r12 (Ax, Ayo) Image ls _ ~ Image 2 
   
  
r42 (Axo, Ayo)M\~ x Ok t12(Axo, Ayl 
  
  
  
  
  
  
   
^ 
Two-Dimensional 
Correlation Function 
r42 (Ax, Ay) 
  
Y- Alignment Error Signal X- Alignment Error Signal 
Figure 1 Image Matching Characteristics of the 
Two-Dimensional Correlation Function 
other moved in the x or y directions, the one-dimen- 
sional curves shown at the top right and left will be 
generated at the output of a correlator. For image 
alignment purposes, such a sequence of trial motions 
can be carried out until motion in any direction gives 
a decreasing correlation measurement. When this 
point is reached, the two images are superimposed 
(aligned, matched) by definition. 
A more convenient set of alignment signals to 
work with are shown in the drawing to the right and 
left below the correlation function. These correlation 
measurements, labeled the x and y alignment error 
signals, can be generated directly from the correlation 
measurements. They have the desired functional char- 
acteristics of an error feedback signal—zero when the 
images are aligned, and positive or negative depend- 
ing on the direction of misalignment. Signals of this 
type are required for automatic image matching 
systems. 
We will now examine these error signals in more 
detail. Consider the image matching conditions shown 
in Figure 2. Here the image matching process is re- 
lated to the aperture of the correlator. A sequence of 
superimposed images is shown beginning with the 
perfectly matched condition. The curves above and 
below the image pair show the general shape of the x 
and y alignment correlation error signals. In (a) the X 
and Y error signals are zero since the images are per- 
fectly matched. In (b) the upper curve shows no Y 
error, while that below the measurement indicates that 
image 1 should be moved in the negative X direction 
to achieve perfect alignment. The image condition 
shown in (c) is similar to (b) except that now there is 
a Y error signal indicating Y misalignment. The draw- 
ings of (d) show the output measurements for both X 
and Y misalignment. A significant characteristic of 
the error signals is that they are mutually related. An 
COMPARISON OF CORRELATION TECHNIQUES 
* Correlator Y - Error Output Signals 
  
     
   
ss 
(c) -+Ayo 
cl 
Ue V uw 
*xo *xo 
   
(d) +Axo, Ayo 
  
  
  
  
Correlator X- Error Output Signals 
Figure 2 Relation of Correlator X and Y Error 
Output Signals to Stereo Image 
Misalignment 
error measured in one direction causes the sensitivity 
of the correlation error measurement to decrease in: 
the other direction. 
TERRAIN-SLOPE DISTORTION EFFECTS 
When conjugate images in stereo photographs are 
superimposed in the aperture of a correlator, the 
amount of detail that overlaps is a function of the 
terrain that the conjugate images represent. Stereo 
images are exactly alike only if the terrain is flat and 
perfect vertical photographs are used. In this pre- 
sentation, we will only consider (1) conjugate images 
in perfect vertical photographs, and (2) plane-pro- 
jective (first-order) distortions. 
The effect of terrain slope on a stereo image is 
shown in Figure 3. The drawings illustrate how an 
image is distorted relative to its flat terrain projec- 
tion; X-slope terrain magnifies the image along the X 
Correlator 
Aperture 
Image 1 
Terrain 
P Type 
Flat 
> X 
Reference 
F+X SI 
Image ope > Eid > | : + i > I 
- i / 
.(b).^ 
Ei > MT 
/ 
k+Y Slope J» => I = t ex 
N // 
ET, x +x 
/ NIS 
*XSI / 
same YEUX 
Image 2 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Correlator X-Error 
Output Signal 
  
  
  
Figure 3 Terrain Slope Effects on Stereo-Image 
Matching 
73 
ia.