grandma video sequence: (a) Original frames. SpRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM

RF with DGA scheme [10,11], (h) modified MRF with DGA scheme, (i) MRF with Graph COPs obtained using (l) MRF with DGA scheme [10,11], (m) modified MRF with DGA sche


puting 15 (2014) 121–135 129

where an object in the scene moves very slow, or very fast, or stops,and moves further with better accuracy (less effect of silhouettes).

Claire is a news reader video sequence. The movement of objectClaire in the scene is unpredictable. The movement of Claire is dif-ferent from one frame to another. Since, the scene has undergoneillumination variation, it is very difficult to identify the detailedinformation of collar, tie, face, and hair regions. In Grandma videosequence, the object Grandma moves for some times, then tem-porarily stops her movement for some time, and again resumes.This is a poorly illuminated sequence. Different regions in the faceand hair of the Grandma are very similar with that of the back-ground wall. The face region has undergone illumination variation.In Container video sequence, there are three moving objects withdifferent speeds. The boundaries of the objects in the scene areblurred. So it is very difficult to identify the exact boundaries ofthe objects in the scene. Similarly, in Deadline sequence, a complexbackground exists, where hair and dress of the object are simi-lar to some part of the background. The movement of the objectin Deadline sequence is not constant throughout the sequence. InKarlsruhe-taxi sequence, there are three objects having differentsizes and speeds. In its background, many similar kinds of confus-
ing static objects are present. Rahul video sequence is captured by alow resolution camera. Here, the movement of Rahul’s head is veryfast than the other parts of the body; and face and hand are havingsimilar color with that of the background.
atial segmentations obtained using (b) MRF with DGA scheme [10,11], (c) modifiedscheme [12], (f) the proposed method. Temporal segmentations obtained using (g)ut scheme [7,22], (j) MRF with SA and ICM scheme [12], (k) the proposed method.me, (n) MRF with Graph Cut scheme [7,22], (o) MRF with SA and ICM scheme [12],


Fig. 5. Results on 12th and 28th frames of Container video sequence: (a) Original frames. Spatial segmentations obtained using (b) MRF with DGA scheme [10,11], (c) modifiedMRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM scheme [12], (f) the proposed method. Temporal segmentations obtained using (g)M raph CV A sche(

coeaasaoffcstft1och

tffim



In the present article, all the considered video sequences areaptured by a fixed camera. Figs. 3(a)–8(a) show a few consideredriginal frames of the above mentioned video sequences. In ourxperiment, the first video sequence considered is Claire which has

single moving object. Here, the 3rd frame is an initial frame andll other frames are the subsequent ones. Initial frame of the videoequence Grandma is the 12th one whereas the remaining framesre the subsequent frames. In Container video sequence, multiplebjects such as ship, trawler, and flying flag are moving. The 4thrame of this sequence is considered as initial frame and all otherrames are subsequent ones. In case of Deadline video sequence, weonsidered 3rd frame as initial and the remaining frames as sub-equent frames. For Karlsruhe-taxi video sequence, we consideredhe 3rd frame as initial frame and rest of the frames as subsequentrames. Rahul, the real life video sequence is considered to assesshe robustness of the proposed approach. Here, we considered the1th frame as the initial one and all other frames as the subsequentnes. In this work, we have done experiment on all frames of theonsidered video sequences. But due to the page constraint, weave reported only few sample results for visual illustration.

As mentioned in Section 3.4, for mutation of each target vec-or, three parameter vectors may be randomly selected either (i)
rom the whole search space in case of conventional DE or (ii)rom a w × w neighborhood of the corresponding target vectorn case of the proposed DDE. It is observed through our experi-
ents that the latter method provides better spatial segmentation


results with respect to average segmentation error with less com-putational time. Here, we have reported results corresponding tothe latter method. For illustration, results of six video sequencesClaire, Grandma, Container, Deadline, Karlsruhe-taxi, and Rahul arereported in this article. Figs. 3–8 represent the results for theClaire, Grandma, Container, Deadline, Karlsruhe-taxi, and Rahul videosequences, respectively.

Values of the parameters for MRF with DGA scheme [10,11],modified MRF with DGA scheme, MRF with Graph Cut scheme[7,22], MRF with SA and ICM [12], and the proposed method areput in Tables 1–5, correspondingly.

