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Published in IET Computer Vision

Received on 1st August 2009

Revised on 27th June 2010

doi: 10.1049/iet-cvi.2009.0075

ISSN 1751-9632

Robust mean-shift tracking with corrected

background-weighted histogram

J. Ning

1,2,3

L. Zhang

D. Zhang

C. Wu

The State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an, People’s Republic of China

Department of Computing, The Hong Kong Polytechnic University, Kowloon, Hong Kong, People’s Republic of China

College of Information Engineering, Northwest A&F University, Yangling, People’s Republic of China

E-mail: cslzhang@comp.polyu.edu.hk

Abstract: The background-weighted histogram (BWH) algorithm proposed by Comaniciu et al. attempts to reduce the

interference of background in target localisation in mean-shift tracking. However, the authors prove that the weights assigned

to pixels in the target candidate region by BWH are proportional to those without background information, that is, BWH does

not introduce any new information because the mean-shift iteration formula is invariant to the scale transformation of

weights. Then a corrected BWH (CBWH) formula is proposed by transforming only the target model but not the target

candidate model. The CBWH scheme can effectively reduce background’s interference in target localisation. The

experimental results show that CBWH can lead to faster convergence and more accurate localisation than the usual target

representation in mean-shift tracking. Even if the target is not well initialised, the proposed algorithm can still robustly track

the object, which is hard to achieve by the conventional target representation.

1 Introduction

Object tracking is an important task in computer vision. Many

algorithms [1] have been proposed to solve the various

problems arisen from noises, clutters and occlusions in the

appearance model of the target to be tracked. Among

various object-tracking methods, the mean-shift tracking

algorithm [2–4] is a popular one because of its simplicity

and efﬁciency. Mean shift is a non-parametric density

estimator that iteratively computes the nearest mode of a

sample distribution [5]. After it was introduced to the ﬁeld

of computer vision [6], mean shift has been adopted to

solve various problems, such as image ﬁltering,

segmentation [7–11] and object tracking [2, 3, 12 –18].

In the mean-shift tracking algorithm, the colour histogram

is used to represent the target because of its robustness to

scaling, rotation and partial occlusion [2, 3, 19]. However,

the mean-shift algorithm is prone to local minima when

some of the target features are present in the background.

Therefore Comaniciu et al. [3] further proposed the

background-weighted histogram (BWH) to decrease

background interference in target representation. The

strategy of BWH is to derive a simple representation of the

background features and to use it to select the salient

components from the target model and target candidate

model. More speciﬁcally, BWH attempts to decrease the

probability of prominent background features in the target

model and candidate model and thus reduce the

background’s interference in target localisation. Such an

idea is reasonable and intuitive, and some works have been

proposed to follow this idea [20–22].In[20], the object is

partitioned into a number of fragments and then the target

model of each fragment is enhanced by using BWH.

Different from the original BWH transformation, the

weights of background features are derived from the

differences between the fragment and background colours.

In [21], the target is represented by combining BWH and

adaptive kernel density estimation, which extends the

searching range of the mean-shift algorithm. In addition,

Allen et al. [22] proposed a parallel implementation of

mean-shift algorithm with adaptive scale and BWH and

demonstrated the efﬁciency of their technique in a single

instruction multiple data computer. All the above BWH-

based methods aim to decrease the distraction of

background in target location to enhance mean-shift

tracking. Unfortunately, all of them do not notice that the

BWH transformation formula proposed in [3] is actually

incorrect, which will be proved in this paper.

In this paper, we demonstrate that the BWH algorithm will

simultaneously decrease the probability of prominent

background features in the target model and target

candidate model. Thus, BWH is equivalent to a scale

transformation of the weights obtained by the usual target

representation method in the target candidate region.

Meanwhile, the mean-shift iteration formula is invariant to

the scale transformation of weights. Therefore the mean-

shift tracking with BWH in [3, 20–22] is exactly the same

as the mean-shift tracking with usual target representation.

Based on the mean-shift iteration formula, the key to

effectively exploit the background information is to

decrease the weights of prominent background features. To

this end, we propose to transform only the target model but

62 IET Comput. Vis., 2012, Vol. 6, Iss. 1, pp. 62 –69

The Institution of Engineering and Technology 2012 doi: 10.1049/iet-cvi.2009.0075

www.ietdl.org

not the target candidate model. A new formula for computing

the pixel weights in the target candidate region is then

derived. The proposed corrected background-weighted

histogram (CBWH) can truly achieve what the original

BWH method wants: reduce the interference of background

in target localisation . An important advantage of the

proposed CBWH method is that it can work robustly even

if the target model contains much background information.

