e of the vehicle, local 
ur during this selection 
1 be affected by those 
be erroneous. For this 
le, many more than one 
' instantaneous velocity 
n by averaging the 
ole selected points, the 
hicle is found. For the 
points are selected from 
7 ], ..., n) represent the 
| of n points at time 
neous velocity vectors, 
ctor of the vehicle by: 
(12) 
vector of the vehicle at 
locity vector of i" point 
he selected and tracked 
some of the vi vectors 
erroneous. So, before 
viv of the vehicle, the 
1. Then the value of n 
nts decreases. For the 
idard deviation of the n 
luation: 
(13) 
splacement vectors or 
tors computed in video 
1sformed to the object 
bject space. For this 
ning two points within 
| the road and aligned 
sured precisely. In this 
ines along the road by 
le measurement tape, 
RESULTS 
real-time estimation of 
incalibrated monocular 
) extract 3D geometric 
r to solve the speed 
onstraints are required 
ese constraints and the 
performed with those 
at the imaged scene is 
uired images must be 
san easily be rectified. 
: of 30 fps and with an 
[he pixel size which 
camera is 9 microns. 
. We capture images in 
'cond), meaning that a 
nds after the previous 
    
  
frame had been obtained. In order to solve the real time speed 
estimation problem, the authors have written a software system 
in C++ programming language. This software system has been 
used for all of the computations and test applications. Our 
software consists of two steps which contains offline and online 
operations, for details refer to (Dogan, et. al, 2010). The 
operations of step I are performed offline at the beginning of the 
speed estimation problem and it contains rectification 
procedures. After step I has been completed, the real time 
procedures begin. We have used OpenCV API functions to 
perform the capturing images from camera and eliminate 
undesired background changes operations. The rest of the 
operations are performed with our own codes written with 
Visual Studio C++ 2010. The total time of the operations takes 
about 30 milliseconds for our real time applications with a 
laptop computer (Intel Core i7 2.6 Ghz CPU, 8 GB RAM). 
Figure 2 shows a general view of our software. 
  
Figure 2. Estimation of speed. 
Accuracy of the estimated speed of our system is +1-2 km/h. 
We tested the system by comparing the estimated speeds to GPS 
measured speeds which measures speeds with very high 
accuracy about 0.1 knot (0.05 m/s) or 0.018 km/h (Keskin and 
Say, 2006), (Al-Gaadi, 2005). 
5. CONCLUSIONS 
In this paper, we have explained the real time speed estimation 
problem and its solution by using monocular video images of 
the vehicle. The accuracy of the estimated speed had been 
obtained and is approximately +1- 2 km/h. The sparse optical 
  
flow technique is a very effective technique for the speed 
estimation of the vehicles. 
In our earlier study, we have used our technique for the speed 
estimation of the vehicles from side view images of the road 
scene (Dogan, et. al, 2010). In this current paper, we have 
modified some steps of our earlier system and used a camera 
tilted downward a bridge and so we have acquired the top view 
images of the road scene. As seen from the results related to the 
test experiments, both of our methods give the same accuracy. 
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