Introducing New Parameters to Compare the Accuracy and Reliability of Mean-Shift Based Tracking Algorithms

Signal & Image Processing : An International Journal (SIPIJ) Vol.2, No.3, September 2011
DOI : 10.5121/sipij.2011.2305 47
INTRODUCING NEW PARAMETERS TO COMPARE
THE ACCURACY AND RELIABILITY OF MEAN-SHIFT
BASED TRACKING ALGORITHMS
S.A. Mohammadi1
and M.R. Mahzoun2
1
Department of ICT Engineering, IHU University, Tehran, Iran
seyed_amir_mohammadi@yahoo.com
2
Department of ICT Engineering, IHU University, Tehran, Iran
rezamahzoun@yahoo.com
ABSTRACT
Mean shift algorithms are among the most functional tracking methods which are accurate and have
almost simple computation. Different versions of this algorithm are developed which are differ in template
updating and their window sizes. To measure the reliability and accuracy of these methods one should
normally rely on visual results or number of iteration. In this paper we introduce two new parameters
which can be used to compare the algorithms especially when their results are close to each other.
KEYWORDS
Object tracking, Mean-shift algorithm, Adaptive template, Bhattacharyya coefficients
1. INTRODUCTION
Real time object tracking is an important practical application of computer vision with a wide
variety of usages in different subjects such as surveillance systems, road traffics, weather
forecasting, machine and human interfaces, video compression, astronomy, and a lot of military
issues [1-10]. Among different tracking algorithms, mean shift based methods have their special
places because of their simplicity in computation while have good accuracies. Updating the target
model and making the tracking window size dynamic are two important factors which have made
authors develop versions of mean shift tracking algorithms [11-14]. To have a good judgment
about the accuracy and reliability of different methods we should use acceptable robust
parameters. The comparisons are often done by visual observation while considering the number
of iteration in the process. Normally the lesser iteration indicates on higher speed of the tracker,
although sometimes it is not satisfactory agument. For example the tracker may loss the target
during its process, causing its window be fix in one position which can result in unreliable
iteration number. To cope with these kind of problems, one solution is to make and use of more
related comparison parametrs.
In this paper after a survey on mean shift algorithm and two developed version of that, we
introduce two comparison factors naming them MCC and NV. Using mentioned factors we
compare the results of the algorithms.

48
2. BASIC MEAN-SHIFT (MS) TRACKING ALGORITHM
We use the basis of MS algorithm to introduce our parameters. Target features and way of
modelling it, target candidates and geometric relations between target model and candidate are
the main subject of the algorithm.
2.1. Target features and modelling
In MS tracking algorithm the target feature is the colour PDF1
of target locale which is shown by
q in colour space. The probable place of target with center of y in next frame contains target
candidate. To make target candidate model the PDF of its locale shown by p(y) is used. Both
PDFs (target and candidate), contains a good approximation of intrinsic feature of target. As one
of the trackers evaluation parameters is their processing time, normally to reduce that only some
of histogram bars are selected and used. So the target and candidate model is defined as:
Target Model: { }
ˆ 1...
u
q u m
= 1
ˆ 1
m
u
u q
= =
∑
Candidate Model: { }
ˆ ˆ
( ) ( ) 1...
u
p y p y u m
= = 1
ˆ 1
m
u
u p
= =
∑
Where u indicates on colours exist in target and candidate locales, and u
q and u
p are normalized
target and candidate models. Although histograms are not the best nonparametric approximation
of densities but they can be good criterions for target tracking [2]. The similarity of two patterns
determine (explained later) by Equation (1).
ˆ ˆ ˆ
( ) [ ( ), ]
p y p y q
ρ
≡ (1)
In this equation ˆ( )
p y measures the similarity between two models while its local maximums
indicate on similarity value between target candidate in new frame and the target in first frame.
2.2. Target Model
In our image, target model is shown by a rectangular or circular zone. The function
2
: {1... }
b R m
→ sets index *
( )
i
b x corresponds to quantized histogram bar in colour space to a
pixel locates at *
i
x . The values corresponding to existed colour is determines by:
2
* *
1
ˆ ( ) [ ( ) ]
n
u i i
i
q C k x b x u
δ
=
= −
∑ (2)
where δ is kronecker delta function. The normalization coefficient, C, under condition
1
ˆ 1
m
u
u q
= =
∑ is defined as
2
*
1
1
( )
n
i
i
C
k x
=
=
∑
(3)
1
Probability Density Function

