Research and Application of Target Tracking Algorithm

Bailin Lin

, Zheng’an Xiao

School of Physics and Mechanical

﹠

Electrical Engineering, Hubei University of Education, Wuhan, China

Keywords: Particle filter, mean shift, target tracking.

Abstract: This paper studies the principle of particle filtering and mean shift algorithm, analyzes the influence of

particle number on particle filter, and carries out tracking experiments on the target of the sports ship. Using

the method of polynomial fitting, the actual motion trajectory of the ship was manually sampled and

compared with the method trajectory of this article. The real-time performance of the algorithm is analyzed

and the experimental results are given.

1 INTRODUCTION

The purpose of video target tracking is to analyze

the video sequence captured by the sensor and

correlate the same moving target in different frames

of the image sequence to obtain the complete motion

track of each moving target. The essence of target

tracking is to analyze the video sequence captured

by the image sensor and calculate the position, size

and movement speed of the target in each frame of

the image. As a main branch of the field of computer

vision, the research of video target tracking method

is increasingly applied to security, intelligent video

surveillance, intelligent traffic management, military

robot vision and other fields. This article takes sports

ship target tracking as an example to carry out

relevant algorithms and experimental research. The

system that is formed is shown in Figure 1.1. The

shipping monitoring system collects images or video

and transmits it to image processing equipment,

detecting targets according to ship template

matching, and Track your goals.

Figure 1.1 Block Diagram of Ship Automatic Tracking

System.

In this paper, the sports ship is taken as the

tracking target, and each frame of image in the video

is taken as the object of processing, and the image is

enhanced. Then, the target ship is tracked by

Kalman and particle filter respectively.

2.ALGORITHM PRINCIPLE

ANALYSIS

2.1 MeanShift Algorithm

Mean Shift is a typical algorithm for the offset

vector. In the target tracking, the probability density

function is used to iteratively search for the target

color feature to track the target. Now commonly

referred to as Mean Shift algorithm belongs to the

search and match category in the tracking.

According to the maximum similarity of the tracking

template, the mean value of the current point and the

mean value of the shifted point are automatically

found in the neighboring area. This is a relatively

simple density estimation model. Constant search

until the calculated offset point is the last pixel to

scan the entire image. [1,2]. The specific process of

the algorithm is as follows:

(1) The target model of the initial frame

In the target search window space, the interval is

divided into K equal intervals, and the central pixel

coordinate of the search window in the initial frame

is set as the coordinate of the i-th pixel in the image

space area. In addition,

(

)

is used to represent

the kernel function selected during processing and

the window width is h. Then the probability of the u-

th eigenvalue can be expressed by formula (5.1):

(2.1)

In (2.1), the membership of the color

corresponding to the characteristic value u in the

coordinates can be judged by b and, in the color

space, C as the constant coefficient makes

probability and normalization:

∑

(2.2)

(2)Current frame model

According to the establishment of the initial

frame model, the probability of the u-th feature

value of the search window in the current frame can

also be expressed as:

(2.3)

In equation (2.3), the central pixel coordinates

corresponding to the current frame search window in

the initial frame model correspond to C in equation

(2.1).

（2）Similarity function

The similarity between the target model and the

current frame model in the initial frame can be

described by a similarity function, which is defined

as Equation (2.4):

(2.4)

among them

In the feature interval, the desired MeanShift

vector can be obtained when the similarity function

ρ(y) is at the maximum value[3]:

（2.5）

2.2Particle Filter Fundamentals

The basic idea of particle filtering is to first generate

a set of random samples in the state space based on

the empirical conditional distribution of the system

state vectors. These samples are called particles, and

then the weights and positions of the particles are

continuously adjusted according to the

measurements, and the particles are adjusted. The

information corrects the initial distribution of

experience conditions. The essence of this approach

is to approximate the associated probability

distributions using discrete random measures

consisting of particles and their weights, and

recursively update the discrete random densities

according to the algorithm. When the sample size is

large, this Monte Carlo description approximates the

true nonlinear stochastic system of the state variable,

and the precision can be approximated to the optimal

estimate. It is a very effective nonlinear filtering

technique [4].

Particle filtering, also known as sequential

Monte Carlo method (SMC), refers to finding a

series of random samples that can approximately

express the probability density function

()

zxp |

in the state space, and replacing the integral

operation with an arithmetic mean value to obtain

the state minimum variance The process of

estimation. These random samples are called

"particles."

