Journal of Computational Information Systems5:6(2009) 1841-1846 Available at http://www.JofCI.org

1553-9105/ Copyright 2009 Binary Information Press December, 2009

Object Tracking Based on Dynamic Template and Motion Prediction

Zhiyu ZHOU1, , Jianxin ZHANG2, Li FANG3

1 College of Information and Electronics, Zhejiang Sci-Tech UniversityHangzhou 310018China 2 College of Mechanical Engineering and Automation, Zhejiang Sci-Tech University, Hangzhou 310018China

3 College of Science and Arts, Zhejiang Sci-Tech UniversityHangzhou 311121China

Abstract

In order to eliminate the impact of the background on the template and reduce the computation scale of matching during tracking, a new object tracking algorithm is proposed in this paper based on dynamic template and motion prediction. When using the similarity sequential detection algorithm (SSDA), it matches only with the pixels in the template, which reduces the risk of disturbances from the background. Moreover, the template is updated continuously to ensure the correctness of the template data. By taking the area of the actual curve in a region as the background value and using the least square of the difference between the simulation sequence and the first order accumulating generated operator (AGO) sequence, the traditional GM(1,1) model can be optimized. Furthermore, the initial searching point is obtained by the prediction of the GM(1,1) model, which can reduce the searching region and enhance the real-time performance of tracking. While the tracked object is occluded, its location is acquired by replacing the real value with the prediction value, thus the motion continuity and the tracking robustness are guaranteed. Experimental results show that the method is effective.

Keywords: SSDA; Dynamic Template; Motion Prediction; Object Tracking

1. Introduction

Motion object tracking [1-3] is one of the important researching focuses in computer vision field, which has significantly practical value in many fields such as aircraft-assisted navigation, weather forecasting, military guidance, traffic monitoring and medical diagnosis, etc. The image template matching has become a major method for object tracking. The keys of this method are to calculate the correlation extent of certain characteristics between two frames and to obtain the correlation values by correlation calculation with the template image and the image to be matched. In terms of these correlation values, we can decide whether these two images match or not. The main methods of image matching include the similarity sequential detection algorithm(SSDA) method and its improvement [4], the absolute balance search (ABS) method and its improvement [5], the mean absolute differences (MAD) and its improvement [6], the normalized cross correlation algorithm (NCC) and its improvement [7] and so on.

The similarity index is the most important technical index in visual tracking, directly determining the accuracy and robustness of object tracking. Therefore, many researchers have put forward their own methods to solve the problems in object tracking. References [8-9] uses the adaptive template combined with the particle filter for tracking. Under the particle filter tracking framework in reference [9], the adaptive observation model of the object template adopts the hybrid Gaussian model containing three components, and an incremental EM algorithm is utilized to update the result on-line, which gives a good

Corresponding author. Email addresses: zhouzhiyu1993@163.com (Zhiyu ZHOU)

1842 Z. Zhou et al. /Journal of Computational Information Systems 5:6(2009) 1841-1846 solution to the template updating problem. To overcome the problem of template drift, reference [10] proposes a group of expressions which can precisely describe the impact of the template drift on the template updating filter so that the filter can adaptively achieve the approximate optimal balance between timely updating objects appearance and avoiding template drift in the space and time after taking into account the effect of template drift. Reference [11] uses the initial searching point of the Kalman prediction to enable the object tracking algorithm so as to avoid the background disturbance as well as shorten the searching distance. As the Kalman filter is a linear prediction and it assumes the motion status in advance, an object tracking method based on the improved SSDA and the grey prediction is proposed in this paper on the basis of reference [4] and the grey system theory.

2. SSDA Based on Dynamic Template

The traditional SSDA algorithm has constant template size. When the object size changes in sequence image, its template contains a large amount of background data, resulting in drift of the tracked point on the object. Once the tracked point moves out from the object, the object will be lost. On one hand, if the template image is not amended, it will not be able to adapt to changes in dynamic scenes; on the other hand, the improper amending of the template image with occlusion will also cause a sharp increase of matching errors, resulting in false matching and the loss of the tracked object. Therefore, selecting a suitable template image updating strategy can overcome the impact of the objects size variation in sequence image on the result of image matching and tracking to some extent.

