random displacement of the image elements due to 
micro relief within the scan pattern, and (2) photo- 
graphic grain. Also the video signal-generation process 
at the PMT’s introduces quantum noise because of 
the high bandwidth of the process and the limited 
illumination which can be provided with reasonable 
CRT life.* Under conditions of low contrast and 
high-background density in the imagery, PMT noise 
often becomes the predominant output of the PMT's; 
that is, the video signal-to-noise ratio may be substan- 
tially less than unity. 
As was noted, each video-correlator channel is 
basically a cross-correlator. These cross-correlators 
produce control signals which are relatively noise-free 
by processing noisy video signals. Stated simply, a 
cross-correlator performs the mathematical operation 
T 
Cr = fs ovo oa (1) 
where C(7) is defined as the cross-correlation between 
the video signals, v,(t) and vy(t), and 7 is the time 
displacement produced by a position displacement 
Ax or Ay. Basically, a signal-to-noise ratio improve- 
ment is obtained in the correlator channel because 
the noise present in the individual cycles of v, and v, 
is averaged over a time, T, which is much greater than 
their average period. 
As Equation (1) indicates, C(7) is a function of the 
amplitudes of the video signals v, and v, as well as 
the time difference 7. To eliminate the dependence 
on signal amplitude, the video signals in the auto- 
mated analytical stereoplotter are normalized using 
automatic gain-control (AGC) amplifiers. The AGC 
amplifier outputs are passed through bandpass filters 
and converted to binary wave trains so that the re- 
quired multiplications can be performed in simple 
logic circuits. 
Because of the above equipment features, equation 
(1) gives only general information about the actual 
video correlator outputs. To obtain more complete 
information, it is also necessary to consider the in- 
formation content of the imagery, the spatial and 
temporal bandwidth limitations of the flying-spot 
scanners, and the overall signal-to-noise ratio in each 
video channel. A complete mathematical analysis of 
the cross-correlation channel gives: 
*An accompanying paper (J. J. Edmond, “Orthophoto Genera- 
tion") gives a more complete discussion of flying-spot scanner noise. 
Significant noise sources not mentioned here are CRT wear patterns 
and phosphor noise; however, these can generally be removed by a 
"leveler" system which employs a separate PMT to detect CRT output 
fluctuations and electronic circuitry to compensate the video signals. 
C(Ax) = 
© 
DU. ] ; WAX 
Loin! [in 2 d 
= sin Bh foe Gyy(w) cos v 2 ; 
  
Ay=0 (2) 
where 
C(Ax) = average cross-correlation for Ax relative 
image displacement 
H; (jw) = transfer function of the electro-optical 
system 
Gyy(w) = cross-power density spectrum for the 
photographic imagery 
e; -[S? to, 2]. i7 122 
S? - mean-square signal 
c,;? 7 mean-square noise in video channel i 
v 7 scanning-spot velocity 
For the condition Ax = 0, implying that the images 
are matched, the integral in equation (2) becomes 
equal to the mean-square signal, S2, and the term 
within the brackets becomes S2/o,0,, à simple func- 
tion of the video signal-to-noise ratio. C(Ax) is thus a 
measure of the image quality, as seen by the corre- 
lator at a particular point in the stereomodel. 
A similar analysis for a parallax channel gives: 
  
  
P.(Ax)S 
2 1 2 AX 
C2 
umi 53/2 
x sin i; fien G, y (c) sin 7 tal. 
—00 
Ay =0 (3) 
where P, (Ax) is the average x parallax for Ax relative 
image displacement. In examining equations (2) and 
(3), note that the major difference is that C(Ax) con- 
tains a cosine term while P, (Ax) contains a sine term. 
This difference results from the quadrature networks, 
and produces an even function for C(Ax) and an odd 
function for P, (Ax), as shown in Figure 3. 
Most automatic stereoperception systems contain 
special features which adapt the scanning and correla- 
tion process to the particular requirements of photo- 
grammetric instruments. An example is the computer 
control of the scan generator in the automated ana- 
lytical stereoplotters, noted in the discussion of 
Figure 1, in which the size and shape of the scan 
patterns for each photograph are controlled. The 
scan-shaping process implements a first-order trans- 
formation of a reference model-coordinate scan pat- 
tern to photo-coordinate patterns for each photo- 
graph. As indicated in Figure 4, this transformation 
compensates the scan patterns for perspective distor- 
  
  
CHAPELLE, WHITESIDE, AND BYBEE 
Sho b oa 4n AN be PA UA