IMPLEMENTATION OF A NEW METHOD FOR MAKING RAPID AND RELIABLE 
EPIPOLAR IMAGES WITHOUT USING CONTROL POINTS 
E.G. Parmehr, F. Karimi Nejad 
Department of Geomatics and Surveying Engineering, Faculty of Engineering. 
University of Tehran, Tehran, P.O. Box 11365-4563, Iran. 
parmehr@ut.ac.ir , fatemeh_ karımi nejad@yahoo.com 
Commission V, WG V/5 
KEY WORDS: Geometric, Radiometric, Digital, Non-metric, Camera, Method, 3D, Measurement 
ABSTRACT 
Epipolarization is the most important constraint used in automatic dense matching for increasing speed and reliability of matching 
method. There were many methods for making epipolar images. Most of these methods, which need camera calibration and camera 
specifications, have been explained in the literature. But in our method we do not need camera specifications. We have calculated 
relative orientation elements. We have changed images according to these elements, which mean rotation, translation and scale 
changing of images. We have changed geometry of images, but images are consisted of geometry and radiometry properties. Then 
we should change radiometric properties so that new images will be created. For these reasons we resample each image. New images 
are epipolar. We have tested this method on stereo mouse and tooth images taken with a 3.2 Mega pixel digital camera. The main 
advantage of this method is its independency to camera characteristics in any exposure position. Preparing control points is one of the 
hard stages in some fields such as medical applications. Therefore this stage will be eliminated. Stereoscopic viewing, Relative 
measurement and three-dimensional model are the main products easily created by this method. One of the most important 
applications is in medical applications. We do not need control points and without making any problem for the patient we measure. 
This method is possible even with a non-metric digital camera. This method is fast and accurate therefore it can be used in animation 
and many other applications. We have solved interior orientation parameters before we have started our procedure. 
1. INTRODUCTION 
For increasing the speed of matching process, images should be 
epipolar which means corresponding objects are elongated of 
each other. After epipolarity of images, each area is reduced to a 
linear area. Therefore mismatching probability is reduced and 
computation is reliable. Hardware, based or software based 
methods exist for generating epipolar images. In hardware 
based method, CCD cameras should be installed in a stable and 
elongated position. The vertical movement is zero. This 
installation reduces our movement ability. Software based 
method is an image based or object based method. In both 
methods, control points are required. In some instances such as 
relative calculations or 3D reconstruction without control 
points, measuring is possible. Production of control points in 
medical cases is a difficult task for the patient. 
  
   
  
Epipolar Plane 
pipolar li 
  
  
  
  
  
  
  
  
  
  
  
  
Epipolar lines Epipolar Images 
Figurcl. Geometry and radiometry correction 
Then we decided to design an epipolarity method 
without control points. If a constraint is exerted on images, 
which means two corresponding image points with two 
projective centers of images have to construct a plane which 
intersects two image planes in two lines, then these lines would 
be epipolar lines. By rotating each image around perpendicular 
lines of each image plane, two lines are elongated with each 
other. After these processes, two images are corrected according 
to the geometry, and then radiometric correction is done. 
Therefore, corresponding lines are elongated with each other. 
2. CORRECTIONS 
In our method, geometric and radiometric corrections should be 
done for generation epipolar images. In the geometric 
correction, the below process is done; 
1- interior orientation 
2- relative orientation or making epipolar plane 
Conformal transformation is used for interior orientation. For 
producing epipolar plane constraint, four points (two 
corresponding image points and two projective center points) 
should be in the same coordinate system. Equations 1, 2, and 3 
express the relation between the original image and the epipolar 
image. 
bx by bz 
xem (D 
x" y z" 
  
    
   
  
  
   
    
  
  
  
  
      
   
  
  
  
  
  
  
  
  
  
  
  
  
   
    
   
   
   
   
   
   
    
   
    
    
   
     
    
    
   
   
    
Inte! 
Whe 
xl,y 
bx, t 
R, R 
Only 
solv 
imag 
radi 
To 
"Oly 
from 
of r 
imag 
Fig 
and 
  
Rest 
In th 
be c 
Ther 
two 
dista 
betw 
time