The Analysis of Target Trajectory Based on Genetic Evolutionary and Particle Filter

(1)

DOI:_{10.12928/TELKOMNIKA.v14i3A.4421} ₂₉₇

The Analysis of Target Trajectory Based on Genetic

Evolutionary and Particle Filter

Yanni Wang*, Junni Zhou

School of Information and Control Engineering, Xi'an University of Architecture and Technology, Xi’an, Shaanxi, 710055, P. R. China

*Corresponding author, e-mail: wangyn02@126.com

Abstract

Aiming at the problem of trajectory recognition of moving objects in video surveillance, an analysis algorithm of the target trajectory based on genetic evolutionary and particle filter is presented, which is combined with genetic algorithm. Firstly generate initial parent particle population in the reference frame, use preferred evolution strategies of genetic algorithm, and select excellent particles of offspring. Then do not the corresponding calculations on the basis of crossover and mutation rules for the unselected particles until reach the number of iterations. At last, calculate object states by the weights of each particle and obtain the target trajectory. The new algorithm is not affected by the background changes. Compared with the existing algorithms, the simulation results show that it easy to realize and has more stable tracking effect.

Keywords: target trajectory, genetic algorithm, preferred evolution, particle filter

1. Introduction

The trajectory analysis of target is one of the key problems in computer vision field, is widely used in many aspects of safety monitoring, medical diagnosis, image signal processing and military surveillance. In recent years, people have done much research on target tracking technology, and have made some important achievements. Literature [1] presented an adaptive hybrid Gauss particle filtering method to deal with change of target in the tracking process. The literature [2] first put the tracking problem to a Bayesian filtering problem for nonlinear and non Gauss, and then to obtain the tracking trajectory through the solution of the filtering problem. The literature [3] introduces an optimized particle filter method which the particle is proportional to its weight. Huang [4] use the diagram of discrete color and local homogeneity criterion obtain significant objects in images, and get target region.

In order to overcome the problem of degradation of the traditional particle filter algorithm, introducing the genetic algorithm idea into the particle filter, put forward a kind of analysis algorithm of target trajectory based on Genetic Evolutionary and Particle Filter (GEPF). Firstly the algorithm gets the initial particles by sampling on the basis of genetic algorithm and selects the excellent particles. Then do not crossover and mutation for not entering progeny particles until the end of the iteration number, and get the target trajectory. This algorithm can track the moving target effectively, and has good robustness for illumination variations.

2. Particle Filter

The particle filter, similar to the literature[5], is a new filter algorithm developed from the last century in the late 90's, its idea is to use random sample describe the probability distribution, adjust the weights of sample particles on the basis of measurements, approximate the real probability distribution, and make the sample mean as the system estimates.

At present, the particle filter algorithm has been widely used in target tracking [6-21], navigation, fault diagnosis, parameter estimation and system identification etc. The general description of the algorithm:

(2)

Initialization. Starting from the first frame k=0, select N sample particle points

 

1 N i k _i

x



according to the probability density function of

/ 1

( )

~

,

1, 2,

,

k k

i i

k x

x

p

_

i





N

, the weight of each particle is

w

₀i



1

 

0/0 ₁

~

(

)

i i

x

p x

 (1)

Prediction. Predict the posterior frame by the previous frame:

/ 1

~

( _k/ _k )

,

1, 2,

,

i i

k k x x

x

p

i

N







(2)

Calculate the particle’s weight.

( / )

(

/

) (

/

)

1 ,

1, 2,

,

k k

i i

i k k k k

k i

x x

p y

x p x

x

w

i

N

p







(3)

Normalize the weights.

,

1, 2,

,

i i k k N i k i

w

i

N

w







(4)

Output the results.

/ / 1

ˆ

N i i

k k k k k

x

w x

_





(5)

/ 1 / 1 / / 1 /

ˆ

(

)(

)

i i i T

k k k k k k k k k k k

p

_

w x

_

x

_

x







(6)

Resampling. Generate new N particles according to the following formula (7).

/ / 1

(

k ki k kj

)

p x



x

_



w

(7)

Set

k

 

k

1

, and repeat the second step to the sixth step.

