As a matching criterion for area correlation, cross-covariances Or 
cross-correlation coefficients, normalized cross-covariances, are widely 
used, since density levels of the left and right images are usually 
different. In general correlation windows for cross-covariances work as a 
high-pass filter that passes higher frequencies than about 1/(2L),L 
being width of correlation windows. Therefore if pixel spacing is s and 
correlation windows consist of / pixels, correlation is performed in a 
frequency band of 1/(23 )-1/(245 ) , or equivalently a logs frequency 
band. Usually it comes to a very wide one even for the relatively small 
number of 2. In fact in our case 4315, the band width becomes 4 
octaves. If terrain is even, this wide band property avails for stable 
matching. But if terrain is undulating, this harms rather than help 
matching. For the higher components in the band turn into noises because 
of perspective distortions. Then matching tends to be unstable and 
wander. 
In order to realize more stable matching, we propose to replace the low- 
pass filters by certain narrow-band-pass filters that should have the 
following features: 
[1]no phase distortions: The filters must be linear and symmetric. 
[2]sharp-cut property: Ideally the filters should be band-pass with one 
octave band width. But in general for obtaining sharp-cut property in 
the frequency domain, an impulse response with long duration is needed, 
which in turn harms the efficiency of image processing. 
[3]robustness to noises: Noises dominate near the highest frequency ££. 
Hence the filter in the last (3rd) step should remove the frequencies 
near ZA. 
From the requirements [1],[2] we use the so-called Laplacian of Gaussian 
(LOG) filter, an implulse response of which is defined by 
  
  
rr ze gt 
Aig (2,4) = PE air E "Je f ke five ged 
/ 2407 rs f 207 )e 
with its Fourier transformation 
c9 CET») 
Hug (war wg) = (wz +03) e ^ 
This filter is derived from the following one-dimensional consideration: 
The Fourier transformation of an appropriate band-pass filter can. be 
obtained in the form of a product of those of a low-pass and a high-pass 
filter Ho (w) , Hu (w) « Moreover a high-pass filter can be obtained by the 
transformation of a low-pass filter, 
Hy cw) = /- Hu ‘w), 
The low-pass filter ‘which has a sharp-cut property in a sense that 
it minimizes a product of RMS duration of the impulse response, 
+60 
2 2 
| 7 |A (w| ar 
—00 
and RMS duration of its Fourier transformation 
= 320 -