RESAMPLING DIGITAL IMAGERY TO EPIPOLAR GEOMETRY 
Woosug Cho 
Toni Schenk 
Department of Geodetic Science and Surveying 
The Ohio State University, Columbus, Ohio 43210-1247 
USA 
Mustafa Madani 
Intergraph Corporation, Huntsville, Alabama 
USA 
Commission III 
ABSTRACT 
Most algorithms in computer vision and digital photogrammetry assume that digital stereo pairs are registered in epipolar 
geometry (normalized images) in order to confine the search of conjugate features along the same scan lines. In this paper we 
describe the procedure of computing normalized images of aerial photographs with respect to the object space. Based on the 
exterior orientation of the stereo pair the rotation matrix for the normalized images is computed. The focal length of the new 
images may be determined according to different criteria. We show the case of minimizing the decrease in resolution. During 
the same process systematic errors of the scanning device can be considered. Several examples demonstrate the feasibility of 
our approach. 
KEY WORDS: Epipolar geometry, Resampling, Normalized image. 
1. INTRODUCTION 
Most algorithms in computer vision and digital photogram- 
metry are based on the assumption that digital stereo pair 
is registered in epipolar geometry. That is, the scan lines 
of stereo pairs are epipolar lines. This condition is satisfied 
when the two camera axes of a stereo vision system are par- 
allel to each other and perpendicular to the camera base. 
In conventional aerial photogrammetry, imagery is obtained 
directly by scanners, such as Landsat or SPOT, or indirectly 
by digitizing aerial photographs. Thus an aerial stereo pair 
is not likely to be in epipolar geometry since the attitude of 
the camera at the instant of exposure is different at every 
exposure station. 
[Kreiling 1976] described a method for recovering the epipo- 
lar geometry from the parameters of an independent relative 
orientation. The epipolar geometry is only recovered with 
respect to the model space. In many instances it is desir- 
able to establish epipolar geometry with respect to object 
space. The procedure to obtain resampled epipolar images 
with exterior orientation elements after absolute orientation 
was developed by [Schenk 90]. In this paper we call the 
resampled epipolar image reconstructed with respect to ob- 
ject space the normalized image. The original photograph 
obtained at the instant of exposure is referred to as the real 
image. The image which is parallel to the XY-plane of the 
object space system is called the true vertical image. 
In this paper we describe the procedure to compute nor- 
malized images of aerial images with respect to the object 
space and the method to minimize the decrease in resolution. 
By considering systematic errors of the scanning device, we 
show that the normalized image is free of geometric distor- 
tion of the scanning device. The next section provides some 
background information followed by a detailed description 
of how to determine normalized images. 
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2. EPIPOLAR GEOMETRY 
Fig. 1 shows a stereo pair in epipolar geometry with C’, C" 
the projection centers. The epipolar plane is defined by the 
two projection centers and object point P. The epipolar 
lines e’,e” are the intersection of the epipolar plane with 
the image planes. The epipoles are the centers of bundles of 
epipolar lines which result from intersecting the photographs 
with all possible epipolar planes. 
  
Figure 1: Epipolar geometry 
The conjugate epipolar lines in Fig. 1 are parallel and iden- 
tical to scan lines. The epipoles are in infinity because of 
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