In the present work, ground truths of the considered videosequences are generated manually. Figs. 3(b)–8(b), 3(c)–8(c),3(d)–8(d) and 3(e)–8(e), respectively show the spatial segmen-tations of the considered frames of Claire, Grandma, Container,Deadline, Karlsruhe-taxi, and Rahul video sequences using MRFwith DGA scheme [10,11], modified MRF with DGA scheme,MRF with Graph Cut scheme [7,22], and MRF with SA andICM scheme [12]. Similarly, the spatial segmentations of theconsidered frames for different video sequences using the pro-posed method are displayed in Figs. 3(f)–8(f). The correspondingtemporal segmentation results of the considered frames for
the same video sequences using these methods are shownrespectively in Figs. 3(g)–8(g), 3(h)–8(h), 3(i)–8(i), 3(j)–8(j),3(k)–8(k), 3(l)–8(l), 3(m)–8(m), 3(n)–8(n), 3(o)–8(o) and 3(p)–8(p),correspondingly show the extracted VOPs of the considered frames


Fig. 6. Results on 27th and 75th frames of Deadline video sequence: (a) Original frames. Spatial segmentations obtained using (b) MRF with DGA scheme [10,11], (c) modifiedMRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM scheme [12], (f) the proposed method. Temporal segmentations obtained using (g)MRF with DGA scheme [10,11], (h) modified MRF with DGA scheme, (i) MRF with Graph Cut scheme [7,22], (j) MRF with SA and ICM scheme [12], (k) the proposed method.VOPs obtained using (l) MRF with DGA scheme [10,11], (m) modified MRF with DGA scheme, (n) MRF with Graph Cut scheme [7,22], (o) MRF with SA and ICM scheme [12],(p) the proposed method.

Table 1Parameters chosen for different video sequences of MRF with DGA scheme [10,11].

Video Crossover probability (CR) Mutation probability (MU) Window size

Claire 0.05 0.02 0.05 0.005 5 × 5Grandma 0.03 0.01 0.07 0.001 5 × 5Container 0.08 0.04 0.04 0.005 5 × 5

ue[smpl

TP

Deadline 0.05 0.009 0.03

Karlsruhe-taxi 0.009 0.008 0.02

Rahul 0.05 0.004 0.01

sing these methods. Fig. 9 displays the average segmentationrrors produced by different methods: MRF with DGA scheme10,11], modified MRF with DGA scheme, MRF with Graph Cutcheme [7,22], MRF with SA and ICM scheme [12], and the proposed
ethod. From this figure, it is observed that the proposed method
rovides better segmentation for all the considered frames (withess average segmentation error) than all other methods.

able 2arameters chosen for different video sequences of modified MRF with DGA scheme.

Video � Crossove

Claire 0.05 0.02 0.008 0.05

Grandma 0.03 0.01 0.001 0.07

Container 0.08 0.04 0.02 0.04

Deadline 0.05 0.009 0.007 0.03

Karlsruhe-taxi 0.009 0.008 0.005 0.02

Rahul 0.05 0.004 0.003 0.01

0.002 5 × 50.001 5 × 50.005 5 × 5

The first video sequence considered for the experiment is Claire.Fig. 3(a) shows few original image frames of this sequence. Fig. 3(b)shows the spatial segmentation results obtained by MRF with DGAscheme [10,11]. Here, the frames of this sequence are modeled with
MRF and corresponding MAP is estimated using DGA algorithm.For subsequent frame segmentation, chromosomes having moreenergy are allowed to evolve through DGA. The parameters used
r probability (CR) Mutation probability (MU) window size

0.005 5 × 50.001 5 × 50.005 5 × 50.002 5 × 50.001 5 × 50.005 5 × 5


Fig. 7. Results on 4th and 6th frames of Karlsruhe-taxi video sequence: (a) Original frames. Spatial segmentations obtained using (b) MRF with DGA scheme [10,11], (c)modified MRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM scheme [12], (f) the proposed method. Temporal segmentations obtainedusing (g) MRF with DGA scheme [10,11], (h) modified MRF with DGA scheme, (i) MRF witmethod. VOPs obtained using (l) MRF with DGA scheme [10,11], (m) modified MRF witscheme [12], (p) the proposed method.

Table 3Parameters chosen for different video sequences of MRF with Graph Cut scheme[7,22].

Video � k

Claire 0.09 0.5 600Grandma 0.05 0.3 1000Container 0.08 0.5 600Deadline 0.06 0.4 900

bTamcI

TP[

spatial segmentation results of the considered Claire frames. The

Karlsruhe-taxi 0.03 0.4 600Rahul 0.07 0.5 550

y MRF with DGA scheme [10,11] for Claire sequence are shown inable 1. The results obtained by modified MRF with DGA schemere shown in Fig. 3(c). Here, multi-layer compound MRF is used to
odel the frames and MAP is estimated using DGA algorithm. The
onsidered parameters for this scheme are reported in Table 2.n MRF with Graph Cut scheme [7,22], the considered frames are

able 4arameters chosen for different video sequences of MRF with SA and ICM scheme12].

