In Fig.4, a symbol “O” represents a neuron. We 
dispose neurons like a rectangular solid. x and y 
are horizontal and vertical coordinates in 
resultant image respectively. The z-coordinate 
represents the parallax in the pixel at the point(x, 
y). 
3 vo; 
Inputl 
Outputl 
HOLL 
VO y 
mr i >y@) 
Output2 
Input2 
os 
Fig.5 Model of neuron in our method 
A model of neuron used in our method has two 
outputs as shown in Fig.5. We use sigmoid 
function for the output1(v) to compare output of 
each neuron on the same pixel(x, y). However, We 
use Eq.(5) instead of Eq.(3) to represent that a 
difference of height had better be small, i.e., 
  
ML 1.0 
2 ? 
1.0- exp - a = vt) -6+| 6) 
wherea is constant. 
We use Eq.(6) for the output2(v?) to transmit 
information between neurons on the different 
pixels(x, y), i.e., 
£D Q) yo 
(2) _ 1 yf = max(v, > p Sn 
vi ; . (6) 
0 otherwize 
In Eq.(5), vU and v) are the outputl and 
x,y,z x,y,z 
the output2 of the neuron at the coordinate(x, y, z), 
respectively. Using these outputs, the neuron 
with the maximum outputl among neurons on 
the same pixel(x, y) sends “1” to neurons on 
different pixels(x, y), and others send “0”. Finally, 
we determine the parallax from the z-coordinate 
of the neuron with “1” of output2. By using the 
above method, we can avoid local minima due to 
the step function, and prevent that all output of 
neurons show same values caused by using the 
sigmoid function. 
4-2. Estimation Function 
Using the above network, we can define the 
estimation function E as 
vr, Z 
mei YO 
(2) y) 
X,y,z Veni yj k 
          
o y=0 z=0 2.2.2 
(7) 
In Eq.(7), Cor(x, y, z) is the correlation coefficient 
at the parallax z of the pixel(x, y). W, and W, 
are the weights of the first and the second terms, 
respectively. X, Y are the horizontal size and the 
vertical size of an image. Z is the searching range 
of the parallax. I and J are the horizontal size and 
the vertical size of the comparison range of height. 
The first term of the right side is the term that 
represents it is better that the correlation 
coefficient corresponding a neuron with large 
output1 is large. The second term of the right side 
is the term represents that a difference of height 
had better be small. 
The solution is the combination of coordinates, (x, 
y, z), that gives the minimum value of E. 
Concretely the value z of X2 = “1” is the 
3,92 
parallax of the pixel(x, y). 
4-3. Threshold and Connection Weight 
We define thresholds and connection weights of 
each neuron based on the network structure and 
the estimation function discussed above. The 
principle of Hopfield model is to prevent a neuron 
against a restriction from having large output, 
other neurons suppress that neuron. We define 
thresholds and connection weights of each neuron 
concretely on this principle. 
26 International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 
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