Then we have to handle two problems remained. Firstly,
although system model deals with three-dimensional ellipsoid,
pedestrian behavior model deals with behavior on two-
dimension plane. Therefore we assume that ellipsoid is upright
on the floor and set the coordinates parallel to the floor (ground
coordinates). At the same time, we calculate the angle between
camera coordinates and the ground coordinates. Secondly,
behavior model assumes that destinations of every pedestrian
are known in advance. However, in case of on-line tracking, we
cannot know their destination in advance. Therefore, we omit
the term about destination in this model, the term (b) in
equation (4). After this step, all we have to do is to set initial
position, shape and velocity for all people to be tracked.
4.4 Observation Model
We also model an observation model for filtering step.
Observation model is a probability distribution of z, on x,
modeled by tracking method. We make both color and range
model stochastically. The model is in a form of a product of
color observation model and range observation model as
follows:
p(zix,) = Pcotor(Zi|X,) Prange(Zi|X,) (6)
4.4.1 Color Observation Model: Peolor(Z4X,) is a probability
distribution according to the similarity between color
histograms of pixels in the ellipsoid at time 7-1 and 7. We use
Bhattacharyya coefficient B as follows, a coefficient correlation
of color histogram as used in existing works (e.g. Wu and
Nevatia (2007) and Ali and Dailey (2009)).
B = 24.4, Lun (7)
where m = pixel value
d; = normalized histogram at time t
d, ,, — relative frequency of pixel value m in histogram d
We calculate this for each color r, 2 and b, and define
Peolor(Z{|X;) as a product of them.
4.4. Range Observation Model: Pans X) is a
probability distribution according to the similarity between
shape of predicted ellipsoid and observed object in actuality.
For pixel P included in the ellipse made by projection of
predicted ellipsoid to the obtained image, let d(P) the distance
from observed coordinates P(X, Y, Z) to the center of ellipsoid
O. Let P' the point that half line from O to P intersects the
ellipsoid, and d(P) the distance from O to P'. Here, we
describe P,ange(Z;[X;) as follows:
Prange (2, | X,) =1 [x(ao- «ey | (8)
if | d(P)-d(P)|>1 , then| d(P)-d(P)|=1
where / = number of pixel P in total
5. APPLICATION
5.1 Observation Conditions and Parameter Settings
We apply the proposed method to the data acquired at the ticket
gate of Tama-Plaza station, the railway station in the popular
residential area about 20km west from central Tokyo. We took
the data in the morning, the commuter rush hour and confirmed
that people behavior was under the complex situations. The
stereo video camera used in this observation is consisted of two
cameras (SONY-DFW, 1.2 million pixels), set about one meter
spaced, calibrated in advance. Frame rate is set at. 7.5
[frames/sec] from the constraints of the stereo synchronization
process. In this condition, the video was taken from a point
about 10m height, looking down obliquely (figure 5).
Platform #2
Platform #1 :
North Exit South Exit
os J
Figure 5. Example of obtained image
In the proposed method, we need to set some initial values and
parameters in advance. We set the number of particles as N=500,
For the state vector, we get the initial position of people
manually and set as the position (x, y, z). The size of the
ellipsoid is set to w=0.4[m], h=1.6[m] and d-0.3[m]
considering the size of people. We also set the initial velocity of
each person manually. For the variance of system model, we set
«= (10, 5, 10, 0.05, 005, 0.05) [em] after some trials. Finally
we calculate the angle between camera and ground coordinate
as o=0.62[rad].
5.2 Results and Discussions
We apply this method for 30 seconds (226 frames). During this
period 51 people with 3,384 frames in total are to be tracked.
We make a performance verification of the proposed method by
comparison of the position of the person obtained from tracking
result with manually read from the image. As a result, we
succeeded in 2,626 frames (78%) in total and 40 people of 44
are correctly tracked to the ticket gate (table 6).
Table 6. Tracking result with comparison by system model
Success # of
Svst del # of success | Success person
ten mode frame rate tracked to the
ticket gate
Proposed 2626 78% 40 / 44
Noise only 1808 53% 35/44
With destination 2238 66% 28/44 ps
Figure 7 shows a part of the results. Points in the image show
the center of obtained ellipsoid by tracking. The numbers
associated with points on the image is a unique number given to
each ellipsoid, which is corresponding to the tracked person.
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