If the background varies very small, the traditional SSDA algorithm can achieve the tracking and locking of the object. But during the actual tracking process the objects shape can changes continuously. So in order to accurately track the object, the template must be updated constantly. The basic idea of the algorithm is as follows: First assume that the object had been tracked and located in the i-th frame; then the centroid of the object in the frame is centered to acquire the template T; finally the binary template image B is extracted out from T. With T & B, the improved SSDA matching algorithm is as follows [4]:

= =

++=M

i

N

jjiTyjxiRjiB

NMjiD

1 1),(),(),(1),( (1)

In (1), ),( jiD is the similarity degree, ),( jiR is the real-time image, and ),( jiT is the current NM template image whose binary image is ),( jiB .While matching with this method, only the

template pixels relevant to the object are used. Suppose the pixel in the current template image ),( jiT , whose corresponding pixel has value of 1 in the binary image ),( jiB , to be p, then only using p for representing the similarity measure can improve the accuracy and correctness of the correlation tracking. In the following steps, the prediction point of the i+1 frame is taken as the centre for template matching in order to find the best matching point. Finally after calculating the size of the object and adjusting it, the new template is extracted from the i1 frame.

Since in this algorithm only the pixels of the template image corresponding to the black region in the binary template image are used to calculate, the effect on the object matching brought by the background pixels contained in the template image can be effectively reduced. During the matching and tracking process in sequence image, if the image located at the best matching position of current image is simply used as the template image for matching the next frame of image, the tracking result can easily affected by the image where one frame suddenly varies and deviates from the correct matching location, resulting in false matching. So in this paper the GM(1,1) model is introduced to predict the initial searching point. In addition, in order to solve the problem of occlusion, we introduce an occlusion judgment criterion based on shape information. Once the occlusion occurs, the prediction value of GM(1,1) model is used to replace the real value to lock the object range.

Z. Zhou et al. /Journal of Computational Information Systems 5:6(2009) 1841-1846 1843

3. Improved GM(1,1) Model

The grey system theory regards the random variant as the grey variant varying in a certain scope and the random process as the grey process which is varying in a certain scope and period. The grey variant is handled by the data generating method, which organizes the original data without regularity to be the generated data with strong regularity for researching. The grey prediction is to use the grey dynamic model to predict the eigenvalues of main actions or certain index of the system as well as the data generated in a certain moment in the future as the development of the system.

Suppose (0) (0) (0) (0)( (1), (2), , ( ))X x x x n= " to be the original sequence and (1) (1) (1) (1)( (1), (2), , ( ))X x x x n= " to be the first order accumulated generating sequence, then the

following grey different equation (0) (1)( ) ( )x k az k b+ = (2)

is the original form of GM(1,1) model, where

)()(1

)0()1( ixkxk

i=

= , k=1,2,,n. (3) The simulation and prediction accuracy of GM(1,1) model depends on the constants of a and b, which in

turn depend on the original sequence and the construction formula of the background value. The traditional GM(1,1) model constructs its background value via the formula of (1) (1) (1)( ) 0.5 ( ) 0.5 ( 1)z k x k x k= + , which accounts for the simulation error and the adaptability of GM(1,1) model. The AGO sequence )1(x of traditional GM(1,1) model is always concave no matter whether the original sequence )0(x is concave or convex, so the mean generation value of background with consecutive neighbors is always larger than the actual background value, resulting in hysteresis error. When data of the original sequence change slowly,

(1) ( )x k and )1()1( kx are less different. Hence the model error is small while replacing kk dttx1 )1( )( with the sequence of the mean value of consecutive neighbors. However, when the sequence data change dramatically, the background value constructed by this method often has a greater hysteresis error. In order to reduce the hysteresis error caused by the background value, we adopt the area of the actual curve in a region as the background value proposed in reference [13]:

)1(ln)(ln)1()()( )1()1(

)1()1()1(

=kxkx

kxkxkz , k=2,3,,n. (4)

If )1()( )1()1( = kxkx , we can get )1()( )1()1( = kxkz . If Tbaa ),(= is parameter vector and

=

)(

)3()2(

)0(

)0(

)0(

nx

xx

Y # ,

=)(

)3()2(

)1(

)1(

)1(

nz

zz

B #

1

11

# , (5)

the least square estimation parameters of GM(1,1) model bkazkx =+ )()( )1()0( satisfy YBBBa TT 1)(

= , thus they can be solved out. If we build the grey difference model using the n-th component of )1(x sequence as the initial condition, the time response of the winterization equation

1844 Z. Zhou et al. /Journal of Computational Information Systems 5:6(2009) 1841-1846

baxdt

dx =+ )1()1(

is

abcetx at += )( t=1,2,,n; (6)

where

=

=

= ni

ai

n

i

ai

e

eabix

c

1

2

1

)1( ))(( , which is obtained with the least error sum of squares.