3. The Analysis of Target Trajectory Based on Genetic Evolutionary and Particle Filter Genetic algorithm [22-24] is a search heuristic algorithm to solve the optimization problem in the field of artificial intelligence, is often used to generate useful solutions to optimization and search problems. Evolutionary algorithm is developing by some phenomena in evolutionary biology, including heredity, mutation, natural selection and hybridization. Genetic algorithm is likely to converge to a local optimum when the improper circumstances of fitness function, but could not reach the global optimum.

3.1. Genetic Algorithm

Genetic algorithm is a fast, simple, strong fault tolerance algorithm, and its general steps for coding, initial population, the calculation of similarity, reproduction, crossover and mutation have six steps. The replication of probability is , the crossover probability is ,

(3)

mutation probability is . Reproduction probability is in the range of 0.5-0.75, crossover probability is in the range of 0.15-0.35, . The concrete steps of genetic algorithm are given below:

Step 1: Sample coding and similarity calculation

Number the new sampling particle , , … , , define the parent sample

, , , … , . Using the color feature of the target, calculate the template and the similarity of

sampling point. After every observation, get the similarity of each sampling point. The similarity is . Normalized the similarity coefficient:

/

,

1, 2,

,

i i i

p

p i

N









(8)

Step 2: Preferred reproduction

Take sample the normalized similarity coefficients using resampling method with the traditional polynomial. The samples of similar large coefficients obtained greater probability of being selected to copy the offspring, and the samples with small similarity coefficient obtain a smaller probability to be selected for replicating offspring. After every election, the sample was selected is out of the parent generation. Residual samples do not continue to choose until the resulting offspring numbers reach .

Polynomial resampling has better real-time performance in particle filter algorithm, but the resampling particle of degradation is serious. The traditional genetic algorithms have worse real-time when they do preferred reproduction using limit threshold method.

The larger similarity with equal probability copy for offspring, the optimization is not prominent. Preferred reproduction using polynomial resampling can guarantee the tracking algorithm has better real-time. Defining the number of samples by limit random number is available for the diversity of samples space, reduces the particle degradation degree.

Step 3: Cross reproduction

Select two samples randomly in the remaining samples of after preferred reproduction do hybridization. The selected samples are i and ́. Set the random number

a=0.25-0.45 as the exchange rate. Cross propagation formula are the below:

(1

)

i i i

k k k

x



ax

 

a x

(9)

' '

(1

)

i i i

k k k

x



ax

 

a x

(10)

Do not make the new

x

_kiand

x

_ki' as the offspring until the numbers of cross generation reach

Np

_t. The methods of samples cross breeding using the random number as the exchange rate can improve the diversity of samples. Compared with the traditional genetic algorithm which uses fixed coefficient as exchange rate, the method with random number can operate reproduction flexibly, and has better performance in increasing the diversity of all particles.

Step 4: Mutate reproduction.

Mutate reproduction is to bring the new sample to sample population. Select

c t

N



Np



Np

samples randomly in the remaining of

N



Np

_cand do mutate breeding. After Mutation the samples are:

/ 1

ˆ

i i

k k k k

x



x

_

x





(11)

In above formula (11),

x

_{k k}_/ _₁is a transition matrix of Markov chain,



~

N

(0,1)

In the traditional genetic algorithm, sample mutation produce new samples using fixed probability. So the effect to solve the problem of particle degradation is limit.

(4)

3.2. The Analysis of Target Trajectory Based on Genetic Evolutionary and Particle Filter Genetic algorithm is a kind of evolutionary algorithm. Owing to the problem of particle degradation and great computation, introduce the selection, crossover and mutation operation in genetic algorithm into the particle filtering, instead of the traditional algorithm and overcome the deficient phenomenon. The specific implementation steps are as follows:

Step 1: Initial particle population

Select the tracking window in the initial frame manually, and calculate the characteristic parameters of the target samples. Similar to the particle filter, starting from the first frame k=0,

generate M particles

 

1 M i k _i

x

 _{by the uniform distribution}

p x

(

)

_{, each particle weight is} 0

1 w



 

0/0 1

~

(

),

1, 2,

,

M i

x i

x

p

x

i

M





(12)

So, get the parent particle population genetic. Step 2: Preferred evolution

First of all, predict the parent particles whether occur in the next moment, and then select initial probability density function of the parent particle state using Bayesian estimation.

