ACKGROUND SUBTRACTION WITH ADAPTIVE

SPATIO-TEMPORAL NEIGHBORHOOD ANALYSIS

Marco Cristani and Vittorio Murino

Computer Science Dep., Universit

a degli Studi of Verona, Strada Le Grazie 15, Verona, Italy

Keywords:

Surveillance, Motion analysis, Robustness.

Abstract:

In the literature, visual surveillance methods based on joint pixel and region analysis for background sub-

traction are proven to be effective in discovering foreground objects in cluttered scenes. Typically, per-pixel

foreground detection is contextualized in a local neighborhood region in order to limit false alarms. However,

such methods have an heavy computational cost, depending on the size of the surrounding region considered

for each pixel. In this paper, we propose an original and efﬁcient joint pixel-region analysis technique able

to automatically select the sampling rate with which pixels in different areas are checked out, while adapting

the size of the neighborhood region considered. The algorithm has been validated on standard videos with

benchmark tests, proving the goodness of the approach, especially in terms of quality of the detection with

respect to the frame rate achieved.

1 INTRODUCTION

Background subtraction is a fundamental step in auto-

mated video surveillance. It aims at classifying pixel

values as background (BG), i.e., the expected part of

the monitored scene, and the foreground (FG), i.e., the

interesting visual information (e.g., moving objects).

It is widely accepted that BG subtraction cannot be

adequately performed by per-pixel methods, i.e., con-

sidering every temporal pixel evolution as an indepen-

dent process. Instead, per-pixel methods augmented

with per-region strategies (also called hybrid meth-

ods, see Section 2) better behave, deciding the class

of a pixel value by inspecting the related neighbor-

hood. Using hybrid schemes, several BG subtraction

issues can be effectively faced (Toyama et al., 1999);

anyway, the price to pay in hybrid systems is undoubt-

edly an increase of the computational load required.

In this paper, we propose a hybrid BG subtrac-

tion scheme which gives two contributes to the related

state of the art: ﬁrst, it is accurate, i.e., the number

of false alarms is low: this is due to a dynamic def-

inition of the neighborhood zone around each pixel

which permits to capture aperiodic chromatic oscil-

lations of scene components, such as boats in a har-

bour scenario or moving tree branches. Second, our

method is fast, outperforming the time performances

of the most-known BG subtraction algorithms. In

practice, zones where the background is static with

the same visual aspect are seldom observed. Vice

versa, zones where the background varies or where

foreground is visible are examined more often. We

call our method adaptive spatio-temporal neighbor-

hood analysis (ASTNA). Experiments carried out on

standard and ad-hoc benchmark data show the good-

ness of ASTNA.

The rest of the paper is organized as follows. Sec-

tion 2 reviews brieﬂy the state of the art of the back-

ground subtraction methods; details of the proposed

strategy are reported in Section 3; in Section 4, ex-

periments on real data and critical observations are

reported, and, ﬁnally, in Section 5 conclusions are

drawn and future perspectives envisaged.

2 RELATED LITERATURE

The actual BG subtraction literature is large and mul-

tifaceted; here we propose a taxonomy in which the

BG subtraction methods are organized in i) per pixel,

ii) per region, iii) per frame, and iv) hybrid methods.

The class of per-pixel approaches is formed by meth-

ods that perform BG/FG discrimination by consider-

ing each pixel signal as an independent process. One

of the ﬁrst BG modeling was proposed in the surveil-

lance system Pﬁnder (Wren, et al., 1997), where

each pixel signal was modeled as a uni-modal Gaus-

sian distribution. In (Stauffer and Grimson, 1999),

484

Cristani M. and Murino V. (2008).

BACKGROUND SUBTRACTION WITH ADAPTIVE SPATIO-TEMPORAL NEIGHBORHOOD ANALYSIS.

