International Archives of the
f al. i.
UY kn (3)
AR.
X A
Urn =
CR hs
Transition matrix relates positions and speed vectors at previ-
ous time step to those of current one, while V relates acceleration
values to the change in positions and speed vectors. They are
defined as follows, where A: is the time interval between range
frames. In this research, At = 30ms.
|i 0 «^0 d oto 9
0r 9 0-070 9
00.1 940 «0 "0
600 60 1 00 0 O9 .
D,, = 4
t ) 49 gp TAE 0 (4)
0 0 0 6 01 0 A
0.0. 0. 0. A ud aiU
0 0.0. 0.0.0... 85]
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0 0.5Ar° 0 0
At 0 0 0
0 At 0 0 Y
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0 0 0 0.5A£
0 0 AL 0
0 0 0 At
In addition, the state vector uy, is predicted by identifying the
swing phase. The discrete Kalman filter updates the state vector
of si» based on the measurements as follows.
Men = Hsyn se (6)
Where my, denotes the measurements of pedestrian n at time
step k. H relate the state vector sy, to measurements Men. €
represents the measurement error.
Pr bn
PL ka (7)
PR, kan
DRykn
Men =
H = (8)
Based on these algorithms, the velocities of each pedestrians n at
range frame k are firstly predicted by measurement my, a. Next,
a search area is defined by using velocity and direction. If foot
candidates of the current frame are found inside the search area,
the nearest ones are selected to compose the updated my, .Other-
wise, missing counter starts. If the missing counter is larger than
a given threshold, e.g. 40 frames ( = 2 sec ), then the tracing of
the trajectory stops. Otherwise, the predicted my , is employed as
the updated one to update the state vector Sia and Kalman gain.
The process continues until all the trajectories are traced.
Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
(b) Laser Points
(a) Video Image
Figure 3: A snapshot of video image and laser points
2.3 Efficiency and Accuracy Assessment
Efficiency and Accuracy of the system is assessed to answer the
following questions, what percentage of the pedestrians are mea-
sured by the sensor system (measurement ratio), what percent-
age of the pedestrians are successfully tracked using the track-
ing algorithm (success ratio), what is their relationship with the
change of pedestrians’ density. Laser points are manually over-
lapped with the video images that are taken from the ceiling. A
comparison is conducted manually to find whether pedestrians on
video images have corresponding laser points on their feet. Fig-
ure 3 shows a snapshot of video and laser points. The methods of
overlapping and accuracy assessment are stated below.
2.3.1 Overlapping: In order to overlap a video and laser
points, we need two requirements: 1) geometric registration, 2)
temporal registration. In geometric registration, both images are
required to be registered with each other so that they can have the
same resolution and same coordinate system. In temporal reg-
istration, time-synchronization is correspondingly required. By
satisfying both requirements, we can overlap these images.
Firstly, geometric correction of video image is conducted to sat-
isfy the geometric requirements. This correction mainly removes
a lens distortion shown as figure 3(a). Corner points of 60cm by
60cm tiles are used as reference points for geometric correction.
Secondly, we set an "event" which can be recognized by both
video and laser range image to satisfy the temporal requirement.
[n this event, we make a pump and dump a cardboard captured
shown in figure3(b) and by using these event the laser time and
video time are synchronized.
2.3.2 Accuracy Assessment: We assume that the accuracy is
dependent on pedestrians’ density y and the number of sensors.
Therefore. we set nine conditions as follows and conduct the ac-
curacy assessment on each condition. The conditions are based
on the number of sensors; three sensors, four sensors and six sen-
sors; and on pedestrians’ density; low-density, mid-density and
high-density listed below.
e Low-density: à = 0.1 [persons/m?].
e Mid-density: jj — 0.5 [persons/m" ].
e High-density: jj — 0.8 [persons/m' ].
Where, ji represents an average of pedestrian density 4.
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