The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
Figure 2. Mitigation of occlusion by using 
multiple laser range scanners 
2.2 People Tracking 
2.2.1 Calibration 
In order to integrate each laser scanner's local coordinate 
system to common one, Helmert transformation is conducted 
for each coordinate system. Since each laser scanner is installed 
that scans at same horizontal plane, the overlapping 
measurement data by other sensors corresponds to same shapes. 
By referring this information, the transformation of shift and 
rotation is conducted manually by integrating the redundant 
common shapes’ features. 
2.2.2 Background Subtraction 
Obtained range data contains both moving objects (e.g. 
pedestrians' legs) and static objects (e.g. walls, poles, etc.). 
When a certain amount of frames are stored (e.g. 512 frames), a 
histogram of the range value at each sampling angle is 
calculated. Since the mode value in the histogram can be 
regarded as static objects, the range standing for the mode value 
is registered as a background object. By iterating this process 
for all sampling angles, a background image is obtained. In 
order to extract only moving objects, range data near from 
background value (e.g. within 30cm) are subtracted. 
where p(x) = probability density function 
x = feature vector of the obtained trajectories 
K( ) = kernel function 
n = the number of data 
h = bandwidth of the kernel function 
d = dimension of the feature vector 
In this paper, the feature vector of the probability density is 
defined as (x, y, angle). This means the calculated probability 
density corresponds to the traffic volume at the site (x, y) and 
the walking angle. Therefore, the higher value of p{x) 
corresponds to higher populated site in the flow directions. To 
learn the probability density p(x), we calculate equation (1) by 
using the trajectories’ vertices (x, y, angle). As the kernel 
function, Gaussian kernel is adopted as follows. 
(2) 
where x = feature vector of the obtained trajectories 
d = dimension of the feature vector 
2.3.2 Extraction of Congested Area 
In order to extract prominently congested areas, the target area 
is divided as same interval 2-dimentional grid. Then, we define 
an index of congestion at each cell as follows. 
C = -^x 2 +y 2 Jp(x,y,a)da (3) 
2.2.3 Tracking 
People tracking is achieved by conducting spatio-temporal 
clustering. Firstly, By regarding a certain laser point within 
moving objects as the first centre point, nearby points from the 
centre point are searched (e.g. within 15cm). Similarly, by 
regarding the already searched point as the next centre point, 
same process is iterated until nearby points are not found. 
Additionally, in a previous frame, nearby points from current 
searched points are searched as well. If clustered points are 
found in a previous frame, previous cluster's ID is inherited to 
the current cluster. Otherwise, new ID is registered to the new 
cluster. By extending same cluster’s centroid from previous 
frames, the time-series people positions are obtained. 
2.3 Crowds Flow Detection 
2.3.1 Probability Density Distribution of Crowds Flow 
Based on the trajectories data obtained by above mentioned 
processes, several properties of crowds flow characteristics are 
extracted, which are main stream paths, the average and 
variance of the vectors, traffic density, velocity variance, and 
those spatial distributions. Particularly, we describe the crowds 
flow characteristics as a probability density distribution by 
using kernel density estimation method (KDE). The KDE is 
defined as follows. 
(1) 
where C = an index of congestion 
x, y = position of trajectories’ vectors 
a = angle of trajectories’ vectors 
p(x,y,a) = probability density mentioned above 
x,y = average vector calculated as follows 
jcos a- p(x, y, a) da 
jp(x,y,a)da 
p(x,y,a)da 
\p{x,y,a)da 
(4) 
(5) 
Firstly, an average vector (x,y) of the feature vector within 
each grid cell is calculated by equation (4, 5). The length of the 
average vector stands for a kind of variance of angles. 
Therefore, in the case that the length shows near zero, the 
directional vectors include a variety of directions, so that it can 
be assumed as congested area. Contrary, in the case that the 
length shows near one, the directional vectors have almost same 
directions, i.e. the crowds flow can be regarded as not 
congested. Finally, we define an index of congestion as a 
product of a traffic volume and negative value of length of the 
average vector as shown equation (3). 
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