In Proceedings of the Third International Conference on Computer Vision Theory and Applications, pages 484-489

DOI: 10.5220/0001072704840489

 SciTePress

the pixel evolution is modeled as a multimodal sig-

nal, described with a time-adaptive mixture of Gaus-

sian components (TAPPMOG). In (Suter and Wang,

2005), the authors speciﬁed i) how to cope with color

signals (the original version was proposed for gray

values), proposing a normalization of the RGB space

taken from (Mittal and Paragios, 2004), ii) how to

avoid overﬁtting and underﬁtting (due to values of the

variances too low or too high), proposing a thresh-

olding operation, and iii) how to deal with sudden

and global changes of the illumination, by tuning the

learning rate parameter. For the latter, the idea was

to increase the learning rate when the foreground in-

creases from one frame to another more than 70%: in

this way the BG model can faster evolve and produce

less false alarms. Note that this model cannot more

be called TAPPMOG, because global reasoning is ap-

plied.

In (Zivkovic, 2004), the number of Gaussian com-

ponents is automatically chosen, using a Maximum

A-Posteriori (MAP) test and employing a negative

Dirichlet prior, able to associate more than a single

Gaussian component where the BG exhibits a mul-

timodal behavior, thus allowing a faster BG mainte-

nance.

Another per-pixel approach is proposed in (Mittal and

Paragios, 2004): this model uses a non-parametric

prediction algorithm to estimate the probability den-

sity function of each pixel, which is continuously up-

dated to capture fast gray level variations. In (Nakai,

1995), pixel value probability densities, represented

as normalized histograms, are accumulated over time,

and BG label are assigned by the Maximum A Poste-

riori criterion.

Region-based algorithms usually divide the frames

into blocks and calculate block-speciﬁc features;

change detection is then achieved via block match-

ing, considering for example fusion of edge and in-

tensity information (Noriega and Bernier, 2006). In

(Heikkila and Pietikainen, 2006) a region model de-

scribing local texture characteristic is presented:the

method is prone to errors when shadows and sudden

global changes of illumination occur.

Frame-level class is formed by methods that look for

global changes in the scene. Usually, they are used

jointly with other pixel or region BG subtraction ap-

proaches. In (Stenger et al., 2001), a graphical model

was used to adequately model illumination changes of

the scene. In (Ohta, 2001), a BG model was chosen

from a set of pre-computed ones, in order to minimize

massive false alarm.

Hybrid models describe the BG evolution using

jointly pixel and region models, and adding in gen-

eral post-processing steps. In Wallﬂower (Toyama et

al., 1999), a 3-stage algorithm is presented, which op-

erates respectively at pixel, region and frame level.

Wallﬂower test sequences are widely used as compar-

ative benchmark for BG subtraction algorithms. In

(Wang and Suter, 2006), a non parametric, per pixel

FG estimation is followed by a set of morphological

operations in order to solve a set of BG subtraction

common issues. In (Kottow et al., 2004) a region level

step, in which the scene is modeled by a set of local

spatial-range codebook vectors, is followed by an al-

gorithm that decides at the frame-level whether an ob-

ject has been detected, and several mechanisms that

update the background and foreground set of code-

book vectors. For a good BG subtraction methods re-

view, see (Piccardi, 2004).

3 PROPOSED METHOD

Let n, n = 1,... ,N be a pixel location, z

be the pixel

signal observed at location n and z

(t)

be a realization

of such signal at time t. The decision to classify z

(t)

as BG or FG is given by a two-step process. The ﬁrst

step is the per-pixel (PP) process, the second step is

the per-region (PR) process.

3.1 The Per-pixel Process

The PP process controls whether the per-pixel infor-

mation is sufﬁcient to explain z

(t)

as a BG value. In

this paper, each pixel signal is modeled using a set

of R Gaussian pdf’s N (·), as proposed by (Stauffer

and Grimson, 1999). The probability of observing the

value z

(t)

is:

P(z

(t)

) =

∑

r=1

(t)

n,r

N (z

(t)

|µ

(t)

n,r

,σ

(t)

n,r

) (1)

where w

(t)

n,r

, µ

(t)

n,r

and σ

(t)

n,r

are the time adaptive mix-

ing coefﬁcients, the mean, and the standard deviation,

respectively, of the r-th Gaussian of the mixture as-

sociated with z

(t)

. At each time instant, the Gaus-

sian components are evaluated in descending order

with respect to w/σ to ﬁnd the ﬁrst matching with

(t)

(a match occurs if the value falls within 2.5σ of

the mean of the component). If no match occurs, the

least ranked component is replaced with a new Gaus-

sian with the mean equal to the current value, high

variance and a low mixing coefﬁcient. If r

hit

is the

matched Gaussian component, the value z

(t)

is labeled

FG if

hit

∑

r=1

(t)

> T (2)

BACKGROUND SUBTRACTION WITH ADAPTIVE SPATIO-TEMPORAL NEIGHBORHOOD ANALYSIS

485

where T is a standard threshold, the summation

∑

hit

r=1

(t)

represents the probability that the Gaussian

components considered do model the background.

We call the test in (2) as the background per-pixel test

(BG PP test), which is true (= 1) if the value is labeled

BG (z

(t)

∈BG), false (= 0) vice versa. For further de-

tails, see (Stauffer and Grimson, 1999).

3.2 The Per-region Process

If z

(t)

is not recognized as BG by the BG PP test, then

the PR process determines if z

(t)

is similar to another

BG signal value, located in a close position n

. In

formulae, z

(t)

is labeled BG by the PR process if the

following background per-region test (BG PR test) is

true:

∈G

(t)

∈ N (µ

,σ

)

(t)

∈ BG

(3)

where

indicate or and and operators respec-

tively, G

is the squared neighborhood zone related to

location n and

k addresses whatever Gaussian compo-

nent that models the pixel location n

, which satisﬁes

the condition above. Eq.(3) is true if z

(t)

matches with

a particular Gaussian component located at position

and the signal value z

(t)

, modeled by such Gaus-

sian pdf, is labeled BG by the PP process. The BG

labeling mechanism exploited in the PR process mir-

rors the policy proposed in (Elgammal et al., 2000). If

some part of the background (a tree branch for exam-

ple) moves to occupy a new pixel, but it was not part

of the per-pixel model for that pixel, then it will be de-

tected as a FG object by a classical per-pixel method.

However, this object will have a high probability to

be a part of the BG distribution in its original posi-

tion. Clearly, the bigger the neighborhood zone G

the heavier will be the computational load required

for evaluating Eq.(3). In this paper, we propose to

adopt a strategy for changing G

on-line, in order to

turn down the computational effort. From here, we

indicate with s

(t)

half the size of the neighborhood

zone G

at time t, resulting in a square of odd size

1 + 2s

(t)

. At time t = 0, s

(0)

= s

min

, where s

min

in-

dicates the smallest length permitted. In this paper,

we set s

min

as 0, resulting in a neighborhood zone of

a single pixel location. At time t = 1, if the BG PP

test is negative (i.e., we have a FG per-pixel detection

at location n), the PR process does not contributes to

ﬁnd a BG neighborhood signal similar to z

(1)

; there-

fore, the whole process will give a FG detection at

position n. After this, s

is enlarged by a factor γ

obtaining a squared region of size b1 + 2 ∗ γ

c. If the

PR+PP process continues to identify a FG value at po-

sition n, a maximal length s

max

is considered. Vicev-

ersa, if the PR test is positive, we have a BG detection,

and the growing process of s

stops. Conversely, let

us suppose that at frame t the BG PP test is positive.

This means that the per-pixel statistic is enough to ex-

plain the pixel signal z

(t)

as a BG instance. Therefore,

having a large neighborhood zone of size s

to ana-

lyze brings to a useless computational burden. Con-

sequently, the size s

(t)

is diminished by the factor γ

Hence, if the PP BG test continues to be positive, then

is diminished until the smallest size s

min

is reached.

