3.1.2 Cooperative Process: The winning neuron locates the 
center of a topological neighbourhood of cooperating neurons. 
Let the topological neighbourhood be denoted by 
i(x> 
= exp ( 
2a 2 (n) 
(14) 
In Eq.(10) , the parameter °’ °’ *’ 2 should begin with 
the value chosen as required . We use following choices in the 
formula of Eq.(10): 
ct 0 = 0.35, ^ =0.1, t 2 = 1000, r, = 1 000/ 
/ 
d. . 
Let the lateral distance ^ ’ 1 between winning neuron i and 
excited neuron j be denoted by 
Where the discrete vector J defines the position of excited 
4. EXPERIMENT AND RESULT 
In figure 3, a 1000x1400 pixel gray image, which is about 
urban area, is shown. It mainly covers urban road, construction 
and water area. In figure 4, a 810 xl 180 pixel laser point clouds 
image is shown. It is obtained by ILPIS-3D ,a 3D laser scanner , 
which is product of OpTech, in March, 2005. The scanner has 
350meter measurable distance, lOmillimeter nominal accuracy 
and 2000Hz frequency. The image segmentation using 
histogram threshold value algorithm, K-NN algorithm and SOM 
based on the directional wavelet transform at multiple-scale is 
implemented as following: 
neuron j and J defines the discrete position of winning neuron 
i . Another unique feature of SOM algorithm is that the size of 
the topological neighbourhood shrinks with time. This 
requirement is satisfied by making the width of the 
A, 
topological neighbourhood function decrease with* time. 
A popular choice for the dependence of C ' W 
n is the exponential decay described by 
on discrete time 
f 
a ( ri) = <7 0 exp 
V 
(16) 
3.1.3 Adaptive Process: In this process, the synaptic weight 
vector Wj of neuron j in the network is required to change in 
relation to the input vector X and the numerical value of 
topological neighbourhood function are also required to change. 
The self-adapting of the synaptic weight is expressed as follows : 
Aw, = A ■ h JtKà (X - Wj) Xj e c, (17) 
the synaptic weight Wj (n+1) at time n+1 is defined by : 
Wj(n+i) =Wj(ii) +A(rù hj i(jd (rì) (X-WjXrù )(18) 
X 
L is the learning-rating parameter of SOM 
(a)Aerial image 
(b)Histogram thresholding 
segmentation 
(c)K-means segmentation (d)Multi-scale segmentation 
on SOM 
Figure 3.Aerial image and segmentation