the difference between the distance from i to j and 
the difference from k to I. 
The synaptic 
is defined as: 
connection welght between two neurons 
Tikjlm = (Cikjlm - 51jm - 8 kim) 
where 8 ijn = 1 if i=), otherwise 0; 0 kim = 1 
If 1=k, otherwise 0. The deformation of the cost fun- 
ction to the Lyapunov function of a Hopfield network 
with the neuron is defined as Vik = Pik, Vj = Pj|. 
The concrete convergence programm in the (10) equli- 
ty is proved difficult. We use an approximate energy 
C as followed. The mateamatical proof refers to 
3]. 
À Eikm = - [ E x 2 Cita - Sim - Okiw? 
Pj] * 2] APikn (11) 
According to the Hopfield updating rule 
| Ar 
Pik — 0, if fi > cun - Bim - 
8 kim) Pj1 +3 | <o 
Pik 1 if im x 2 Cm - 8 iim - 
Skim Pj1 +3 | >0 
no change if p x 3 (Cikjim - 9 1j - 
8 kim) Pj1 +23 | =0 
The optimal solution is completed when the Hopfield 
network is at its minimum energy point. However, it 
may settle down into one of the many locally stable 
state. So we cannot only rely on the stable point ln 
the Hopfield network to get a full satisfication in 
the stereo matching process. We adopt stereo fusion 
layer for our further decisive basis. Another reason 
for the stereo fusion layer is that the (interest 
points is so sparse that the result of the matching 
result cannot reconstruct the real surface of the 
object. Only when the pattern recognition layer and 
the stereo fusion layer convergence simultaneously, 
the result of the system is reliable. In the next 
section, we will discuss the stereo fusion layer. 
The discrete (binary output) state was chosen in the 
pattern matching layer rather than the continuous 
value because of its simplicity in computational 
complexity. However, using a discrete Hopfield net- 
work, a number of local minima may not be avoided 
owing to the discontinuity of energy function caused 
by the discontinual interest points. 
4. STEREO FUSION LAYER 
The function of the stereo fusion layer is: It match 
the other points which are not the interest points. 
It perform the minimum of a energy fuenection which 
is based on the stereo fusion criterion. The stereo 
fusion is completed in local segments which is conf- 
420 
ined by the interest points. The surface of this 
local area is smooth for there is not salient point 
in this segment and so that this network may not 
fall into a local minimum point. The calculation of 
different segments is in separate and parallel way. 
There is no relation between the different segments 
for the depth may be discontinual at the interest 
point. But the difference of disparity between the 
neibour points in one segment should be very small, 
owing to the object rigidity and surface smoothness. 
This layer is formed by another Hopfield network 
proposed by Y.S. Zhang [4]. The stereo fusion is 
assumed along the epipolar line. The energy funeloa 
is given by : 
r Je D 2 
= D) - P,(iek y 
i * * gpl PG D - PRüek DI^ Vi, jk 
T € D 
14 EL Fi Enñles Toit 
= Vt, no 8, y? (13) 
By comparising with the standard Hopfield network in 
two dimensional application: 
D _D 
- am z = >; 2 pTijkin Vijk Vimo 
: * * Zu V ima (13) 
We can get 
Tijkim = - 8% 81) 8 judy 
"ES 811 8 jme 8 kn 
11, j,k = - EP4L) - Pelo J) 1? 
Where 2D+1 is the maximum disparity, 8S is an index 
set for four nearest neighbours at polnta (Ll), Nr 
and Ne is the image window row and column sise, res- 
pectively. More detailed convergence of the network 
refers to the paper by Y.S. Zhang [4]. 
-6. THE COMPOUND DECISION LAYER 
The pattern matching layer match the Interest points 
while the stereo fusion layer match the other points 
according to the stereo fusion eriterion. The stereo 
fusion area is eonfined by the interest points 80 
that the stereo fusion process is guided by the pat- 
tern matching layer. While the pattern matching layer 
and the stereo fusion may fall into local minimum 
points in the convergence process so that a compound 
decision layer is employeed to complete cooperative 
decision to enforce the reliability of the matching 
result. 
Fig. 5 shows the possible matehing cell between the 
left image and right image. We are supposed that 
there are two possible set of correspondence : 
{i «> |, j «=n, k —> n 
of fies] je,