Summarizing, the size of s

(t)

changes as follows:

(t)











max

if PP test=0∧

PR test=0 ∧ s

(t−1)

max

(t−1)

+ γ

if PP test=0 ∧ PR test=0

(t−1)

if PP test=0 ∧ PR test=1

(t−1)

− γ

if PP test=1 ∧ s

(t−1)

min

if PP test=1 ∧ s

(t−1)

min

(4)

A graphical example of the process is given in Fig.1.

When the smallest size s

min

has been reached for

the location n, if the signal z

(t)

is detected as BG sim-

ply by the BG PP process, we decide to sample it ev-

ery bI(n)

(t)

c frames, where I(n)

(t)

is a skipping time

set initially to 0, which increments by a factor γ

each

time z

(t)

is discovered consecutively as BG by the BG

PP test. This happens until the maximal skip interval

max

is reached. During the skip, the Gaussian param-

eters that describe the signal z

are left unchanged.

This temporal sampling process stops immediately as

soon as the BG PP test is negative, and I(n)

(t)

is set to

The quality of the results obtained justiﬁes the

heuristic aspect of the proposed method.

4 EXPERIMENTS AND

DISCUSSION

Several tests have been performed to validate the pro-

posed approach. In the ﬁrst benchmark, the well-

known “Wallﬂower” dataset (Toyama et al., 1999) has

been considered; it contains sequences which present

different hard BG subtraction issues; each sequence

has a ground truth frame. Here, we processed four

of the most difﬁcult sequences of the dataset, i.e.,

sequences whose best BG subtraction results are far

from the ground truth. The sequences are: 1)Waving

Tree (WT): a tree is swaying and a person walks in

front of the tree; 2)Camouﬂage (C): a person walks in

front of a monitor, which has rolling interference bars

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

486

n’

(1)

t=1

(2)

t=2,

BG PP test

t=2,

BG PR test

t=3,

BG PP test

t=3,

BG PR test

(2)

t=4,

BG PP test

+ BG PR test

(3)

(2)

(3)

n’

(1)

(3)

(4)

(2)

n’

(2)

Figure 1: Scheme of ASTNA: At time t = 1, suppose that

only the blue pixels are sampled. At time t = 2 location z

(2)

is detected as FG (the pixel is rounded by a red square) by

the BG PP test, but the BG PR test is positive, having the

region G

(2)

a BG pixel value z

0(2)

similar to z

(2)

inside. The

other values z

(2)

and z

(2)

are detected as FG by the PR BG

test, thus their neighborhood zones are enlarged. At time

t = 3 the value z

(3)

is labelled BG by the PR test, while

the pixel value z

(3)

is labelled BG by the PP test, and its

neighborhood zone can be diminished. Only BG values are

detected at time t = 4.

on the screen. The bars include color similar to the

persons clothing; 3)Bootstrapping (B): a busy cafe-

teria where each frame contains FG objects; 4)Fore-

ground Aperture (FA): a person with uniformly col-

ored shirt wakes up and begins to move. Consider-

ing the other three Wallﬂower sequences, two of them

refer i) to the capacity of the background model to

incorporate a moved object in the background model

after a reasonable time it is still, and ii) to the capacity

of the background model to adapt to a gradual change

of illumination. Both these problems are solved by

the ordinary TAPPMOG, and thus our model does not

add any deterioration in the performance. The third

sequence present an instance of the sudden global

change in illumination issue. Our method fails in this

case, being absent a per-frame module. Anyway, such

problem does not represent an important issue, be-

ing present several techniques able to solve it with

very low computational effort (for example, using a

set of pre-learnt global model of the scene, and using

the most appropriate, as done in (Ohta, 2001)). An-

other issue that we do not face in this papers are the

shadows issue, another problem in video surveillance.

This will be addressed in a future work, as explained

in the last section.