Video � �

Claire 0.009 0.008 0.007 1.0Grandma 0.05 0.009 0.007 5.19Container 0.01 0.009 0.001 2.44Deadline 0.009 0.006 0.003 1.3Karlsruhe-taxi 0.01 0.008 0.007 2.44Rahul 0.009 0.005 0.001 5.0

h Graph Cut scheme [7,22], (j) MRF with SA and ICM scheme [12], (k) the proposedh DGA scheme, (n) MRF with Graph Cut scheme [7,22], (o) MRF with SA and ICM

modeled with MRF and corresponding MAP is estimated usingGraph Cut scheme. Parameters of this approach are provided inTable 3. Fig. 3(d) shows the spatial segmentation of this scheme. InMRF with SA and ICM scheme [12], frames are segmented by mod-eling it with multi-layer compound MRF model followed by thehybrid algorithm for MAP estimation. Figure 3(e) shows spatial seg-mentation results. The MRF parameters chosen for this sequenceare displayed in Table 4. For the proposed method, frames of thissequence are modeled with the multi-layer compound MRF model.

Segmentation of the initial frame is obtained by estimatingMAP of the MRF model using the proposed DDE algorithm. Changeinformation based subsequent frame segmentation scheme is usedto segment the subsequent frames of this sequence. Fig. 3(f) shows

parameters used by the proposed scheme are reported in Table 5.Temporal segmentation is obtained using original frame difference

Table 5Parameters chosen for different video sequences of the proposed method.

Video � � Windowsize

Crossoverprobability(CR)

Claire 0.009 0.008 0.003 1.0 5 × 5 0.9Grandma 0.03 0.01 0.001 0.01 5 × 5 0.8Container 0.08 0.01 0.001 0.05 5 × 5 0.9Deadline 0.009 0.008 0.003 0.1 5 × 5 0.7Karlsruhe-taxi 0.01 0.007 0.005 0.15 5 × 5 0.5Rahul 0.005 0.004 0.01 0.9 5 × 5 0.7


Fig. 8. Results on 11th and 26th frames of Rahul video sequence: (a) Original frames. Spatial segmentations obtained using (b) MRF with DGA scheme [10,11], (c) modifiedMRF with DGA scheme, (d) MRF with Graph Cut scheme [7,22], (e) MRF with SA and ICM scheme [12], (f) the proposed method. Temporal segmentations obtained using (g)M raph CV A sche(

fsabM[sSFc



ollowed by thresholding technique for both MRF with DGAcheme [10,11] and its modified version. Temporal segmentationsre shown in Fig. 3(g) and (h). Label frame difference followedy thresholding scheme is used for temporal segmentation forRF with Graph Cut scheme [7,22], MRF with SA and ICM scheme

12], and the proposed method. Fig. 3(i)–(k) shows the temporal
egmentation of MRF with Graph Cut scheme [7,22], MRF withA and ICM scheme [12], and the proposed method, respectively.ig. 3(l)–(p) correspondingly show the extracted VOPs of theonsidered frames using these methods.
Fig. 9. Average Segm


To demonstrate the effectiveness of the proposed approach overother methods, for typical illustration, let us consider the output ofthe Claire video sequence. From Fig. 3(b)–(f), it is noticed that thenose, eye, some parts of face, and few parts of shirt are not properlysegmented using MRF with DGA scheme [10,11] and its modifiedversion. It produces more small patches in the shirt region. MRF
with Graph Cut scheme [7,22] merges eyes, nose, and lip regions tothe face region of Claire. It is also seen from the figures that somepart of the head, face and the body of the Claire are not properly seg-mented using MRF with SA and ICM scheme [12]. This may be due
entation Error


Table 6Average execution time (in seconds).