49
2.3. Target candidate
It is assumed that { } 1...
i h
X i n
= are the loci of normalized target candidate pixels centered at y on
current frame. Using weighted function k(x) which has similar window sizes similar to target's,
the values for target candidate model related to colours u=1,…m can be computed as below:
2
1
ˆ ( ) ( ) [ ( ) ]
n i
u h i
i
h y x
p y C k b X u
h
δ
=
−
= −
∑ (4)
where h
C is normalization coefficient (y independent), computed by;
2
1
1
( )
h
n i
i
h
C
y x
k
h
=
=
−
∑
(5)
2.4. Bhattacharyya coefficients
In order to compute the similarity between target and a candidate we can use the Bhattacharyya
coefficients. Using Bhattacharyya coefficients the similarity will be computed in the form of
metric distance between discrete distribution of target and candidate [5] pixels as below;
ˆ ˆ
( ) 1 [ ( ), ]
d y p y q
ρ
= − (6)
where ˆ ˆ
[ ( ), ]
p y q
ρ can be found using Equation (7).
1
ˆ ˆ ˆ ˆ ˆ
( ) [ ( ), ] m
u u
u
p y p y q p q
ρ =
≡ = ∑ (7)
For the ideal similarity the value of (7) approach to one. A complete explanation about
Bhattacharyya coefficients can be found in [2].
2.5. Target localization
In order to find the new position of target in current frame, the distance obtained using Equation 6
should reach its minimum value. The tracking process starts from a point (and its vicinity) which
it was the target place in previous frame and continue until the mentioned distance reach to
predefined minimum (Equation 6) or maximum iteration happens.
3. DEVELOPED MEAN-SHIFT ALGORITHMS
3.1. CBWH tracking algorithm
Using background histogram ( ˆu
o ) a transfer function (Vu) has developed to decrease the effects
of background colours on target model [1]. The related algorithm named BWH 2
. It is shown that
the performance of BWM algorithm will increase if we use Equation 8 for target model only in
the first frame and using Equation 4 for other frames [3]. This algorithm known as CBWH 3
.
Equation 8 is a transformation that decreases the effect of background colour on target model
computed by Equation 9.
2
Background Weighted Histogram
3
Corrected Background Weighted Histogram

50
*
1...
ˆ
{ min( ,1)}
ˆ
u u m
u
o
v
o
=
= (8)
2
* *
1
ˆ ( ) [ ( ) ]
n
u u i i
i
q C v k x b x u
δ
=
′ ′
= −
∑ (9)
where
∑
∑ =
= −
=
′
m
u i
u
n
i i u
x
b
v
x
k
C
1
*
1
2
*
]
)
(
[
)
(
1
δ
(10)
In CBWH firstly the target background ˆu
o is computed then we make the transfer function vu
using Equation 8.
3.2. Self-Adaptive size tracking algorithm
The size of tracking window in basic MS is not target adaptive. In [1] the coloured model is
computed within +/-10% of target window. Using Equation 11 the new size of the window is
ermined. Here opt
h is the window size corresponds to the most probable target selected by
Bhattacharyya coefficients.
(1 )
new prew opt
h h h
γ γ
= + − (11)
The results obtained by this method show that this algorithm works well in the case of targets
with decreasing size but fails when the target is being zoomed. Moreover as the value of γ is
constant, the rate of window size change is not proportion to target size change. To cope with this
problem an algorithm is proposed [4] which adaptively changes the size of track window base on
a parameter named MSIIM.
4. INTRODUCING NEW COMPARISON PARAMETERS
Evaluation of algorithms is a challenging issue especially when the results are close to each other.
Here we are to introduce two parameters which are extracted from the structure of MS algorithm.
The first one is the mean of confidence coefficient (MCC) shown in Equation 12,
1
n
i
i
CC
MCC
n
=
=
∑ (12)
Where
1( ( ) )
x
n
i
n
MS i MinDist
CC
x
= −
=
∑
(13)
Here n
CC is the confidence coefficient in frame n which represents the mean distance between
the center of target candidate in frame n and process exit criterion (MinDist). MS in frame n is the
difference between the centers of target candidate (found i time in current frame) and target
(found in frame n of previous try).
The second parameter, NV, is the normalized variance of n
CC with respect to MCC, defined as:

51
2
1
( )
n
i
i
CC MCC
NV
n
=
−
=
∑ (14)
If the MS distance was smaller than MinDist the center of target candidate (correspond to MS)
will be selected as new target position, else, this position is used in place of target center in
previous frame to compute the target position in current frame. The mean of target candidates
distances from MinDist computed by Equation 14, represents the accuracy of tracking process on
that frame. Variance is used to show the reliability of the method. The smaller values indicate on
more repeatability of the results. Considering presented parameters and the results of MS
trackers, we evaluate them as below:
1. Using process iteration to show the accuracy and speed of tracking,
2. Using visual judgment,
3. Using Equations 12 and 14.
Here we compare different MS algorithms by tracking the target locale of Figure 1 over test video
frames.
Figure 2 shows the comparison of MS methods over BALL video test. The target has quick
motion while its size changes. It can be seen that the CBWH algorithm has the best performance
while the other two methods had some fails due to their low accuracies, and the high speed of the
ball.
Figure 3 shows another test using PLAYER video frames. Here the target is the player head and
the purpose is comparing the mentioned algorithms using their average value of iterations.
Although the results are similar to each other, but as in CBWH the target model made more
accurate its MCC, NV and iteration are better than others'.
Figure 1. The locale of tracked targets in test videos
Figure 2. Ball tracking in BALL video test, using (from the top) basic Mean-Shif, CBWH
and Self-adaptive size algorithms

52
Table 1 illustrate the stochastic results of the above tests. The values of MCC, NV, and iteration
for each of the three algorithms for both BALL and PLAYER test videos are colleted in this table.
As mentioned before, for those results which are similar to vision (e.g. Figure 3) it is difficult to
say which algorithm works better. The values in Table 1 help us to compare the algorithms,
quantitatively. Here the overall result shows the better performance of CBWH algorithm.
5. CONCLUSION
Number of iteration in each frame and visual observation are basic parameters to compare the
performances of Mean-Shift based tracking methods. In some cases such as when the results are
high correlated it is hard to compare the algorithms by mentioned parameters. In this paper we
presented two new parameters in order to compare the accuracy and reliability of MS based
trackers. The result of examined video tests show even in the case of closeness of tracker outputs
it is possible to have a good assessment regarding algorithms performances using proposed
parameters.
Figure 3. Head tracking in PLAYER video test, using (from the top) basic Mean-Shift,
CBWH and Self-adaptive-size algorithms
Video Tests Algorithms MCC NV Iteration
BALL
MeanShift(std) 0.157247 0.004017 6.3462
CBWH 0.125175 0.003644 4.2885
Self-Adapt 0.126628 0.003684 6.4615
PLAYER
MeanShift(std) 0.122522 0.003572 3.7414
CBWH 0.118467 0.002577 3.2414
Adapt 0.168233 0.020356 3.5517
Table 1. Comparison of the Mean-Shift based algorithms.

53
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