0 0 0

(

)

( )

p x y



p x

(13)

The prediction equation is:

1: 1 1 1 1: 1 1

(

_k _k

)

(

_k _k

) (

_k _k

)

p x y

_





p x x

_

P x

_

y

_

dx

_ (14)

Particle state in the next moment:

1: 1 1: 1

1: 1

(

) (

)

(

)

(

)

k k k k

k k

p y x

p x y

p y y

 





(15)

Calculate each particle’s weight.

/ 1

(

/

),

1, 2,

,

i i

k k k k

w



p y

x

_

i





M

(16)

Compare each weight coefficient with the acceptance probability. If meet the following conditions, the particle is the preferred particle, it need further evolution. Obtain the optimized particle accounts for about 0.6-0.7 of the total number of particles through the experiment analysis.

0.65

i k

k M

i k i

w







(17)

The particles which not get preferred continue to perform the following operations, crossover and mutation.

Step 3: Crossover operation

Select two particles which do not optimize randomly, crossover operation in accordance with the following rules:

' 1₍ ₎ 1₍ ₎

2 2

i i j

k k k

(5)

' 1₍ ₎ 1₍ ₎

2 2

j j i

k k k

x 

 

 x 

 

 x (19)

,  are the cross coefficient, their value is 0 < ,< 1. Thus, most parent individuals are parental genetic after cross. At the same time, according to the condition whether particle probability density meets the following fitness function. If meet with the condition, use new individuals instead of the parent generation particle.

Set





1 max( ( i)), max( ( j))

k k

mean mean p x p x (20)





2 min( ( ik)), min( ( kj))

mean mean p x p x (21)

So '

( ik) ( 1 2)

p x mean mean mean (22)

To the new generation particles, update using the same formula (22). Step 4: Mutation operation

Select a random particle from the remaining particles did not participate in the operation after optimization and cross, mutate using the following formula:

0.65

i i

k k

x x  f (23)

f

is Gauss distribution: 2

~ ( , )

f N   (24)

2 1/ 2 1 2 2

( : , ) (2 ) exp( ( ) / 2)

p x        x   (25)

Use the new

x

_ki' instead of

x

_ki, otherwise do not replace. Because the number of this part of the particle is less, so this operation has only small amplitude variation.

Step 5: Judgment of termination condition

When the evolution algebra t is higher than the threshold of T, the individual of maximum fitness in the evolutionary process is the optimal output result, the operation is terminated.

t



T

(26)

Output the weight and the state of current particle individual. According to the experiments, the selection of T is in 15-20 generation in general.

Step 6 Determine the targets

Each particle has its weight and state. The particles involved in operating can determine the state at the end of each stage. After the end of the evolutionary process, all particles’ states compose the target.

M

is the total number of samples.

1

i i

k k

w

M





(27)

1 M

i i

k k k

x

w x



(6)

x

is the true state of the target at

k

moment.

The algorithm based on the genetic evolutionary and particle filter has better performance than the other particle filter, it reduce the calculation, decrease the complexity.

Flow chart of the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter is shown in Figure 1:

Figure 1. Flow chart of the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter

4. The Analysis of Simulation

Let’s do comprehensive tests for the new algorithm. The simulation environment in Intel (R) Core (TM) 2 Duo CPU E7400, frequency 2.80GHz, configuration memory 1.00GB in PC machine. The software is version MATLAB 7.0 and above. Detect and track the target in the self recorded video.

First, select the tracking window size of w 3-5 in the initial frame, and calculate the characteristic parameters such as color histogram of tracking target. And then track the target trajectory according to the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter.

Experiment 1, tracking for single moving target

Use the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter (GEPF) track the single moving target in the self recorded video.

From the beginning of the reference frame, make the position of motion human in the frame as the origin, track the walking route of the people, and draw the trajectory curve in the two-dimensional plane. Draw the actual motion trajectory at the same time. The tracking trajectory results are shown in Figure 2:

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(a) Reference frame (b) The tracking trajectory of GEPF Figure 2. The tracking trajectory results of single moving target

Experiment 2, tracking for multiple moving targets

Use the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter track the multiple moving targets in the self recorded video.