The particle filter algorithm is as follows:

Combining the SIS with the particle resampling

method, a complete particle filter algorithm can be

obtained. Specific steps are as follows:

1) Initialization

Based on the distribution, random sampling in

the vicinity to obtain a series of particles

2）SIS

Usually the importance

distribution

()

kkk

zxxq

:11:0

−

can be simplified to

sample N particles accordingly

()

−

∝

xxpx

3) Calculate weights

Calculate the weight of each particle

()

and

normalize it

() () ()

∑

www

4) A posteriori probability estimate

Output a set of weighted

particles

(){}

Niwx

,...,2,1,, =

, according to the

weighted average or maximum posterior probability

[]

)(

uxb

kCq

−

⎟

⎠

⎞

⎜

⎝

⎛

−

∑

()

[]

∑

−

⎟

⎠

⎞

⎜

⎝

⎛

−

uxb

kCyp

)(

()() ()

∑∑

⎟

⎠

⎞

⎜

⎝

⎛

−

qypqy

ˆˆ

ρρ

()

[]

∑

−=

uxb

()

01,

xiy

gwx

yyym

−

⎥

⎦

⎤

⎢

⎣

⎡

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

−

=−=

∑

of the particle, to obtain the posterior probability

estimate of the current time k.

5) Particle resampling

According to the particle weights, the sample set

is re-sampled, the large-weighted particles are

divided into multiple particles, the small-weighted

particles are deleted, and the new N particles are

obtained.

6) State transfer

When k+1 arrives, record the observations and

repeat from 2 to 6.

3. SPORTS SHIP TRACKING

EXPERIMENT

3.1 Mean Shift Tracking Algorithm

The traditional Mean Shift algorithm was used for

target tracking in the experiment. The first is the

initialization of the target tracking, which can be

used to obtain the circumscribed rectangle of the

initial target that needs to be tracked. However, the

main research focus of this paper is to track the

algorithm and not focus on the target detection

module, so the manual selection method is selected

by the mouse. Then calculate the histogram

distribution of the search window weighted by the

kernel function, and use the same method to

calculate the histogram distribution of the

corresponding window of the Nth frame; use the

principle of maximum similarity of the distribution

of the two target templates to maximize the search

window along the density increase. Move in the

direction to get the true position of the target. The

tracking steps are as follows:

1) Calculate the probability density of the target

template, the target estimated position and the

nuclear window width h;

2) Using the target position of the initial frame to

calculate the candidate target template;

3) Calculate the weight value of each point in the

current window;

4) Calculate the new position of the target

（3.1）

The Mean Shift algorithm continuously iterates

and finally finds the optimal position of the target in

the image sequence.

In the experiment, the tracking window is first

determined, the tracking target model of the initial

frame is set, the target to be tracked is selected in the

first frame, and a rectangle, that is, the ship feature

search window containing the ship's target is framed,

also called the tracked target area, and cut This area

is shown in Figure 3.1. After the end of the tracking,

observe the record tracking results, as shown in

Figures 3.2 to 3.5.

Figure 3.1 Image Selection.

Figure 3.2 Frame 20.

Figure 3.3 Frame 50.

∑

⎟

⎠

⎞

⎜

⎝

⎛

−

⎟

⎠

⎞

⎜

⎝

⎛

−

gwx

Figure 3.4Frame 70.

Figure 3.5 Frame 100.

From the experimental results, it can be seen that the

two ships are staggered at the 50 frames, but the

tracking frame is slightly shifted at a video around

the middle 100th frame, but after that, the tracking

frame is restored accurately until the final 273th

frame. Observe the tracking trajectory is basically in

line with the movement, but the occurrence of up

and down jump, on the one hand, there is tracking

error, but the main reason is that there is no use of a

tripod in the video capture process, the image jitter,

it is acceptable error range.

3.2 Ship Tracking Based on Particle

Filter

Particles used in target tracking usually refer to

target status information, including target position,

size, color, and motion information. The specific

implementation steps are as follows [5]:

1) Initialization

The initial position of the target

is selected

and N particles are randomly distributed near

2) Get particle weight

Assuming the system is in a state such as

XXX ,...,

, Any

X , i = 1, 2, ..., n, we call a

particle that represents a particle-centric image

block. Each particle's position, color, edge, and

other information together form the current state of

the moment. Z is the observed value of the system at

this time, and

)(

:1 kk

xzp

is obtained based on

historical information. To estimate the exact position

of the target X, it is necessary to operate on the

particles. Each particle

X corresponds to a

rectangular frame, and the color in the frame is

counted to obtain a 16-dimensional color histogram

vector

. Each color histogram has 16 bins

containing 16 grayscale values (0~255/16). After the

statistics are finished, The

H is normalized so that

the sum of the squares of each bin is 1, which is a

16-dimensional unit vector.

