CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation 
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A second function depicts a dense traffic situation at the same 
distance. The possibility for zero velocity shall be 0.5 (since 
jam cues more likely move slowly forward), while speeds of 
10-30 shall be most likely and speeds larger than 50 simply 
impossible. By linear interpolation between the support points, 
this results in the functions depicted in Figure 3. 
Assuming that the possibilities evolve linearly over the 
dimension of density, we can derive 2D functions given a 
certain distance. The function for a position right in front of an 
intersection is shown in Figure 4. 
By linear interpolation along the third axis d, we receive a cubic 
membership function (Figure 5). 
u(v,D.d) 
Velocity v 
Figure 5: 3D membership function with slices at v=10, v=70, 
D=80, d=0 and d= 100 
and its standard deviation: 
i 
(2) 
By applying a minimum threshold on the summed up weights 
of a section, we meet the circumstance that there are only false 
alarms in a free flow section. If the sum of the weights of a 
section is below the threshold, all detections of this section are 
removed. 
Finally, objects with a velocity v, < v — 2 • cr are regarded as 
outliers and eliminated. Then, a refined and unweighted average 
velocity is determined from the remaining detections. The 
resulting distribution is unbiased under the assumption that all 
false alarms have been eliminated. 
Figure 6: Velocity distribution and cutting-off criteria (red) per 
road section for each lane 
4. RESULTS 
3.3.2 Evaluation of velocity information 
Before the evaluation of the speed, the road is split into sections 
of length 50m and, near to intersections, of only 20m (sees 
Figure 6). Every detected object is assigned to one section and 
contributes to the section density. After the determination of the 
section density, the possibility /u A is derived from the above 
described 3D membership function for each object. 
The fuzzy possibility serves a weight in the calculation of a 
weighted average velocity for each section: 
Xva<( v i>A>4) 
" = 2>,(v„a,v) <0 
/ 
The concept has been tested on two different sets of image data 
so far. The results are shown in Figure 7. One image shows a 
highway section with free flowing traffic. Here, the detection 
was carried out by a blob detection algorithm as explained in 
(Lenhart et al.). In this case, the refinement was able to 
eliminate all false alarms and redundant objects that arose from 
the automatic detection. 
The second image shows a more complex scene with an urban 
highway section and an exit leading to an intersection with a 
traffic light. In this case, the detection has been carried out 
manually, however, considering a reasonable detection 
characteristic and quality. In this example, 12 objects have been 
correctly removed, leaving only one false alarm that could not 
be eliminated due to faulty tracking. 
In both examples, the correctness of the detection could be 
significantly increased by approximately 30%.