All the RGB sequences are captured at resolution

of 160 × 120 pixels, sampled at 4Hz. In our pure

MATLAB implementation, on a Pentium IV, 3Ghz,

1Gb RAM, we set A

max

= 5,I

max

= 4, γ

= γ

= 0.2;

such quantities are intuitive and easy to set. For each

sequence, we show qualitative results in Fig.2: for

lack of space only the results related to the TAPP-

MOG (Stauffer and Grimson, 1999) and Elgammal

(Elgammal et al., 2000) methods are reported

): for

a more extensive listing of the existent results, please

see (Toyama et al., 1999). In Fig.3, a wider set of

Figure 2: Wallﬂower qualitative results: on the 1st col.,

the test frames; on the 2nd col. the ground truth; the 3rd

col. shows the TAPPMOG results; Elgammal results and

results obtained with our method ASTNA are on the last

two columns, respectively.

quantitative results are provided in terms of amount

of false positive and false negative FG detections.

In particular, Wallﬂower, SACON, Tracey Lab LP

and Bayesian Decision refer to (Toyama et al., 1999;

Wang and Suter, 2006; Kottow et al., 2004; Nakai,

1995) respectively, which have been previously dis-

cussed in Section 2.

As visible, all the results provided by ASTNA

are comparable with the best performances obtained

by other techniques; in particular, our method reach

optimal results in the Waving Tree test, by correctly

modelling as BG the tree. In the Bootstrap test, our

method correctly considers as BG the light reﬂexes

on the ﬂoor, even if they are irregularly occurring

with sudden small displacements. This because our

method learns the zones of the scene in which oscil-

lating or ﬂickering background is present, permitting

to use in those areas large neighborhood zones. At the

same time, zones in which the BG is still and stable

are considered as formed by independent pixel loca-

tions with minimal 1-pixel neighborhood zone, and,

as a consequence, they are more sensible to FG occur-

rences. Another observation is that our method can be

thought as improving the performances of the TAPP-

MOG method. Actually, TAPPMOG models over

the same pixel different Gaussian components, taking

into account different chromatic modes of the back-

ground. Our method permits to share these modes

among adjacent pixels locations, if necessary. One

Regarding the Elgammal method, the neighborhood

zone is represented by a ﬁxed squared zone of size 5 for

all the pixel locations n = 1, ... ,N.

BACKGROUND SUBTRACTION WITH ADAPTIVE SPATIO-TEMPORAL NEIGHBORHOOD ANALYSIS

487

13019

3101

310

3411

2688

823

1173

1996

2899

2900

f.neg.

f.pos.

t.e.

Elgammal

10059

2217

870

3087

1732

1033

2765

220

2398

2618

1533

1589

f.neg.

f.pos.

t.e.

TAPPMOG

14043

2501

1974

4485

2143

2764

4907

1538

2130

3688

629

334

963

f.neg.

f.pos.

t.e.

Bayesian

decision

7219

2403

356

2759

1974

2066

1998

2067

191

136

327

f.neg.

f.pos.

t.e.

Tracey LAB

4084

1508

521

2029

1150

125

1275

462

509

230

271

f.neg.

f.pos.

t.e.

SACON

9170

320

649

969

2025

365

2390

229

2706

2935

877

1999

2876

f.neg.

f.pos.

t.e.

Wallflower

T.Err.FABCWTErr.

Methods

7031

1900

360

2260

2349

2422

2239

881

3120

253

100

353

f.neg.

f.pos.

t.e.

ASTNA

Figure 3: Quantitative results obtained by the proposed

ASTNA method: f.neg, f.pos.,t.e. and T.Err mean false

negative, false positive per-pixel FG detections, total er-

rors on the speciﬁc sequence and total errors summed on

all the sequences analyzed, respectively. Our method out-

performed the most effective general purposes BG subtrac-

tion scheme (Wallﬂower, Bayesian decision, TAPPMOG,

Elgammal), and is comparable with methods which are

more time demanding (see Tab.1) and strongly constrained

by data-driven initial hypotheses (SACON and Tracey Lab

LP).

Table 1: Times of execution in seconds of the different

BG subtraction methods when applied to the Wallﬂower se-

quences.