Video MRF with DGAscheme [10,11]

Modified MRF withDGA scheme

MRF with GraphCut scheme [7,22]

MRF with SA andICM scheme [12]

Proposed method

Claire 11.00 ± 2.18 17.50 ± 4.33 28.50 ± 13.43 33.50 ± 33.75 24.50 ± 12.99Grandma 15.50 ± 2.60 25.25 ± 5.63 37.50 ± 18.19 35.75 ± 85.30 26.50 ± 16.45Container 10.50 ± 2.41 17.25 ± 3.90 29.50 ± 17.92 41.25 ± 45.47 23.50 ± 14.72Deadline 38.25 ± 21.22 51.25 ± 28.58 64.50 ± 37.24 75.00 ± 77.94 60.25 ± 35.18Karlsruhe-taxi 22.50 ± 7.40 32.50 ± 16.54 55.50 ± 28.57 55.25 ± 42.80 49.50 ± 25.97Rahul 7.25 ± 0.87 12.25 ± 1.95 25.00 ± 15.59 25.25 ± 22.22 22.25 ± 15.81

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he bold value indicates that the method takes maximum execution time among alndicates that the method takes minimum execution time among all the technique

o the premature convergence of ICM used in [12]. The proposedtrategy based on DDE, on the other hand, can segment these partsroperly. Fig. 9 displays the average segmentation error of differentonsidered video sequences. From this figure, it is observed that theroposed method produces better results than those obtained byll other methods.

From the segmentation results of Grandma video sequenceeported in Fig. 4(b)–(f), it is seen that few parts of the face regionre segmented as background using both MRF with DGA scheme10,11] and its modified version. It is also noticed that few parts ofoise and eye are merged to face region and more patches present

n the body part. MRF with Graph Cut scheme [7,22] merges theace, hair, and neck regions into a single region. MRF with SA andCM scheme [12] segments these parts into small patches. The pro-osed technique, on the other hand, properly segments these partsith less amount of average segmentation error.

Incase of Container video sequence, MRF with DGA scheme10,11], its modified version, MRF with Graph Cut scheme [7,22]nd MRF with SA and ICM scheme [12] segment more parts of theontainer as water region. On the other hand the proposed methodroduces better segments.

From Fig. 6(b)–(f), it is also visually seen that the proposedethod provides better segmentation results of Deadline video

equence than all other schemes. From the segmentation results ofarlsruhe-taxi video sequence displayed in Fig. 7(b)–(f), it is foundhat few small cars and tree are merged to road for both MRF withGA scheme [10,11] and its modified version. MRF with Graphut scheme [7,22] merges all static small cars into a single regionnd unable to segment the tree. Whereas, MRF with SA and ICMcheme [12] properly segment static small cars but merges the treeith the road. On the other hand, the proposed method properly

egments all static small cars as well as the tree. If we visually ana-yze the segmentation results of Rahul video sequence as depictedn Fig. 8(b)–(f), it is noticed that the face and the neck region ofahul are not properly segmented by MRF with DGA scheme [10,11]nd its modified version, whereas face, neck, and hair regions areerged into a single region by MRF with Graph Cut scheme [7,22].n the other hand MRF with SA and ICM scheme [12] and the pro-osed method provide similar results except a few parts of face andeck regions.

All simulations have been done using visual C++on a machineith Pentium(R)4 CPU 2.40 GHz and 512 MB RAM. Table 6 shows

he average computational time (±standard deviation) required foregmenting the considered video frames using different methods.rom this table, it is seen that MRF with SA and ICM scheme [12]equires maximum average time for segmenting frames of the con-idered video sequences whereas MRF with DGA scheme [10,11]akes the least amount of average execution time. In MRF with SAnd ICM scheme [12], SA was used initially to find out the subop-
imal solutions and then ICM was executed to find out the nearptimal solutions, thereby making it computation intensive. MRFith Graph Cut scheme [7,22] takes less average time than MRFith SA and ICM scheme [12] and more average time than other
echniques for segmenting frames of the considered video. Whereas the italic valueegmenting frames of the considered video.

methods for segmenting frames. On the other hand, MRF with DGAscheme [10,11] takes the least amount of average time for seg-menting the image frames as elitism is used and mutation maynot occur always. The proposed method explores the search spacequickly using DDE; thereby produces the output with moderateaverage execution time. The minimum and maximum average exe-cution times required for segmenting all considered frames amongdifferent methods are highlighted in Table 6.

The results reported in this article were obtained with the opti-mal values of the MRF model bonding parameters ˛, ˇ, and � . Thevalue of affects the number of regions in segmentation. Largevalue of merges contextually less variate regions. On the otherhand, small value of produces smaller regions which are con-textually less variate. encourages pixels to have the same labelin consecutive image frames. Fragmentation can occur due to highvalue of ˇ. Similarly, small value of � produces thicker boundaryand high value of � will result in thinner boundary. Fig. 10(a)–(c)displays the spatial segmentations of Walk-Run [44] (it is a highresolution video of size 640 × 480) video sequence obtained by theproposed method with large values of ˛, ˇ, and � , respectively.Fig. 10(d)–(f) shows the spatial segmentations obtained by the pro-posed method with small values of ˛, ˇ, and � , respectively.

