+09 5 
J a^ | Hen |o 
co 
is a Gaussian/7/. Then the Fourier transformation of a required band-pass 
filter can be obtained as the difference of two Gaussians (DOG) with 
scale parameters g,A ' 
a? (m+ pt) w? 
mae me2 
Hpe(w) = H, (w) Hy (w) = 6€ m e 
Among the DOG filters, the most narrow-band-pass is obtained by uz 
k = Ato — 0, with the peak frequency w, = (2/Cka>) In(Hk)), aS 
2 2 2 
  
w e w 
Hpe(w) = € - @ c we ; 
wr 
It is, regardless of coefficients, in the form of Fourier Transformation 
of the Laplacian of Gaussian (LOG) with wp ={2/ C. The half band width 
of the LOG filters is only 1.6 octaves. 
The LOG filter that involves a 2nd differentiation operator can also be 
regarded as one for edge extraction, since zero-crossings of the LOG- 
filtered images designate positions of edges. Marr and Poggio/4/ assert 
that the principle of human stereopsis would lie in the correspondence of 
edges in the images produced through the LOG filters with different 
scales. 
We employ, as band-pass-filters in 3 steps of matching, the LOG filters 
with different scales by one octave in order hrig,;, hrc2 and hrcs- They 
are illustrated in Fig.3. The principal frequencies are set €3 69 o1 
= 1, Q 52 7 1/2.. and w = 1/4 for. .h , hpg2 and hres 
respectively. This follows Pa the aquirenent fii, Loo he ries? 
hLG1 must almost vanish near w= 7 to supress noises. The positive 
support widths w are 4, 9 and 18 respectively. 
A search range should be narrower than the principal wevelength of the 
band-pass filter. Hence the range is set to +3 pixels on the reduced 
right patch in every step. 
Further we check whether zero-crossings exist or not within a range of 
+3 pixels around every grid point on the reduced left image in every 
X Ww) 
hc LaplacianxGaussian 
hie(r) 
    
   
    
  
LE ved " 
O0 m8 n4 n/2 nw 
Fig. 3 Laplacian of Gaussian filters 
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