gray-level based image matching (Zhang Z., 1992), it gives 
consideration to spatial relationships, and global consistency has 
been improved immensely. Probabilistic relaxation can be used in 
not only feature based image matching, but also area based image 
matching. An outline of the latter follows. 
The set of candidate points on the right image for point i on the 
left image and corresponding similarity measurements are J = 
[3A 293, jm and' p (1, 33, where" 2544, ^42, 
., jm,and o (i, j) canbethe correlation coefficients of 
two image window centring in point i on left image and point 
j on right image separately. The initial probability that point j 
is the conjugate of point i is the normalised similarity 
measurement: 
p? pae 
iJ m 
> pli) 
k=0 
The consistent coefficient c is defined as the similarity 
measurement by bridge mode: 
c(i,j; k,l) 7 p ( (i, k), resampling (j, 1) ) 
where (i, k) isthe segment of the left image (j, 1) isthe 
segment of the right image, resampling (j, 1) is the resampled 
image segment of (j, 1) relativeto (i, k) and p{} is the 
similarity measurement by bridge mode. The correct form of the 
probability in each iteration is: 
4,72. GS (if kl) *P, 1) 
D 
where D is the neighbour area. Then the probability in r-th 
iteration is: 
p EPI Al vary,) 
where a is a constant relative to the speed of the convergence. 
The probabilistic relaxation of global image matching is a iterative 
procedure. Because the probability is relative to the matching 
results of neighbouring points and the Bridge Mode of image 
matching is used for correcting the geometric distortion, the 
globally consistent results acquired after the processing converges. 
3.4 Neural Network Method of Image Matching 
The neural network is another effective method used frequently 
in many fields including pattern recognition. Similar to relaxation, 
the Hopfield model of neural networking can be used in global 
image matching. Suppose that there are m*n target points on the 
left epipolar image, and the range of x-parallax is [-p, pl. A 
neural network with m*n* (2p+1) neurones, corresponding to all 
possible candidate conjugate points, is created. The initial stage of 
each neuron is: 
if point j is candidate conjugate point 
if point j is not candidate conjugate point 
The strength of the connection between neuron (i,j) and (k,l) can 
be defined as the same as the consistent coefficient in probabilistic 
relaxation: 
W(i,j; k,l) = p{(i,k), resampling (j,1) } 
where (i,k) isthe segment of left image (j,1) is the segment 
428 
of right image, resampling (j,1) is the resampled image 
segment of (j, 1) relative to (i, k) and p{} is the 
similarity measurement by bridge mode. The stage of each neuron 
will change according to the following rule: 
v, (t1) 7 Lif) , 9, WGjiDv, (0) *0,,»0 
kei lej 
v, (0-049, > WG,;k,Dv, (0) *0, «0 
where 0 is the threshold of neuron (i, j). 
The energy function is defined as: 
E- „Ay vire) Wid, kD, +=) (S iru 
27 kil 27167 
where W represents the consistent strength between neuron (i,j) 
and neuron (k, 1). The more consistent they are, the smaller the 
first term of the formula above is. The second term of the formula 
means that there is only one conjugate point corresponding to grid 
point i on the left image, that is, only one neuron, or one of the 
candidate points corresponding to grid point i, is active with the 
value v=1 and others are not active with the values v=0. 
In this case, the second term is a minimum. According to the rule 
of minimum energy in the network, iterative calculation may 
change the stages of the neurones until the network tends to be 
stable and converge, that is: 
v, Kt +1) =v, (D 
All of the points, corresponding to v=1, are the optimal global 
solution. From above it can be seen, through defining the 
consistent coefficient as the strength of the connection, that the 
Hopfield network can perform relaxation processing. An 
advantage of this technique is that relaxation processing can be 
performed in real time since the Hopfield network can be 
implemented by conventional analog circuits. Further, not only 
can the correct matching result be contained, but also break-lines 
and occlusions can be processed, based on the new concept of the 
zero matching with v =0. Because of these aspects, the stability 
of the image match has been enhanced. 
4. EFFECTIVENESS OF THE VIRTUOZO DPW 
Effectiveness is an important factor for a commercial DPW. 
Although the capability of computers will improve in the future, 
processing in real time needs effective algorithms. Currently, if 
the effectiveness of a DPW is low, it is not viable. Fast algorithms 
are necessary. It is quite evident from speed of VirtuoZo that this 
is one of our most significant achievements within digital 
photogrammetry. In comparison with other similar systems, the 
effectiveness of VirtuoZo is better by a factor five. 
4.1 Fast Resampling along Epipolar Line 
The angle and increment in the y direction for each epipolar line 
is required so that the coordinates of every pixel in the epipolar 
line can be computed with an add operation instead of 
multiplication and division operations. Then, keeping the relative 
position in the x direction, the required pixel is acquired by linear 
interpolation in one dimension (the y direction) with it's two 
nearest pixels, instead of a bilinear interpolation in two dimension 
with four pixels resampling along epipolar lines by image 
rectification. This procedure yields a factor two improvement in 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996 
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