Methods WT C B FA

SACON 47.33 49.33 50.52 81.5

TAPPMOG 64.15 65.04 67.46 108.44

Elgammal 75.20 67.80 72.16 108.64

ASTNA 33.49 28.12 33.02 39.52

can afford that similar results can be provided by aug-

menting the number of per-pixel Gaussian compo-

nents, but doing this way occasional reﬂections of

the background cannot effectively be modeled. As

a further result, on Table 1 the total execution time

needed by the different algorithms to process the test

sequences is reported. One can notice the timings of

SACON, which is the only one that outperforms our

method for what concerns quality of the results. All

the other methods of Fig.3 not reported in Table 1 ex-

hibit worse performances.

These results show that ASTNA outperforms both

the ﬁxed-neighborhood zones method (Elgammal et

al., 2000) and the classical TAPPMOG method. This

last result is due to the fact that the computational ef-

fort required by ASTNA to inspect a neighborhood

zone for each pixel is counterbalanced by the fact that

ASTNA avoids to sample locations with stable pixel

value at each iteration.

To give a better insight on how our method per-

forms, we consider another hard sequence, 320 × 240

pixels, 1170 frames long, in which a docking scenario

is portrayed. In Fig.4a) some frames are shown and

one can notice that reﬂecting sea and oscillating boats

are present.

Figure 4: Dock sequence: a) some frames of the sequence

(the face of the person is obscured due to the anonymity

issues); b) TAPPMOG results; c) Elgammal results; d)

ASTNA neighborhood image: brighter pixels mean wider

neighborhood zones for that pixel; d) ASTNA results. Note

that in all these results were not applied morphological op-

erations to clean up small FG detections.

During the sequence, a person arrives near the

camera, goes up on a boat, and lastly goes away. The

images in Fig.4d), at each pixel, indicate the area of

the related neighborhood zone calculated by our algo-

rithm. As one can note, our method considers bigger

zones only where signiﬁcant oscillations are present

(near the masts). The time occurred for process such

sequence is 1478.20 sec. for Elgammal, 1067.60

sec. for TAPPMOG and 374.28 sec. for ASTNA.

In Fig.5, the time required for each iteration is re-

ported, for all the three methods, at different frames;

it is evident that our method is upper-bounded by the

ﬁxed-neighborhood Elgammal technique, while out-

performs TAPPMOG method after the on-line learn-

ing of the most adapt neighborhood zones has been

performed.

0 20 40 60 80

0.8

0.85

0.9

0.95

frame

sec.

550 600 650

0.1

0.2

0.3

0.4

0.5

0.6

0.7

frame

sec.

Figure 5: Timings for the “Dock” sequence: the dashed

line, the point-dashed line and the solid line indicates TAPP-

MOG, Elgammal and ASTNA timings, respectively.

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

488

5 CONCLUSIONS AND FUTURE

PERSPECTIVES

In this paper, we focus on producing a strategy which

is able to perform background subtraction in a fast and

robust way. The idea is to use an already present ef-

fective background subtraction technique, which op-

erates per-pixel, namely the TAPPMOG algorithm,

and to adapt it in order to deal with patch of pix-

els. This contributes to avoid false alarms caused

by irregular scene variations, such as happens in a

sea-docking scenario. Hence, we introduce a method

which effectively selects the area of support over

which the algorithm can operate. The idea is that, the

larger the background variations, the wider will be the

pixel area where the algorithm can look for a unsta-

ble background pixel. The proposed method is also

able to change the sampling rate with which the pixels

values are processed: in short, where no foreground

activities are present, and where the background is

spatially stable, the sampling rate will become very

low, otherwise it will be high. This permits to com-

pensate the computational burden to to the per region

processing, improving time performances. In the fu-

ture, we intend to apply the RGB normalization of

(Suter and Wang, 2005) in order to cope successfully

with the shadows, and to add the Gaussian model se-

lection algorithm proposed by (Zivkovic, 2004), (for

the explanation of such methods, see Sec. 2 in order

to further speed up the BG subtraction performances.

Our goal is to use this method as a base module in a

distributed video surveillance framework, where the

computational load has to be maintained as low as

possible.

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