Selection of optimal values of ˛, ˇ, and � is critical. To bet-ter assess the effects of ˛, ˇ, and � on spatial segmentation, weobtained different results by considering different combination of˛, ˇ, and � values in the ranges [0, 2.5], [0, 1.0], and [0, 0.7], respec-tively. The spatial segmentation, temporal segmentation, and VOPof Walk-Run video sequence obtained by the proposed method withoptimal values of parameters ˛, ˇ, and � are shown in Fig. 11(b)–(d),respectively.

The crossover probability (CR) and scaling factor (F) are thecontrol parameters of the proposed DDE. The CR controls howmany parameters of the target vector and the mutated vector areexchanged. A large value of CR speeds up the convergence of theDDE and solution may stuck to a local optima; whereas a smallvalue of CR degrades the convergence speed but may obtain nearglobal optimum solution. So good choice of CR is a critical issuefor balancing both convergence speed and solution quality. In thisregard, we empirically found that CR ∈ [0.5, 0.9] is a good choice forvideo frame segmentation. In the proposed DDE, the scaling factorF is randomly drawn from a Gaussian distribution with mean 0 andvariance 1. Segmented output obtained using the proposed DDEalso depends on the size of the neighborhood. If we increase theneighborhood size, the convergence speed of the DDE may decreaseand may merge more small regions to a single region. On the otherhand, if we decrease the neighborhood size, the convergence speedmay increase and may produce more small regions which are notdistinct with respect to their spatial continuity. Hence a properchoice of neighborhood size is an important factor. From the exper-
iment it is found that the neighborhood size between 5 × 5 to 7 × 7produces better results.
Parameters of both MRF with DGA scheme [10,11] and its mod-ified schemes are determined on trial and error basis. It is found


Fig. 10. Spatial segmentations obtained by the proposed method with (a) large value of = 2.3, (b) large value of = 9.3, (c) large value of � = 5.3, (d) small value of = 0.1,(e) small value of = 0.009, (f) small value of � = 0.001.

F Spatias

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ig. 11. Result on 3th frame of Walk-Run video sequence: (a) Original frame, (b)egmentation, (d) VOP obtained using the proposed method.

rom the experiments that the parameters set to similar values aseported in [45] produce better results. For MRF with Graph Cutcheme [7,22], parameters are also empirically determined. Fromhe experiment it is found that it produces better segmented resultsith these set of parameter values. Parameters of MRF with SA and

CM schemes [12] are set according to those values reported in [46].ables 1–5 display the parameter values for different consideredideo sequences by various methods.

. Conclusions and future works

In this article, moving objects from a given video sequencere detected using a multi-layer compound MRF model with DDEs optimization technique. In the proposed method, consideredRF model preserves the boundary information of the segmented

egions. The proposed DDE algorithm explores the search spaceuickly for finding out the optimum segmentation. From the results

t is found that the proposed DDE based algorithm provides betteregmented results (with respect to average segmentation error)han those obtained using MRF with DGA scheme [10,11], its mod-fied version, MRF with Graph Cut scheme [7,22], and MRF withA and ICM scheme [12]. The present approach could also iden-ify the locations of the moving objects well. The proposed methods less computation intensive than MRF with Graph Cut scheme7,22] and MRF with SA and ICM scheme [12]. Here, the parametersf the considered MRF model are chosen on a trial and error basis.o make the system more robust and automatic, these parametersould be determined using some parameter estimation algorithms.
allipeddia et al. discussed some heuristic techniques to determine
he control parameters of DE algorithm in [47]. These mechanismsay also be incorporated to determine the control parameters of

he proposed DDE. The performance of DE algorithm also depends

l segmentation with optimal values of = 0.1, = 0.05, and � = 0.1, (c) Temporal

on selection of vectors for mutation operation. Recent literature[48–52] briefly discuss about the selection procedure of vectorsfor mutation operation. In future, instead of random selection wewill incorporate such kind of mechanism for selecting vectors toimprove the performance of the DDE.

Acknowledgements

The authors like to thank the reviewers for their thorough andconstructive comments, which helped a lot to enhance the qual-ity of the manuscript. Funding by U.S. Army through the project“Processing and Analysis of Aircraft Images with Machine LearningTechniques for Locating Objects of Interest” (Contract No. FA5209-08-P-0241) is also gratefully acknowledged.

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Documents

Moving object detection using Markov Random Field and Distributed Differential Evolution