and driver assistance systems or intelligent vehicle systems 
(Guo, et al., 2005). 
Traffic surveillance systems generally involve those 
applications which require global information on the general 
traffic situation of the roadways rather than individual vehicles 
travelling on the roads. For example, estimation of the speed of 
a traffic flow of a roadway at different times and dates (Dailey, 
et al, 2000), (Schoepflin and Dailey, 2003) belongs to this 
group, as well as determination of the traffic density, timing of 
the traffic lights, signalization works, etc. 
2. RECTIFICATION OF FRAMES 
Due to the nature of the images’ perspective effects, certain 
geometric properties such as lengths, angels and area ratios are 
distorted. These distortion effects must be corrected. If the 
image plane is in the ideal case, then any parallel line in the 
vertical planes must remain parallel in the image plane. 
Similarly, the parallel lines on the horizontal plane must also 
remain parallel in the image plane. If the image plane is far 
away from the ideal situation, these parallel lines will not be 
parallel in the image plane. This means that those parallel lines 
in the object space intersect to each other on the image plane. 
Intersection points of the parallel lines are known as vanishing 
points. By using vanishing points and their corresponding 
vanishing planes at the horizontal and vertical directions, the 
images can be rectified by using vanishing points geometry 
(Heuvel, 2000), (Simond and Rives, 2003), (Cipolla, et al., 
1999), (Grammatikopoulos, et al., 2002) so that they represent 
the ideal case. For this purpose, we used two methods. The first 
one is finding the lines manually and the second one is finding 
the vanishing lines automatically by using the Hough 
transformation. After Hough transformation, we compute the 
intersection points (vanishing points) of the selected lines in the 
image coordinate system. By using those vanishing points we 
rectify the image by making the vanishing lines parallel to each 
other. Figure 1 shows original and rectified frames. 
  
Figure 1. The original (left) and the rectified (right) frame. 
When the rectification parameters are found for the first time, 
they can be used until the camera changes its position. Thus, at 
the beginning of the speed estimation application, at first the 
rectification parameters can be found for the first time and these 
parameters can be used as long as the camera stays stable. For 
the speed estimation problem, after rectification parameters 
have been found, it is not necessary to rectify the whole image. 
Instead, only the selected and tracked point coordinates may be 
rectified for speed improvement of the real time computational 
cost. But however, we give the wholly rectified image on the 
right image of the Figure 1, for visual evaluation of the reader. 
    
3. SPEED ESTIMATION 
At the first step, enough number of points from the vehicle 
should be selected, and these points should be tracked at least 
on two successive video frames. 
3.1 Automatic Selection of Points to be Tracked 
In order to track moving objects with video images, points to be 
tracked which belong to the object on the successive video 
frames, should be selected automatically. It is well known that 
good features to be tracked are corner points which have large 
spatial gradients in two orthogonal directions. Since the corner 
points cannot be on an edge (except endpoints), aperture 
problem does not occur. One of the most frequently used 
definitions of a corner point is given in (Harris and Stephens, 
1988). This definition defines a corner point by a matrix which 
is expressed by second order derivatives. These derivatives are 
partial derivatives of pixel intensities on an image and are 2x, 
02y and Ox0y. By computing second order derivatives of pixels 
of an image, a new image can be formed. This new image is 
called “Hessian image”. The name “Hessian” arises from the 
Hessian matrix that is computed around a point (Dogan, et. al, 
2010). The Hessian matrix in 2D space is defined by: 
2 A 
2 
je (1) 
2 20 
AU ru. 
OyOx oy 
Shi and Tomasi (1994), suggest that a reasonable criterion for 
feature selection is for the minimum eigenvalue of the spatial 
gradient matrix to be no less than some predefined threshold. 
This ensures that the matrix is well conditioned and above the 
noise level of the image so that its inverse does not 
unreasonably amplify possible noise in a certain critical 
directions. 
When it is desired to extract precise geometric information from 
the images, the corner points should be found within a sub-pixel 
accuracy. For this purpose, the all candidate pixels around the 
corner point can be used. By using the smallest eigenvalues at 
those points, a parabola can be fitted to represent the spatial 
location of the corner point. The coordinates of the maximum of 
the parabola is assumed to be the best location for being a 
corner. Thus the computed coordinates are obtained in subpixel 
precision (Dogan, et. al, 2010). 
In our system, as soon as the camera begins for image 
acquisition, points are selected continuously in real time from 
the frame images. On the first frame, points are selected and on 
the next frames those points are tracked and instantaneous 
velocity vectors of those points are computed. 
3.2 Tracking of Selected Points 
For speed estimation, correspondence of each selected point on 
the first frame on which the vehicle appears for the first time, 
must be found on the next (successive) frame. In the ideal case, 
correspondence of a selected point must be the same point on 
the next frame. In order to find the corresponding point, there is 
no prior information other than the point itself. If we assume 
  
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