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BEFORE ORIENTATION AFTER ORIENTATION 
Normalized 
Real To Photograph 
Photograph y 
   
   
T4 T3 
col 
col 
T4 
pee 
Pixel Image 
row row . Epipolar 
Pixel Image 
Figure 4: Relationship between photograph and pixel image, 
both in real and epipolar position 
T»: Projective transformation between original photograph 
and normalized photograph. The detailed procedure is de- 
scribed in Section 3.2. 
Ts: Definition of coordinate system for the pixel image in 
epipolar geometry (normalized image). In order to minimize 
the decrease in resolution (or to optimize the size), first the 
four corners of the pixel image((0,0), (0,N), (N,0), (N,N)) 
are transformed to real photographs and then to normalized 
photo coordinates through 71,75. The following procedure 
defines the normalized image coordinate system. 
1. Determine maximum y coordinate of four corner points 
in both images. This defines row 0 in both normalized 
images. 
2. Determine z and y differences of corner points in both 
photos and compute the maximum distance d,,,, in 
either z or y direction (both photos). This determines 
the size of the epipolar pixel image in photo coordi- 
nates. 
3. Change from photo coordinates to pixel coordinates by 
using the relationship dmaz — resolution pixel image. 
T4: Transformation from normalized image to pixel image in 
order to perform resampling. This is accomplished by using 
T3, T, and 7. 
4. EXPERIMENTAL RESULTS 
The procedure discussed in section 3 to compute normalized 
images, has been implemented and tested with several pairs 
of aerial images. Some of our images are digitized by the 
407 
PhotoScan scanner from Zeiss/Intergraph Corp. and some 
others by the EIKONIX camera (EC850). Here, we present 
the “Munich” model, scanned with the EIKONIX camera 
(see Fig. 5). 
The real images have a resolution of 4096 by 4096, corre- 
sponding to = 60um and 256 gray values. As explained in 
detail in [Chen and Schenk 92], the EIKONIX camera in- 
troduces distortion to the scanned image. We remove this 
distortion during the procedure of computing normalized 
images. Fig. 6 shows the images normalized with respect to 
the object space. Note the curved margins of the normal- 
ized images. This is the effect of the camera distortion (now 
removed!). The transformation (71) discussed in section 3.3 
must be well known in order to assure the correct geometry 
in normalized images. In our example, its accuracy is less 
than a half pixel in 4K resolution. 
The normalized image coordinate system is established by 
transforming the four corner points of the pixel image so 
that the loss of information of the pixel image is minimized. 
By applying the rotation of the base by common omega (2) 
about the X-axis, we optimize the nonquadratic shape of 
normalized images. For resampling, the bilinear interpo- 
lation method is employed, which may introduce blurring 
effects into the normalized images. 
5. CONCLUSIONS 
We describe the procedure for obtaining the normalized im- 
ages from exterior orientation after absolute orientation. We 
also present a direct solution to compute the coefficients of 
the projective transformation, and show a way to compute 
the inverse transformation parameters directly, without re- 
peating the transformation backward. 
The procedure of computing normalized images is success- 
ful and operational. The normalized images, with removed 
distortion caused by the scanning device, are in epipolar ge- 
ometry with respect to the object space. Since scan lines are 
epipolar lines in normalized images, the automatic match- 
ing procedure for conjugate points will be performed on the 
same scan lines. The 3-D surface in object space can be 
reconstructed directly by using matched conjugate points. 
6. ACKNOWLEDGMENTS 
Funding for this research was provided in part by the NASA 
Center for the Commercial Development of Space Compo- 
nent of the Center for Mapping at The Ohio State Univer- 
sity.