The time response of the grey difference equation bkazkx =+ )()( )1()0( is [14]

abe

e

eabix

kx akn

i

ai

n

i

ai

+

=

=

=

1

2

1

)1()1( ))((

)( k=1,2,,n. (7)

The prediction values are

)()1()1()1()1()1()1(

)1()0(

kxkxkxkx +=+=+ k=1,2,,n. (8)

The traditional GM (1, 1) model uses the first component as the initial condition for grey system modeling, but the time response function can not guarantee the best fitting between the original sequence and the simulation sequence because it seriously depends on the development coefficient and can not make the simulation error of the whole sequence smallest. Reference [15] points out that it is lack of strictly

theoretical basis in the traditional GM (1, 1) predicting process to use (1)

x

(1) as the known condition and the solution may not necessarily be the best prediction formula. Reference [15] also improves the initial condition, but the improvement is not complete. In this paper, based on reference[14], after selecting the development coefficient -a and the grey action quantity b, we determine the constant c in the general solution of whitenization weight function by minimizing the sum of squares of differences between the simulation sequence and the first order AGO sequence of )1(x . As a result, the optimal time response function in accordance with the original sequence is constructed. Hence the GM(1,1) model in this paper has the combined advantages of both reference [13] and [14], and it can optimize the background value and the time response function at the same time.

4. Experimental Results and Analysis

The grey model does not model with the time sequence data directly, but accumulate and process the original data to establish the differential equations. So it has the unique effectiveness of weakening the randomicity of sequence and exploring the evolution law of system. To optimize the background value and the time response function both at the same time not only adapts to the case that the original data change gently but also to the case that the sequence data change sharply. The established model by this manner has smaller prediction error and can accurately predict the motion position of object to ensure the motion precision. The neighborhood with the prediction point as the center is taken as the searching window for matching two consecutive frames. This searching window is very effective. It can reduce the risk of being interfered by the complex background and reduce the computational complexity significantly.

Occlusion is the difficulty in object tracking. A fixed template is difficult to effectively track the object with occlusion, so the dynamic template updating method is used. In order to effectively avoid the background disturbance, the matching is done only using the partial template where the object region exists. Then the discrimination criterion of occlusion is used. When there is no occlusion, the searching region

Z. Zhou et al. /Journal of Computational Information Systems 5:6(2009) 1841-1846 1845

predicted by GM(1,1) model is used to match the object, greatly reducing the search template region; When there is occlusion, the real value is replaced with the prediction value of GM(1,1) and the template is no longer updated, thus ensuring the continuity of object motion to solve the occlusion problem in object tracking.

To reduce the computational complexity of the occlusion discrimination function, here we use the area and circumference to describe the geometric dimension of object since a rigid objects shape will be changed while it is occluded. The objects area and circumference can be represented by the contour length and the number of binarization pixels in the template region of two consecutive frames while tracking. Therefore, we can define a maximum threshold and a minimum threshold for the change rates of objects area and circumference in these two frames. When the change rates are larger than the maximum threshold, we can consider that full occlusion takes place; when they are between the maximum threshold and the minimum threshold, partial occlusion takes place.

5. Conclusions

During dynamic tracking, the method in this paper can dynamically change the size of the template according to variations of object and calculate the degree of similarity only using pixels of object region in template, which highlights the characteristics of object itself. It overcomes the defects of mismatching as a result that the template matching is affected by the background. This method uses the area of the actual curve in a region as the background value and determines the constant c in the general solution of whitenization weight function by minimizing the sum of squares of differences between the simulation sequence and the first order AGO sequence of )1(x to construct the optimized time response function meeting for the original sequence, resulting in the improved GM(1,1) model. The improved GM(1,1) model is then used to predict the next position for the next moment. By minimizing the searching region of object, the searching time is shortened and the searching accuracy is improved. Experimental results show that this

(a) Frame 10 (b) Frame 20 (c) Frame 30 (d) Frame 40

(e) Frame 50 (f) Frame 60 (g) Frame 70 (h) Frame 80

(i) Frame 90 (j) Frame 100 (k) Frame 130 (l) Frame 150

Fig.1 Object Tracking Result of Image Sequence

1846 Z. Zhou et al. /Journal of Computational Information Systems 5:6(2009) 1841-1846 algorithm has better tracking precision and can resolve the robust tracking problem while object is occluded, so it has a very wide range of applications.

Acknowledgement

This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y1090256. The authors are grateful for the anonymous reviewers who made constructive comments.

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