The weight

W of each

H can be understood

as the inner product of the color histograms

and

H of the target template, that is, the quantities of

each bin are multiplied and added. This represents

the similarity between the image region represented

by the current particle and the target template. The

higher the weight, the more similar the particle is to

the target. The

XXX ,...,

weight

WWW ,...,

calculated from

)(

:1 kk

xzp

, where ><

HH ,

represents the inner product operation.

3) Predict the current position

From the weighted average of the obtained

particles

XXX ,...,

and the corresponding

weight

WWW ,...,

, the system state can be

estimated:

WXWXWXX *...**

2211

+++= , where

X represents the location information of the center

of the area. The resulting X is approximately equal

to the posterior probability estimate and predicts the

current position of the target.

4) Particle resampling

As the number of tilts of the video increases, the

weights will become more and more concentrated on

a small number of particles. Most of the other

particles have very small weights. Before entering

the next iteration, the particle weights are

redistributed to make them all the same. Therefore,

the particles need to be re-sampled, ie, N particles

XXX

′′′

,...,

are regenerated. The regenerated

particles all come from the original particle set

XXX ,...,

, in which the large particles

generated by the weights generate more new

particles, and the particles having the smaller

weights correspond to fewer new particles.

5) State transfer

At the next moment, the particles are updated,

that is,

′

becomes

′′

. Since the probability that

the state transition from

′

′′

can be obtained

from the state matrix is

)(

1−kk

xxp

, the probability

of changing from

′

′′

is equal to

)(

1−kk

xxp

6) Repeat 2 to 5.

In the experiment, the number of particles was

selected as 200. The particle filter algorithm of this

paper also adopts the method of manually selecting

the tracking target. First, the initial frame is

displayed, and a rectangle, that is, the ship feature

search window containing the ship's target is

selected by using the selection box, and the ship's

edge is cut as far as possible, and right-cut. Use the

[temp,rect]=imcrop(I) format to cut, the image

matrix of the ship model is saved in the temp

variable, and then a histogram is calculated for the

variable; the initial position coordinates of the ship

are stored in the rect variable for calculation The

center coordinates of the ship.

3.3 Error Analysis

In this paper, the distance between the tracking

center point and the actual movement center point is

calculated to calculate the error of comparing the

two algorithms. The center point of the actual

movement uses the manual selection method, writes

a program, selects 9 frames, and determines the

coordinates of the center point; then uses a

polynomial fitting method to perform 6 fittings to fit

the actual motion trajectory; then it calculates the

two tracks separately. The error between the curve

and the trajectory is measured by the error and

variance of the average per frame. The error

calculation result shows the MATLAB running

screenshot, as shown in Table 1.

Table 1 Comparison of tracking errors.

Average per frame error (pixels) Average gap between two

algorithms per frame (pixels)

Particle filter method 3.7212 5.7782

Mean shift method 2.3213

From the above tracking results, it can be seen

that both algorithms have jitter in the tracking

process, but the overall trend is correct, and the

mean error using the mean shift method is smaller

than the particle filter method, and the difference

between the two methods does not exceed 6 pixels.

3.4 Real-time Analysis

Use the tic and toc commands to output the total

running time of the program. The results are shown

in Table 2.

Table 2 Runtime Comparison.

Tracking algorithm Running time (s)

Particle filter algorithm 48.151951

Mean shift algorithm 115.003216

It can be seen that the operation time of the

particle filter algorithm is far less than the mean shift

algorithm, and the real-time performance is better.

This aspect is the reason for the algorithm, and on

the other hand, it is the reason for the design of the

program itself.

3.5 Effect of Particle Number on Particle

Filtering Tracking

Set the number of particles to 100, 200, 500, 1000,

and 2000, and observe the effect on the program.

The change in the running time is shown in Table 3. The error is shown in Table 4.

Table 3 Effect of Particle Number on Running Time.

Number of particles Running time (s)

100 35.889891

200 48.151951

500 63.085486

1000 121.126432

2000 196.054916

Table 4 Effect of Particle Number on Tracking Error.

Number of particles Average per frame error (pixels)

100 3.9718

200 3.7212

500 3.0853

1000 2.7546

2000 2.3691

It can be seen that the number of particles

increases, the amount of calculation increases, the

running time of the program becomes longer, and

the real-time performance becomes worse; the

tracking effect seems to be better intuitively, but the

actual error change is not obvious, which is related

to the number of times of polynomial fitting, Select

manually when the target is selected. The initial

template is inconsistent.

4 CONCLUSIONS

The tracking accuracy and real-time performance of

the two algorithms are compared. It is found that the

accuracy of the particle filter tracking algorithm is

lower than that of the mean-shift algorithm, but the

real-time performance is better. Afterwards, the

effect of particle number on particle filtering was

studied. It was found that as the number of particles

increases, the tracking accuracy increases, but the

running time becomes longer and the real-time

performance becomes worse

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