Background Modeling and Foreground Detection via aReconstructive and Discriminative Subspace Learning Approach

C. Marghes1, T. Bouwmans2, R. Vasiu1

1Multimedia Centre, "Politehnica" University of Timisoara, Timisoara, Romania2Laboratory MIA, University of La Rochelle, La Rochelle, France

Abstract— Background subtraction is one of the basic low-level operations in video analysis. The aim is to separatestatic information called "background" from the movingobjects called "foreground". The background needs to bemodeled and updated over time to allow robust foregrounddetection. Reconstructive subspace learning such as Prin-cipal Component Analysis (PCA) has been widely used inbackground modeling by significantly reducing the data’sdimension. However, reconstructive representations strive tobe as informative as possible in terms of well approximatingthe original data. On the other hand, discriminative meth-ods such as Linear Discriminant Analysis (LDA) providesa supervised reconstruction of the data which will oftengive better classification results when compared to thereconstructive methods. In this paper, we offer to use andvalidate the combination of a reconstructive method witha discriminative one to model robustly the background. Theobjective is firstly to enable a robust model of the backgroundand secondly a robust classification of pixels as backgroundor foreground. Results on different datasets demonstrate theperformance of the proposed approach.

Keywords: Background modeling, Foreground detection, Sub-space learning

1. IntroductionBackground modeling is a key component in a video

surveillance system with static cameras. In the past decade,many background modeling methods [1][2][3] have beenproposed and achieved good perfomance on well-illuminatedscenes. However, the challenging scenes that presentsdynamic backgrounds or illumination changes still re-mained unsolved. Statistical models such as single gaussian[4][5][6], mixture of gausssians [7][8] and kernel densityestimation [9][10][11][12] offer a nice framework to dealwith these challenges. Particularly, subspace learning modelshave recently attracted much attention to address thesechallenges. Subspace learning methods can be classifiedinto two main categories, those of either reconstructive ordiscriminative methods [13][14]. With the reconstructiverepresentations, we strive to be as informative as possiblein terms of well approximating the original data [13]. Theirmain goal is encompassing the variability of the training

data gathered, meaning these representations are not task-dependent. On the other hand, we have discriminative meth-ods that provide a supervised reconstruction of the data.These methods are task-dependent, but are also, however,spatially and computationally far more efficient and theywill often give better classification results when compared tothe reconstructive methods [13]. So, reconstructive subspacelearning models require more effort to construct a robustbackground model in an unsupervised manner rather thanproviding a good classification in the foreground detection.On the other hand, discriminative subspace learning modelsallow a robust classification of pixels as background orforeground but need a supervised initialization. Consideringall of this, we propose to use a mixed method that combinesa reconstructive method (PCA) with a discriminative one(LDA) to model robustly the background. The objectiveis firstly to enable a robust model of the background andsecondly a robust classification of pixels as background orforeground.

Mixed reconstructive and discriminative approaches havebeen developped with success in object category detection[15] object recognition [16], and image classification [17].Recently, Uray et al. [18] applied with success a recon-structive and discriminative approach for face recognition.This method combines a reconstructive method (PCA) witha discriminative one (LDA). In this work, we propose to useand validate this combined reconstructive and discriminativeapproach for background modeling.

Applying this mixed method for background modeling,we used the PCA to model the primary distribution of thepixel values among multiple images, and regards the primarydistribution as the knowledge of the background. Then,this method assumes that the low-rank principal vectors ofthe image space contain discriminative information. So, wecan applied on them the LDA for background/foregroundclassification.

The rest of this paper is organized as follows. Firstly, inSection 2, we provide a short survey on subspace learningpreviously used for background modeling. In Section 3, wepresent the mixed reconstructive and discriminative methodapplied for background modeling and foreground detection.Then, a comparative evaluation is provided upon differentdatasets in Section 4. Finally, the conclusion is establishedin Section 5.

2. Related WorkIn literature, reconstructive subspace learning models have

attracted a lot of attention [19]. In [20], subspace learningbased on PCA is applied on N images to construct abackground model, which is represented by the mean imageand the projection matrix comprising the first p significanteigenvectors of PCA. Foreground segmentation is then ob-tained by computing the difference between the input imageand its reconstruction. The PCA provides a robust modelof the probability distribution function of the background,but not of the moving objects while they do not have asignificant contribution to the model. However, this modelpresents several limitations:

• Influence of foreground objects: The size of theforeground objects must be small and they shouldn’tappear in the same location during a long period in thetraining sequence. In [21][22][23], the authors alleviatespartially these contraints.

