2012/10/26 第11回行動モデル夏の学校

Development of the Automatic HumanTracking Method by Integrationof Pedestrian Behavioral Model
歩行者行動モデルを統合した
人物自動追跡手法の開発
NAKANISHI Wataru / 中西 航
PhD Student
Regional Planning and Information Lab.
Dept. of Civil Engineering, The University of Tokyo
nakanishi@trip.t.u-tokyo.ac.jp

Background• Importance of microscopic understanding of pedestrian
behavior for sophisticated space design and flow control• Detail passenger flow leads to good station improvement works• Automatic human tracking is difficult under situations thatpeople are occluded by others or close to each other2

Background and Purpose• Approach to understanding pedestrian behavior• Sensing and imaging technology::Human tracking using color and range information• Modeling and simulation::Microscopic behavior model considering interaction• To achieve multiple human tracking under complex
situations by integrating observation and simulation
as data assimilation process3

4

General Space State Model• Effective way to stochastically combine observations andsimulations
xt: State Vector at time t, cannot be observed: Human position and shape

xt-1

System modelp  xt | xt 1 zt-1xt

xt+1
Observation
Model p  z t | xt zt

zt+1

zt: Observation Vector at time t, can be observed: 3D Range and color• After observation zt, estimating xt by MAP estimation::Optimal p(xt|z1:t)p  xt | z1:t   p  z t | xt  p  xt | z1:t 1  p  z t | xt   p  xt | xt 1  p  xt 1 | z1:t 1  dxt 1

Particle Filterp  xt | z1:t   p  z t | xt   p  xt | xt 1  p  xt 1 | z1:t 1  dxt 1

p  xt 1 | z1:t 1 Approximate p.d.f.
by weighted particles
ResamplingMove particles byp  xt | z1:t 1 Weight particles byp  xt | z1:t p  xt | xt 1 p  z t | xt Expected value of this particles: Estimated value of xt

5State Vector / Observation Vector
One ellipsoidhx, y, zdxt: State Vector at time t, cannot be observed: Human position and shape• Defined as one ellipsoidxt  ( xt , yt , zt , wt , ht , dt )wzt: Observation Vector at time t, can be observed: 3D Range and color• Defined as 3D coordinates (X, Y, Z)
and color values (r, g, b) at each pixelz   X ,Y , Z , r , g , b 
ij ,tij ,tij ,tij ,tij ,tij ,tij ,t6

Observation Model p  z t | xt xt：State vector at time t(Human shape and position)

xt-1

zt-1

xt

SystemModelxt+1
Observation
Modelzt

zt+1

zt：Observation vector at time t
3D range and color
7

Probability distributionof observation vector
on condition of state vector→Corresponding to existing
tracking method

Model from both color and range observationp  z t | xt   p  zcolort| xt   p  zColor model

ranget| xt Range model

8Color Observation Model• Color Histogram Matching between successive frames• Compare similarity of histograms of two ellipsoids
put-1

tqui

Bhattacharyya coefficient255

   pu qugi 0ibr• Product of each color, r, g, and bp  z tcolor | xt     pu qu
255

r , g ,b i  0

9Range Observation Model• Shape Matching between estimated ellipsoidand observed points x  xt   y  yt   z  zt    1
w/
2
h/
2d/
2
  
2dˆ p
dp

22

 X ,Y , Z 
ij ,tij ,tij ,tDistance from centerof ellipsoid to::observed point d p::surface of ellipsoid dˆ p

Evaluation equation
21ˆ1  d p  d p
I p(I: # of observed points)• p: Observed points inside ellipsoid
are calculated
21rangep  z t | xt   1   d p  dˆ pI p

System Model p  xt | xt 1 
xt：State vector at time t(Human shape and position)

xt-1

zt-1

xt

SystemModel

xt+1
Observation
Model

zt

zt+1

Time-serious changeof state vector→
Corresponding to pedestrian
behavioral model

zt：Observation vector at time t
3D range and color• Most of existing tracking method regard time-serious
change as random walk or uniform motion• Introducing non-linear behavioral model to tracking
method is feature of this research

