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In: Paparoditis N., Pierrot-Deseiiligny ML Mallet CL Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
opposite direction and only those links that appear in both ways 
are kept. 
The global smoothness constraint of optical flow allows to link 
object regions without an explicit matching of their unstable 
appearance. However the drawback of the proposed method is 
its dependency on a good and complete object detection result 
in each picture. To overcome situations when a single person 
could not be detected in one image of the sequence or when a 
link could not be established, images are processed additionally 
being two frames apart. These links are used to establish 
missing connections between the three consecutive images 
while the person's location in the bridged image is interpolated. 
The introduced procedure is applied to the entire sequence. The 
output of the tracking algorithm consists of trajectories which 
reflect the motion of individuals through the image sequence. 
They are used for further processing in the second module of 
the proposed system. 
2.3 Interpretation of trajectories of people 
The derived trajectories of moving people within the observed 
scene are used to initialize the second module analyzing the 
trajectories with regard to motion patterns. The trajectory 
interpretation system aims at bridging the gap between low 
level representation of single trajectories and high level people 
behavior analysis from image sequences. To achieve this goal, 
microscopic motion parameters of single trajectories as well as 
mesoscopic motion parameters of several trajectories have to be 
extracted. A graph is constructed containing microscopic and 
mesoscopic motion parameters to represent a neighborhood of 
trajectories. Additionally. G1S data and macroscopic parameters 
are utilized to recognize predefined scenarios. A hierarchical 
modeling of scenarios is feasible, as the interpretation of 
trajectories is based on the analysis of simple motion 
parameters of one or more trajectories. In the following, the 
module for trajectory analysis is presented in more detail. 
Microscopic and mesoscopic parameters: Microscopic 
motion parameters concern the motion characteristics of one 
single moving person. Hence, the most important microscopic 
motion parameters to exploit are speed and motion direction. In 
addition, further parameters can be calculated from these two 
basic microscopic motion parameters. Figure 2 shows a single 
trajectory depicting some features which are used to calculate 
the following parameters. 
The average speed v of a moving object is calculated using the 
relative distance d re i of a trajectory which is given as the 
Euclidian distance between the points x_l and x_n. Using this 
approach, v is the speed for the effectively covered distance for 
this object within the observed time frame, disregarding any 
multi-directional movements. In contrast, the absolute distance 
d abs is derived from adding the segments dj of one trajectory 
over all time steps i. The acceleration a of a moving object is 
computed by differencing the speeds of two consecutive line 
segments. A further microscopic parameter is straightness, 
calculated from the two different distances mentioned before by 
s = d rc /d ahs . As d abs always receives a bigger number than d reh s 
takes a value near 1 when the trajectory is very straight and a 
much smaller value towards 0 when the trajectory is very 
twisting or even self-overlapping. 
Motion direction is the second basic microscopic motion 
parameter: the direction z(x_i) at a point x_i is the direction of 
the tangent at this point defined by the points xji-l) and 
xji+l). The motion direction is specified counterclockwise 
with reference to a horizontal line. Similar to straightness, the 
standard deviation o z of the motion directions indicates the 
degree of the twists and turnarounds within one trajectory. 
x 3 
x 4 
x 6 
x_2 fry 
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x_l • 
x 5 
'Ll 
Figure 2. Features of a trajectory to calculate microscopic 
motion parameters: points xj and line segments d_i (black), 
direction at point with reference to horizontal line z(x_i) (blue). 
Mesoscopic motion parameters represent the interaction 
between several individuals. Therefore, it is necessary to 
evaluate the proximity of a trajectory with respect to the 
number of neighboring trajectories, their motion directions and 
potential interferences. Figure 3 shows an example of two 
neighboring trajectories. The detection of neighbors is 
accomplished by scanning the surrounding area of existing 
trajectory points at every time step i. For each detected 
neighbor, the offset o_i of each pair of points x i und y_i is 
stored. Comparing length and direction of these offsets during 
the entire image sequence, robust information can be derived if 
neighbors come closer or even touch each other. In addition, the 
motion direction at each point is inspected to detect 
intersections of trajectories. 
Figure 3. Two neighboring trajectories with offsets o_i (green) 
between pairs of points x_i and y_i (black). 
Scenario modeling and scenario recognition: Scenarios are 
modeled hierarchically to recognize complex motion patterns 
based on the extraction of simple microscopic and mesoscopic 
motion parameters, similar to the event detection systems 
mentioned in Section 1. Hence, predefined scenarios consist of 
trajectories and local G1S information in the lower level which 
represent simple image features by coordinates (Figure 4). 
Microscopic motion parameters follow in the next level of 
motion parameters which give a more abstract representation of 
the trajectories. Additionally, mesoscopic motion parameters 
are embedded in this level because they are closely linked to 
microscopic motion parameters and directly derived from the 
trajectories. In the subsequent level, simple events are modeled 
resulting from beforehand defined parameters. These events 
concern single trajectories or try to model information from 
mesoscopic motion parameters. In the highest level of the 
hierarchical scenario modeling, simple events are combined 
with GIS data to complex scenarios representing complex 
motion patterns within the observed scene. 
The goal of the proposed system is to recognize scenarios 
which are predefined as described before. Based on the tracking 
in the first module of the system, motion parameters are 
extracted. These parameters are evaluated to compute 
probabilities of simple occurring events. The combination of 
several simple events leads to the recognition of a predefined 
scenario.