• Background maintenance: It is computationally in-tensive to perform model updating using the batchmode PCA. Moreover without a mechanism of robustanalysis, the outliers or foreground objects may beabsorbed into the background model. Some incrementalmechanims robust to outliers have been developed in[24][25][26][27][28][29][30][31].

• Feature size and type: The application of this modelis mostly limited to gray-scale images and pixel-wiseaspect since the integration of multi-channel data is notstraightforward. It involves much higher dimensionalspace and causes additional difficulty to manage datain general. Recently, Han and Jain [32] proposed anefficient algorithm using a weighted incremental 2-Dimensional Principal Component Analysis. The pro-posed algorithm was applied to 3-channel (RGB) and4-channel (RGB+IR) data. Results show noticeableimprovements in presence of multimodal backgroundand shadows. To solve the pixel-wise limitation, Zhaoet al.[33] [34] used spatio-temporal block instead ofpixel. Results show more robustness robust to noise andfast lighting changes

• Unimodal aspect: The representation is not multimodalso various illumination changes cannot be handledcorrectly. Recently, Dong et al. [35] proposed to use amulti-subspace learning to handle different illuminationchanges. The feature space is organized into clusterswhich represent the different lighting conditions. ALocal Principle Component Analysis (LPCA) transfor-mation is used to learn separately an eigen-subspacefor each cluster. When a current image arrives, thealgorithm selects the learned subspace which sharesthe nearest lighting condition. The results [35] showthat the LPCA algorithm outperforms the original PCA[20] especially under sudden illumination changes. In a

similar way, Kawanishi et al. [36] generated the back-ground image that well expresses the weather and thelighting condition of the scene. This method collects ahuge number of images by super long term surveillance,classifies them according to their time in the day, andapplies the PCA so as to reconstruct the backgroundimage.

PCA, thanks to its different improvements over time, is themost used reconstructive subspace learning method in back-ground modeling. It is reliable when dealing with illumina-tion changes. Furthermore, it can also be implemented inboth incremental and robust way. However, it requires moreeffort to construct a robust background model in an unsuper-vised manner rather than providing a good classification inthe foreground detection. To solve it, Farcas et al. [37][38]used a discriminative approach called Incremental MaximumMargin (IMMC). It derives the online adaptive supervisedsubspace from sequential data samples and incrementallyupdates the eigenvectors of the criterion matrix. IMMC doesnot need to reconstruct the criterion matrix when it receives anew sample, thus the computation is very fast. This approachoutperfoms the reconstructive ones but the main drawbackis that ground truth images are needed for the backgroundinitialization.

3. Proposed MethodIn this section, we present how the mixed method

developed in [18] can be used to model robustly thebackground and to classify pixels as background orforeground. This method used a reconstructive method witha discriminative one combining the advantages of both.This is done by embedding the LDA classification intothe PCA framework. The combined subspace consists ina truncated PCA subspace and a few additional vectorsthat include the discriminative information which wouldbe lost by the discarted principal vectors. In conclusion,the subspace contains both reconstructive information inorder to enable incremental learning and discriminativeinformation to enable efficient classification. PCA is awell known reconstructive method which includes thereconstructive information that can approximate well thetraining data. LDA, on the other hand, is a discriminativemethod which only keeps the discriminative informationabout the images. While the LDA is recognized to besuperior to PCA in recognition tasks, it is less suitable forincremental learning. Therefore both methods will be mixedin order to achieve the best results.

3.1 Problem DefinitionLet n be the number of images in the training set, each

of them containing m pixels, aligned in the columns of thematrix XϵRm×n, let µϵRm be the mean image, and c bethe number of classes the pixels belong to. In our case, the

classes are the background and the foreground, i.e c = 2.The goal of subspace methods is to find subspaces thattransform the input pixels of the input images in a way thatenables efficient classification of pixels of the current image.Reconstructive and discriminative methods offer differentsolutions to this problem.

• Reconstructive methods are designed to find a linearrepresentation that best describes the input data as:

X = UkAk + µ11×n (1)

where k vectors in the columns of Uk =[u1, ..., uk]ϵR

m×k form the reconstructive basis andn vectors in the rows of Ak = [aT1 , ..., a

Tn ]

T ϵRk×n

are the coefficient vectors, meaning the k-dimensionalrepresentations of the training images.

• Discriminative methods are developed in a differentway and are suited for classification tasks. The objectiveis to find a linear function:

g(x) = WT (x− µ), (2)

where W = [w1, ..., w(c−1)]ϵRm×(c−1) is used for

transforming the data into a lower-dimensional classifi-cation space based on which a given sample x is sortedto a specific class. LDA finds the projection directionson which the intraclass scatter is minimized whilst theinter-class scatter is maximized.