Thus, it reduces greatly the sensitivity of mean-shift

tracking to target initialisation. In the experiments, we can

see that even when the initial target is not well selected, the

proposed CBWH algorithm can still correctly track the

object, which is hard to achieve by the usual target

representation.

The rest of the paper is organised as follows. Section 2

introduces brieﬂy the mean-shift algorithm and the BWH

method. Section 3 proves that the BWH method is

equivalent to the conventional mean-shift tracking method,

and then the CBWH algorithm is presented. Section 4

presents experiments to test the proposed CBWH method.

Section 5 concludes the paper.

2 Mean-shift tracking and BWH

2.1 Target representation

In object tracking, a target is usually deﬁned as a rectangle or

an ellipsoidal region in the frame and the colour histogram is

used to represent the target. Denote by {x

∗

}

i=1,...,n

the

normalised pixels in the target region, which has n pixels.

The probability of a feature u, which is actually one of the

m colour histogram bins, in the target model is computed as

[2, 3]

q = {

}

u=1,...,m

;

= C



i=1

k(||x

∗

)

[b(x

∗

) − u] (1)

where

q is the target model,

is the probability of the u

element of

is the Kronecker delta function, b(x

∗

)

associates the pixel x

∗

to the histogram bin, k(x)isan

isotropic kernel proﬁle and constant C is C = 1/S

i=1

(||x

∗

Similarly, the probability of the feature u ¼ 1, 2, ..., m in

the target candidate model from the target candidate region

centred at position y is given by

p = {

(y)}

u=1,...,m

;

(y) = C



i=1

y − x





[b(x

) − u]

(2)

where

p(y) is the target candidate model,

(y)isthe

probability of the u

element of

p(y), {x

}

i=1,...,n

are pixels

in the target candidate region centred at y, h is th e

bandwidth and C

is the normalised constant

= 1/S

i=1

k(||y − x

/h||

2.2 Mean-shift tracking algorithm

A key issue in the mean-shift tracking algorithm is the

computation of an offset from the current location y to a

new location y

according to the mean-shift iteration equation

i=1

g(||(y − x

)/h||

)

i=1

g(||(y − x

/h)||

)

(3)



u=1



(y)



[b(x

) − u] (4)

where g(x) is the shadow of the kernel proﬁle k(x):

g(x) ¼ 2 k

′

(x). For the convenience of expression, we

denote by g

¼ g(y 2 x

/h

). Thus, (3) can be re-written as



i=1



i=1

(5)

With (5), the mean-shift tracking algorithm can ﬁnd the most

similar region to the target object in the new frame.

2.3 Background-weighted histogram (BWH)

In target tracking, often the background information is included

in the detected target region. If the correlation between target

andbackgroundishigh,thelocalisationaccuracyoftheobject

will be decreased. To reduce the interference of salient

background features in target localisation, a representation

model of background features was proposed by Comaniciu

et al. [3] to select discriminative features from the target

region and the target candidate region.

In [3], the background is represented as {

}

u=1,...,m

(with

i=1

= 1) and it is calculated by the surrounding area of

the target. The background region is three times the size of

the target as suggested in [3]. Denote by

∗

the minimal

non-zero value in {

}

u=1,...,m

. The coefﬁcients

= min (

∗

, 1)}

u=1,...,m

(6)

are used to deﬁne a transformation between the

representations of target model and target candidate model.

The transformation reduces the weights of those features

with low v

, that is, the salient features in the background.

Then the new target model is

′

= C

′



i=1

k(||x

∗

)

[b(x

∗

) − u] (7)

with the normalisation constant

′

i=1

k(||x

∗

u=1

[b(x

∗

) − u]

The new target candidate model is

′

(y) = C

′



i=1

y − x





[b(x

) − u] (8)

where

′

i=1

k(||(y − x

)/h||

u=1

[b(x

∗

) − u]

The above BWH transformation aims to reduce the effects of

prominent background features in the target candidate region

on the target localisation. In the next section, however, we

will prove that BWH cannot achieve this goal because it is

equivalent to the usual target representation under the

mean-shift tracking framework.

IET Comput. Vis., 2012, Vol. 6, Iss. 1, pp. 62 – 69 63

doi: 10.1049/iet-cvi.2009.0075

The Institution of Engineering and Technology 2012

www.ietdl.org

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