From the beginning of the reference frame, track the walking route of two people in the same frame, and draw the true trajectory and trajectory curve of GEPF. The tracking results are shown in Figure 3:

(a) Reference frame (b) The tracking trajectory of GEPF with two targets Figure 3. The tracking trajectory results of multiple moving targets

Experiment 3, tracking for small moving target

Use the GEPF algorithm track the small moving target in the self recorded video. In the reference frame, make the position of small motion people as the origin, track the walking route of the moving target, and draw the trajectory curve of GEPF and true trajectory in the two-dimensional plane. The tracking results of the twenty frames are shown as Figure 4.

In the tracking process, the new algorithm use color characteristics of the object, calculate the required parameters combined with the movement vector, and track the small moving targets.

(a) Reference frame (b) The tracking trajectory of GEPF Figure 4. The tracking trajectory results of small moving target

reference frame

0 2 4 6 8 10 12 14 16 18 20 -5

0 5 10

X / Km

Y /

true trajectory GEPF

reference frame

0 2 4 6 8 10 12 14 16 18 20 -10

-5 0 5 10 15

X / Km

Y /

true trajectory of target 1 GEPF of target 1 true trajectory of target 2 GEPF of target 2

reference frame

0 2 4 6 8 10 12 14 16 18 20 -4

-2 0 2 4 6 8 10 12 14 16

X / Km

Y /

true trajectory GEPF

(8)

Experiment 4, the compares of tracking trajectory

Using the GEPF algorithm and traditional particle filter (PF) algorithm, track the targets in 200 frames of the first video stream. Draw the true trajectory of the target and trajectory with PF and GEPF algorithms in the same two-dimensional plane. The compare results between true trajectory and tracking trajectory of the two algorithms are as (a) in Figure 5.

Do the similar simulation with 300 frames of the second video stream. The compare results between true trajectory and tracking trajectory of the PF and GEPF algorithms are as (b) in Figure 5.

(a) The tracking trajectory of 200 frames (b) The tracking trajectory of 300 frames Figure 5. Tracking curves of two kinds of algorithms in the X-Y plane

The above experiments simulate and track moving targets for various video streaming with the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter. In experiment 1, experiment 2 and experiment 3, the new algorithm has good tracking effect for single moving target, multiple moving targets and small moving target. In experiment 4, compared with traditional particle filter algorithm, the tracking trajectory of the new algorithm is closer to the true trajectory for different video streams and different number of frames.

5. Conclusion

According to the problem of tracking targets in video surveillance, we propose an analysis algorithm of the target trajectory based on genetic evolutionary and particle filter. Optimize the generation for the initial particle population using genetic algorithm, and perform crossover and mutation operations with the individual particle which did not enter the progeny. After the evolution operation, obtain the target trajectory. The experiment results show that the new algorithm can track the different moving target effectively, and it has robust to the changes of target’s pose. How to tracking the abnormal target in video images still need further research.

Acknowledgements

This work is supported by the Natural Science Foundation Research Project of Shaanxi Province, China (No. 2016JM6079).

References

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0 2 4 6 8 10 12 14 16 18 20 -8

-6 -4 -2 0 2 4 6 8 10 12

X / Km

Y /

true trajectory PF GEPF

0 5 10 15 20 25 30 -10

-5 0 5 10 15

X / Km

Y /

true trajectory PF GEPF

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(1)

3.2. The Analysis of Target Trajectory Based on Genetic Evolutionary and Particle Filter

Genetic algorithm is a kind of evolutionary algorithm. Owing to the problem of particle degradation and great computation, introduce the selection, crossover and mutation operation in genetic algorithm into the particle filtering, instead of the traditional algorithm and overcome the deficient phenomenon. The specific implementation steps are as follows:

Step 1: Initial particle population

Select the tracking window in the initial frame manually, and calculate the characteristic parameters of the target samples. Similar to the particle filter, starting from the first frame k=0, generate M particles

 

M i k _i

x

 _{by the uniform distribution}

p x

(

)

_{, each particle weight is} 0

1 w



 

0/0 1

~

(

),

1, 2,

,

M i

x i

x

p

x

i

M





(12)

So, get the parent particle population genetic. Step 2: Preferred evolution

First of all, predict the parent particles whether occur in the next moment, and then select initial probability density function of the parent particle state using Bayesian estimation.

0 0 0

(

)

( )

p x y



p x

(13)

The prediction equation is:

1: 1 1 1 1: 1 1

(

_k _k

)

(

_k _k

) (

_k _k

)

p x y

_





p x x

_

P x

_

y

_

dx

_ (14) Particle state in the next moment:

1: 1 1: 1

1: 1

(

) (

)

(

)

(

)

k k k k

k k

p y x

p x y

p y y

 





(15)

Calculate each particle’s weight.

/ 1

(

/

),

1, 2,

,

i i

k k k k

w



p y

x

_

i





M

(16)

0.65

i k

k M

i k i

w







(17)

The particles which not get preferred continue to perform the following operations, crossover and mutation.

Step 3: Crossover operation

Select two particles which do not optimize randomly, crossover operation in accordance with the following rules:

' 1₍ ₎ 1₍ ₎

2 2

i i j

k k k

(2)

' 1₍ ₎ 1₍ ₎

2 2

j j i

k k k

x 

 

 x 

 

 x (19)

Set





1 max( ( i)), max( ( j))

k k

mean mean p x p x (20)





2 min( ( ik)), min( ( kj))

mean mean p x p x (21)

So '

( ik) ( 1 2)

p x mean mean mean (22)

To the new generation particles, update using the same formula (22). Step 4: Mutation operation

Select a random particle from the remaining particles did not participate in the operation after optimization and cross, mutate using the following formula:

0.65 i i k k

x x  f (23)

f

is Gauss distribution: 2

~ ( , )

f N   (24)

2 1/ 2 1 2 2

( : , ) (2 ) exp( ( ) / 2)

p x        x   (25)

Use the new

x

_ki' instead of

x

_ki, otherwise do not replace. Because the number of this part of the particle is less, so this operation has only small amplitude variation.

Step 5: Judgment of termination condition

When the evolution algebra t is higher than the threshold of T, the individual of maximum fitness in the evolutionary process is the optimal output result, the operation is terminated.

t



T

(26)

Output the weight and the state of current particle individual. According to the experiments, the selection of T is in 15-20 generation in general.

Step 6 Determine the targets

M

is the total number of samples.

1

i i

k k

w

M





(27)

1 M

i i

k k k

x

w x



(3)

x

is the true state of the target at

k

moment.

The algorithm based on the genetic evolutionary and particle filter has better performance than the other particle filter, it reduce the calculation, decrease the complexity.

Flow chart of the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter is shown in Figure 1:

Figure 1. Flow chart of the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter

4. The Analysis of Simulation

Experiment 1, tracking for single moving target

Use the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter (GEPF) track the single moving target in the self recorded video.

(4)

(a) Reference frame (b) The tracking trajectory of GEPF Figure 2. The tracking trajectory results of single moving target

Experiment 2, tracking for multiple moving targets

Use the analysis algorithm of the target trajectory based on genetic evolutionary and particle filter track the multiple moving targets in the self recorded video.

(a) Reference frame (b) The tracking trajectory of GEPF with two targets Figure 3. The tracking trajectory results of multiple moving targets

Experiment 3, tracking for small moving target

In the tracking process, the new algorithm use color characteristics of the object, calculate the required parameters combined with the movement vector, and track the small moving targets.

(a) Reference frame (b) The tracking trajectory of GEPF Figure 4. The tracking trajectory results of small moving target

reference frame

0 2 4 6 8 10 12 14 16 18 20

-5 0 5 10

X / Km

Y /

true trajectory GEPF

reference frame

0 2 4 6 8 10 12 14 16 18 20

-10 -5 0 5 10 15

X / Km

Y /

true trajectory of target 1 GEPF of target 1 true trajectory of target 2 GEPF of target 2

reference frame

0 2 4 6 8 10 12 14 16 18 20

-4 -2 0 2 4 6 8 10 12 14 16

X / Km

Y /

true trajectory GEPF

(5)

Experiment 4, the compares of tracking trajectory

Do the similar simulation with 300 frames of the second video stream. The compare results between true trajectory and tracking trajectory of the PF and GEPF algorithms are as (b) in Figure 5.

(a) The tracking trajectory of 200 frames (b) The tracking trajectory of 300 frames Figure 5. Tracking curves of two kinds of algorithms in the X-Y plane

5. Conclusion

Acknowledgements

This work is supported by the Natural Science Foundation Research Project of Shaanxi Province, China (No. 2016JM6079).

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