3.2 Background ModelingThe mixed algorithm loads the training images sequen-

tially and computes the new background image from thecurrent background image and the new input image. Thepurpose is to model the background from the n images fromthe dataset in a way that includes both reconstructive and dis-criminative properties. The reconstructive property is basedon Principal Component Analysis. As most of the visualvariability of the images are contained in the first k principalvectors (where k < n), only the k-dimensional principalsubspace is retained. PCA computes the first k coefficientswhich contain most of the reconstructive information, whilethe discriminative information is lost. In order to keep thediscriminative information, the truncated principal subspacewill be augmented with c−1 additional basis vectors whichmaintain all the information relevant for LDA.

Let us suppose that an augmented PCA subspace (APCA)has already been built from the first n images. The currentaugmented reconstructive model of the background consistsof basis vectors U (n)ϵRm×(k+c−1), mean vector µϵRm andcoefficient vectors A(n)ϵR(k+c−1)×n. In step n + 1, a newAPCA subspace will be computed from the representations(coefficient vectors) of the first n images and the new loadedimage. The subspace update starts with the projection of theimage x(n+1) into the current eigenspace:

a = U (n)T (x(n+1) − µ(n)) (3)

Next step consists in computing the reconstruction y ofthe new image and the residual vector r:

y = U (n)a+ µ(n) (4)

r = x(n+1) − y (5)

The new basis takes into account the residual vector byappending it to the eigenspace. Therefore, the coefficients ofthe new basis become:

A′ =

[A(n) a0 ||r||

]PCA is performed on the matrix A′ and new eigenvectors

U ′′ and mean value µ′ are obtained. The following step isto project the coefficient vectors A′ into the new basis U ′′

[18] and rotate the current basis vectors to match new basisvectors [18]:

A = U ′′T (A′ − µ′11×(n+1)) (6)

U = U ′U ′′ (7)

Once the current background image has been updated,LDA can be performed on the low-dimensional coefficientvectors AϵR(k+c)×(n+1). The discriminative representationis contained in the LDA vectors V ϵR(k+c)×(c−1).

At this point, no reconstructive nor discriminative infor-mation has been lost since all the information has beenincluded in the model. However, the size of the APCA sub-space has increased by one. In order to keep the dimensionof the model, the matrices U ,A and V must be truncated byone.

3.3 Foreground DetectionThe foreground detection is made by comparison of the

reconstructed background with the current image as in [20]:

|y − x(n+1)| > Tthreshold (8)

3.4 Background MaintenanceThe classification is made in two steps: firstly a new image

is projected into the incremental PCA basis and secondlythe obtained coefficient vector is projected onto the low-dimensional LDA vectors. Thus, the classification functionis updated as follows:

g(x) = V TUT (x− µ(n+1)) (9)

In order to truncate subspace by one, the matrices U , Aand V will be divided in submatrices containing the first kdimensions that must be kept and the last c dimensions thatmust be truncated by one:

U =[Uk Uc

]A =

[Ak

Ac

]

V =

[Vk

Vc

]The mean also has to be recomputed depending on the

new basis:

µ(n+1) = µ(n) + U ′µ′ (10)

Next step consists in orthonormalizing Vc and updatingthe APCA basis, coefficients and LDA vectors.

U (n+1) =[Uk UcVc

]A(n+1) =

[Ak

V Tc Ac

]

V (n+1) =

[Vk

(V Tc Vc)

1/2

]4. Results

We compared the proposed approach with classical statis-tical background models (SG[4], MOG [7], KDE [9]), thereconstructive subspace learning models (PCA[20], ICA[39],INMF[40][41] and IRT[42][43]) and the discriminative one(IMMC [37]). The experiments were conducted qualitativelyand quantitavely on the Wallflower dataset [44]. Further-more, we present a qualitative result on the PETS 2006dataset[45].

4.1 Wallflower datasetWe have chosen this particular dataset provided by

Toyama et al. [44] because of how frequent it is used inthis field. This frequency is due to its faithful representationof real-life situations typical of scenes susceptible to videosurveillance. Moreover, it consists of seven video sequences,with each sequence presenting one of the difficulties apractical task is likely to encounter. A brief description ofthe Wallflower image sequences can be made as follows:

• Moved Object (MO): A person enters into a room,makes a phone call, and leaves. The phone and the chairare left in a different position. This video contains 1747images.

• Time of Day (TOD): The light in a room graduallychanges from dark to bright. Then, a person enters theroom and sits down. This video contains 5890 images.

• Light Switch (LS): A room scene begins with the lightson. Then a person enters the room and turns off thelights for a long period. Later, a person walks in the

room and switches on the light. This video contains2715 images.

