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
