International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
matching the laser points of common objects such as wall and
poles by manual operation. An interface that manually handles
these procedures is implemented on the software, thus we can
easily calibrate a number of laser scanners. A detailed description
on registering multiple laser scanners can be found in Zhao and
Shibasaki, 2001.
2.2 Pedestrian Detection
The flow of pedestrians’ tracking is roughly divided into three
parts: 1) Background subtraction, 2) Pedestrian recognition, 3)
Pedestrian tracking. Procedure of how to compute these pro-
cesses in this research is described as follows. A detailed descrip-
tion on following algorithms can be found in Zhao and Shibasaki,
2002.
2.2.1 Background subtraction: In each sampling angle of
range scanning, a histogram is generated using range values from
all range frames being examined. A peak value above a certain
threshold is found out, which tells that an objects is continuously
measured at the identical direction, i.e. the static objects. The
background image is made up of the peak values at all sampling
angles. As a result, by calculating the difference between range
images to the background image, we can get only the moving
objects.
2.2.2 Pedestrian Recognition: — This part consists of the two
processes: 1) clustering process that detects a pedestrian foot. 2)
grouping process that groups two feet to have a pedestrian candi-
date.
Multiple points hit a pedestrians’ foot because of high angle-
resolution (0.5 degree). Therefore, close-by points are firstly
grouped to one typical point using a centroid. We assume a
number of points gathering within 10cm distance as a leg. Next,
grouping process is conducted by grouping two detected feet within
the 30cm distance. In this process, trajectory tracking is firstly
conducted by extending the trajectories that have been extracted
in previous frames, then looking for the seeds of new trajectories
from the foot candidates that are not associated to any existing
trajectories.
2.2.3 Pedestrian Tracking: When a normal pedestrian goes
forward, one of the typical appearances is, at any moment, one
foot swings by pivoting on the other. Two feet interchange their
roles by landing and moving shifts so that the pedestrian steps
forward. According to the ballistic walking model proposed by
Mochon and McMahon, 1980, muscles act only to establish an
initial position and velocity of the feet at the beginning half of
the swing phase, then remain inactive throughout the rest half of
the swing phase.
Here initial position refers to where swing foot and stance foot
meets together. Let v; and v be the speed, a; and ag be the ac-
celeration, p; and pg be the position of left and right foot respec-
tively, where both speed, acceleration and position are restricted
to a horizontal plane, and relative to the two-dimensional global
coordinate system that has been addressed in previous sections.
In the case |v;| > |v], left foot swings forward by pivoting on
right foot. At the beginning half of the swing phase, the left foot
shifts from rear to initial position, and swings from standing still
at an accelerated speed. Here the acceleration |a;| is a function of
1261
Acceleration
à ; |
| | |
2 o- ———— — — - |
| | | , |
| | |
Or dam ss — ———— En. m. a. $— e
{ |
| | |
| beh DELL -»
i | |
| |
| Ï
|
|
Velosity | |
Phase 2
Phase 3
position
Both still Right accelerate Right speed Right decelerate Both still Right keep still Left speed to Right keep still Both still
Lefl keep stil! 1o the Left keep still Left accelerale the maximum Left decelerate
maximum
Figure 2: Pedestrian Walking Model
muscles strength. We define |a,| = f; (muscle strength). During
the rest half of the swing phase, the left foot shifts from initial
to front position, or swings with a negative acceleration from the
maximum speed to standing-still status. Here the negative accel-
eration |a;| comes from factors other than left foot muscles.
We define |a; | — - f; (other forces). During the whole swing phase,
the right foot keeps almost still, so it has |v;| ~ 0 and lar: =
0. In the same way, we can deduce the speed and accelera-
tion parameters when right foot swings forward by pivoting on
left foot, where acceleration |ap| = Jr(Muscle strength) lan] = -
Jr(other forces) at the beginning and end half of swing phase re-
spectively, [vg] = 0 and |agz| ~ 0 during the whole swing phase. In
this research, we simplify the pedestrian model by assuming that
the acceleration and deceleration on both feet from either muscle
strength or other forces (|a; ;4|) are equal and constant during each
swing phase, and they have only smooth changes as the pedes-
trian steps forward. Figure 2 shows an example of the simplified
pedestrian model.
As has been described in previous section, pedestrian model con-
sists of three kinds of state parameters, position (pr), speed
(vse), and acceleration (ay). Position and speed vectors of each
pedestrian change continuously shown in figure 2, while acceler-
ation parameters change by swing phase in a discontinuous way.
A discrete Kalman filter is designed in this research by dividing
the state parameters into two vectors as follows.
Skn = Qs, 1n + Vus n + Ww (1)
Where, sy, consists of the positions and speed vectors of both
feet of pedestrian n at range frame K, while uy, consists of the
acceleration parameters. c is the state estimation error.
Ps
PL
Vi
xn
Vr ( 2)
PR.
Pry,
VR kn
VR o