• Waving Trees (WT): A tree is swaying and a personwalks in front of the tree. This video contains 287images.

• Camouflage (C): A person walks in front of a monitor,which has rolling interference bars on the screen. Thebars include similar color to the person’s clothing. Thisvideo contains 353 images.

• Bootstrapping (B): The image sequence shows a busycafeteria and each frame contains people. This videocontains 3055 images.

• Foreground Aperture (FA): A person with uniformlycolored shirt wakes up and begins to move slowly. Thisvideo contains 2113 images.

The images are 160× 120 pixels. For each sequence, theground truth is provided for one image when the algorithmhas to show its robustness to a specific change in the scene.Thus, the performance is evaluated against hand-segmentedground truth. Three terms are used in the evaluation: FalsePositive (FP) is the number of background pixels that arewrongly marked as foreground; False Negative (FN) is thenumber of foreground pixels that are wrongly marked asbackground; Total Error (TE) is the sum of FP and FN. Fig.2 shows the results obtained by the different algorithms oneach sequence. The PCA results come from [44] and theICA results were provided by Tsai and Lai [39]. The INMFresults were provided by Bucak et al. [41]. For IRT, IMMCand IPCA-LDA, results came from our implementation inMatlab. For IMMC, we present the results obtained differentN which are the number of training frames. The resultswith N=30 and N=100 are called respectively IMMC (30)and IMMC (100). The corresponding scores in terms of FP,FN and TE are shown in Table 1. The proposed methodoutperforms the reconstructive methods (PCA,ICA, INMFand IRT) and the discriminative one (IMMC). Indeed, theproposed method has the lowest number of total errors(10335).

4.2 PETS 2006 datasetThe PETS 2006 dataset consists of seven videos which

contained indoor scenes filmed by different cameras. Theimages are 720× 576 pixels. The goal is to detect people ina station. Fig. 1 shows the original frame 299 of the sequencecalled "S1-T1-Camera 3", the groundth truth, the foregroundmask obtained by IPCA-LDA.

5. ConclusionIn this paper, we used and validated a mixed reconstructive

and discriminative algorithm to model the background invideo sequences. This was done by embedding the LDAclassification into the PCA framework. The given approachcombined the advantages of both. This approach allowus to construct a robust model of the background and

Problem Type

Error MO TD LS WT C B FA Total

Algorithm Type Errors (TE)

SG False neg 0 949 1857 3110 4101 2215 3464

Wren et al.[1] False pos 0 535 15123 357 2040 92 1290 35133

MOG False neg 0 1008 1633 1323 398 1874 2442

Stauffer et al.[2] False pos 0 20 14169 341 3098 217 530 27053

KDE False neg 0 1298 760 170 238 1755 2413

Elgammal et al.[3] False pos 0 125 14153 589 3392 933 624 26450

PCA False neg 0 879 962 1027 350 304 2441

Oliver et al.[20] False pos 1065 16 362 2057 1548 6129 537 17677

ICA False neg 0 1199 1557 3372 3054 2560 2721

Tsai and Lai[39] False pos 0 0 210 148 43 16 428 15308

INMF False neg 0 724 1593 3317 6626 1401 3412

Bucak et al.[41] False pos 0 481 303 652 234 190 165 19098

IRT False neg 0 1282 2822 4525 1491 1734 2438

Li et al.[43] False pos 0 159 389 7 114 2080 12 17053

IMMC (30) False neg 0 1336 2707 4307 1169 2677 2640

Farcas et al. [37] False pos 0 11 16 6 136 506 203 15714

SL-IMMC (100) False neg 0 626 711 4106 1167 2175 2320

Farcas et al. [37] False pos 0 10 15 5 135 503 201 11974

IPCA-LDA False neg 0 443 1107 1426 922 2380 2025

Proposed Method False pos 0 103 49 958 204 142 576 10335

Table 1: Performance Evaluation on the Wallflower dataset [44].

Fig. 1: Sequence PETS 2006. From left to right: Currentimage, ground truth image, result with IPCA-LDA

secondly to classify pixels as background or foreground.Experiments show that the IPCA-LDA is more robust thanthe reconstructive methods(PCA, ICA, INMF and IRT) andthe discriminative one (IMMC). Future developments of thiswork may concern robust PCA approaches.

6. AcknowledgmentsThe authors would like to thank D. Tsai and S. Lai

(Department of Industrial Engineering and Management,Yuan-Ze University, Taiwan) who kindly provided the resultsobtained by their algorithm ICA [39] and S. Bucak (PRIPLaboratory, Michigan State University, USA) who providedthe results obtained by his algorithm INMF [41].

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