Wonkyu Park 
  
In section 2, stereo matching based on epipolarity and scene geometry is described. Section 3 analyzes various 
interpolation schemes. In section 4, the quality of DEMs from our strategy is assessed using truth DEMs in comparison 
with other commercial software packages. 
2 STEREO MATCHING BASED ON EPIPOLARITY AND SCENE GEOMETRY 
2.1 Epipolarity of linear pushbroom sensors 
Generally, epipolar geometry can be established in general stereo images 
and is a very useful clue in processing satellite images to improve 
processing time and accuracy. We have proved that there exists a unique 
epipolar geometry for linear pushbroom satellites that is different from that 
for perspective images (Kim, 1999). We have derived a epipolarity for 
linear pushbroom sensors based on Orun and Natarazan's (1994) camera | 
Reference 
    
   
   
Left Image 
Right Image 
model. 
Coordinate System 
Epipolar geometry can be described as follows: the identical point of one 
point in a left (or right) image lies on a unique curve in a right (or left) Figure 1. Epipolar geometry between 
image. As shown in figure 1, suppose a beam of light is projected from a left stereo images. 
camera center through a point on a left image. Each point lying on the beam 
can be uniquely mapped into a right image as a point. The points form a curve on a right image. The curve is defined as 
an epipolar curve and the equation of the curve derived from Orun and Natarazan's model is shown below (Kim, 1999), 
= A,X, + A» Y, + A3 
"— (AX, * Asy, * Ag)sin Q(x, ) 9 (A;x, * Ay y, * A9) cosQ(x,) 
where (x;, y;) and (x,, y,) are the coordinates of left and right image points, respectively, A;—A9 are parameters that can be 
acquired from the camera model and Q(x,) is a quadratic polynomial of x, (See Kim, 1999 for detail). 
y 
  
Even if the epipolar curve can be defined by a non-linear equation, it can be linearized in short segments (within 10-20 
pixels) for computational efficiency (Kim, 1999). It means that the problem finding conjugate pairs can be converted to 
one-dimensional searching problem. This search space is called local support regions (Lee et al, 2000). Eventually, the 
computation time can be minimized drastically and the accuracy can be increased. 
2.2 Scene geometry 
Because of the difference in incidence angles between a left and right image, Left Image Right Image 
unit areas on the ground are represented by patch with different sizes. In Incident Angle a Incident Angle b 
order to make similarity (or correlation) value calculated from two patches 
meaningful, patches in a left and right image should cover the same area on 
the ground. Taking these into account, patch shapes — patch ratio and patch 
rotation — based on scene geometry are carefully used. 
Let us assume the geometry as shown in figure 2. Let "a" be the incidence 
angle in a left image and "5" be the incidence angle in a right image, then 
patch ratio can be represented as Patchratio = cos(b)/cos(a) (Lee et al., Figure 2. Scene geometry at image 
  
^ eg : 
2000). acquisition time. 
In addition to that, different incidence angles make the orientation of a left and right image different from each other. 
For perspective images, the whole images are rotated to make the orientation of a left and right image identical. This 
process is called as “epipolar resampling”. This process, however, cannot be applied to linear pushbroom images since 
epipolarity for such images are not represented by linear equations (Kim, 1999). For such images, individual patches 
shall be rotated to make the orientation of left and right patches identical (Lee ef al., 2000). Since we know epipolar 
curves in a left and right image, rotating a patch can be done easily by to make parallel to an epipolar curve (or line). If 
the slope of a epipolar line in a left image is L,, the angle gbetween epipolar line and column axis is qarctan( La). The 
rotation of a left patch can be represented by the following affine transformation. 
as 
Y,., =sing*dx+cosgt+dy+Y, 
new 
  
706 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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