10System Model p  xt | xt 1 
• Discrete choice model by Robin et al. (2009)• 33 choice set for each pedestrian
for next step
• Utility function:
Unknown while tracking→omit this terms

Interaction
between pedestrians• Cross nested logit, nests for velocity and angle

1112Application• Commuter rush hourat Tama-Plaza Station, about
30km west from central Tokyo• Passengers moveinterdependently• Conditionof stereo video camera• Frame rate 7.5 fps• Baseline 1m

ColorRange
23.0m

19.5m

Application

13

14Application• Automatic acquisition of• Position and velocity• Passenger flow
• Ticket gate choice

Part of passenger flow data
Platforms

Platforms
Ticket gates
A B C D E
A B

C

D E

Exits

Exits

15

How to improve model?
• What is better observation model?
• What is better system model?
• From tracking result, optimize likelihood…
p  z1:T   p  zT | z1:T 1  p  z1:T 1 p  xt | z1:t  T  p  z t | z1:t 1 t 1log p  z1:T   log  p  zT | z1:T 1  p  z1:T 1 p  z t | xt  p  xt | z1:t 1 p  z t | z1:t 1 p  z t | xt  p  xt | z1:t 1  p  z | x  p  x | z  dxtT

  p  z t | z1:t 1 tt1:t 1( p  z t | xt  p  xt | z1:t 1 )t 1• For any parameter θ in the model,
we can optimize l    log p  z |     log p  z | z , 
• We also have to consider model structure itself
T1:Tt 1

t1:t 1t

Consideration of System Model

16• Problems of Simulation model• In the model from Robin et al., the term “toward destination”
makes much effect than other terms, although we cannot know
destination while tracking• Generally in actual situation we don’t decide our destination
every one second or shorter time step, even if the model
reproduce their behavior correctly
0.9
0.9
Destination is set
0.80.830m away in each direction0.7
0.7
0.6
0.6
(a)
0.5
0.5
0.4
0.4
(b)
0.3
0.3
0.2
0.2
0.1
0.1
00
RL(a)

L

0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
00

RL

(b)

R

Consideration of System Model

17• Consideration of general state space model• From viewpoint of observation, pedestrian position fluctuates if
observation rate is high enough• However observation cannot be smoothed because there isobservation model• System model is not the same as simulation model• System model needs to describe only probability distribution ofnext step on condition of present situation• This may bring about knowledge also for simulation model• Actual structure of human behavior (time step and choice etc.)• Relationship between condition of field and human behavior

18

Trial (Setting)• Dataset: Manually acquired at station (mentioned before)
Total: 3533
• Time step: 0.27[s]2: 539• Choice set: 3 for angle, 3 for velocity 1: 392 5: 582
3: 336
4: 2496: 300• Form: MNL
8: 533Vi   dist disti Distance to ticket gate

7: 275

9: 327(chosen in the future)  angle anglei 30 if candidate 1, 3, 4, 6, 7 and 9otherwise 0Iacc = 1 if candidate 1 to 3 Idec = 1 if candidate 7 to 9
 vi 
 vi  v = 4.87m/s
  acc I acc    dec I dec  max
 vmax  vmax  λ = 2.4 (from previous research)vi : speed vector present leader leaderi  collider collideri

Sum of distance between each candidate i and leader/follower j,which are within 5vi from present position and if angle betweenvi and vj are within 90° then j is leader, otherwise collider

19Trial (Result)• Both leader and collider are positive?
• There is no difference?
• Setting of “collider” is not good?

• Destination is not significant enough• Difference is slight for each candidate?
• Passengers never change
ticket gate choice within this time step?

estimated t-value
value
βdist

-0.336-1.71

βangle-0.0193

-16.6

βacc

-11.6

-10.3

βdec

4.10

5.71

βleader

1.01

5.80

βcollider 1.19

5.89

• Velocity is dominant• How to set parameters of system model from this result?
• Maybe needs smoothing (e.g. interpolation) for any point
between candidatesFuture Works20• Setting system model and running tracking• Comparison between some conditions• Tracking result• Feeding back to parameter values and model structure• Development of the manner to segment condition of field,
and to detect structural changes• On-line estimation of parameters (e.g. dynamic parameter)• On-line detection of structural changes