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The main problem of these methods is the need for the 
auxilary devices, in addition to the camera, and 
consequently the raise of the complexity and the cost. 
2. PROPOSED METHOD 
This new method includes two steps [3]: First, calculating 
an interpolation function based on the height and the 
horizontal angle of the camera. Second, using this function 
to calculate the distance of the object from the camera. 
In the first step, named the primitive evaluation phase, the 
camera is located in a position with a specified height and 
a horizontal angle. Then from this position, we take a 
picture from some lines with equal distance from each 
other. Then, we provide a table in which the first column is 
the number of pixels counted from each line to the bottom 
edge of the captured picture (as the origin line), and the 
second column is the actual distance of that line from the 
camera position. 
Now, by assigning an interpolation method (e.g. Lagrange 
method) to this table, the related interpolation polynomial 
is calculated [2]: 
f(x) = Sf, I (x) 
J=0 
(1) 
n 
IG x) 
i. (x) ee] 
n 
[IG +) 
J i 
i=0,i=j 
In this formula, x is the distance of the object from the 
camera, and n is the number of considered lines in the 
evaluation environment in the first step. 
In the second step of this method - with the same height 
and horizontal angle of the camera - the number of the 
pixels between the bottom edge of the target in the image 
(the nearest edge of an object in the image to the base of 
the camera) and the bottom edge of the captured image is 
counted and considered as x values in the interpolation 
function. 
The output of this function will be the real distance 
between the target in the image and the camera. 
This method has some advantages in comparison to the 
previous methods: 
a) Using only a single camera for the depth finding. 
b) Having no direct dependency on the camera parameters 
like focal length and etc. 
c) Having uncomplicated calculations. 
d) Requiring no auxiliary devices. 
d) Having a constant response time, because of having a 
fixed amount of calculations; so it will be reliable for 
applications in which the response time is important. 
e) The fault of this method for calculating points’ distance 
situated in evaluation domain is too lower. 
f) This method can be used for both stationary and moving 
targets. 
   
    
   
  
   
   
   
   
   
  
   
   
   
   
   
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
However, This method has some limitations such as: 
a) The dependency on the camera height and horizontal 
angle, so that if both or one of them is changed, there will 
be a need to repeat the first step again. 
b) The impracticality of this method for determining the 
distance of the objects situated out of the evaluation 
environment (which have been done in the first step). 
3. THE RESULT OF EXPERIMENT 
In this experiment, some lines are drawn on a uniform 
surface with 5 cm distance from each other. Then a camera 
is mounted in a position with 45cm height and 30 degree 
horizontal angle. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
X | 34 64 92 144 | 136 | 155 | 173 | 189 | 204 | 218 
Y 5 10 15 20 25 30 35 40 45 50 
X | 232 | 245 257. 1 268: | 2791: 288 | 297 | 304 1 31191 319 
ESS 60 65 70 75 80 85 90 95 100 
  
Tablel. X is the number of pixels between these 
lines and the origin line in the captured image 
and Y is actual distance of lines from camera. 
Based on counting the pixels between the image of these 
lines and the origin line (bottom edge of picture) and 
considering their actual distance, Table No. 1 has been 
produced: 
Using this table and the Lagrange interpolation formula, a 
function for distance measurement is defined. Then the 
distance of some random point is calculated with this 
function as the following table: 
  
  
  
  
  
  
  
Calculated Distance 36.53 60.78 86.18 
Actual Distance 36.5 60.9 85.8 
Fault percent __ 0. 020% | 044% 
  
Table2. Comparison between Actual and 
Calculated Distance. 
As it is realized, this method has more accuracy for 
measuring the distance of points lay on the primitive 
environment domain, but out of this domain it is 
impractical. Considering the properties of this method, it 
can be used in depth finding systems which have a 
specified domain, such as the defended systems that react 
to moving objects in a definite field. 
Using this method has no depth limitation provided that the 
primitive evaluation environment is properly defined. It is 
needless to say that for increasing the accuracy of the 
results, the number of lines in the primitive evaluation 
should be increased. 
4. WHY IS THE LAGRANGE METHOD USED? 
There are two famous interpolation methods: The Lagrange 
and the Divided difference of Newton [2]. But for the 
method proposed above, the Lagrange method has given 
better results. Because: