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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008
(2) Provide N with following 103 values: 1, 2, 4, 10, 20, 30, ... ,
100, 110, ... , 900, 910, ... , 1000. For three kinds of traffic
signs in table 1, compute each central projection vector
corresponding to each N with equation (2) and equation (3).
Based on computation of central projection vector, compute its
information entropy with following equation.
sm=-Zm ) i°sm y=U,-i 03 w
*=o
(3) Compute ratio AS of two neighbouring information
entropies with following equation.
AS =S(N i+l )/S(N,) (/=1,2,3,..., 102) (5)
(4) For three kinds of traffic signs, the statistical relation
between the ratio AS and central projection number N is shown
in Figure 2. From Figure 2, we can see that ratio AS gradually
reaches constant 1 when N is 360. Therefore, the central
projection number is 360 during central projection
transformation in this paper.
Figure 2. The statistical relation between the ratio A5 and N
2.3 Recognize traffic sign through PNN
For each detected traffic sign, after its feature vector is
computed by the central projection transformation, we can use
the trained probabilistic neural networks (PNN) to recognize its
exact meaning. The PNN was firstly proposed by Specht in
1990 (Specht, 1990). It is a kind of forward-propagation neural
network developed from the radial basis function neural
network. Its characteristics include less training time, fixed
architecture and generation output with Bayes posterior
probability. Therefore, it has powerful capability of nonlinear
recognition. The PNN has three layers: the first layer is input
layer, the second layer is radial basis layer and the third layer is
output layer. The number of neurons in radial basis layer is
equal to that of input samples. The number of neurons in output
layer is equal to that of classifications of training samples.
Neurons in radial basis layer have thresholds. The architecture
of PNN is shown in Figure 3.
Input layer Radiai basis layer Competitive layer
t \r A f
In Figure 3, R shows the number of elements in input vector. Q
shows the number of input/target pairs. K shows the number of
neurons in output layer. The function of module C is to find the
maximal value in elements of its input vector n2, produce
output value 1 of neuron corresponding to the largest element of
n2, and produce output value 0 of other neurons. In Chinese
standard on traffic signs, the numbers of yellow warning signs,
red prohibition signs and blue mandatory signs are respectively
45, 40 and 29. However, actual kinds of limited speed signs,
limited height signs and limited width signs are more than one.
Therefore, plus actual limited speed signs, limited height signs
and limited width signs, the number of prohibition signs is 53 in
this paper. Training set is obtained from two sources: inner
images of traffic signs in national standard and actual inner
images from detected traffic signs in natural scene images. In
this paper, for yellow warning signs, red prohibition signs and
blue mandatory signs, R in PNN classifiers are 360. K in three
classifiers are respectively 45, 53 and 29. Q in training set for
three classifiers are 61, 110 and 43 respectively.
The process from input to output of PNN is described as
follows.
(1) Input layer receives input vector P / =(P 1 ,P 2 ,...,P^) 1 ,
7=1,2,. ..,Q.
(2) For the z' th (/=1,2,...,0 neuron in radial basis layer, the
distance //, between input vector P, and weight matrix IW, is
firstly computed by following equation.
d t = sqrt((P. -IW/y (P. -1 W ; r )) (6)
Then according to threshold bl, the output of / th neuron a,l is
computed by following equation.
, - n , 1 x n . 1
a I = e
n 1 = d x b 1
(3) The w th element (m=\,2,...,K) in input vector n2 of compete
layer is computed as follows.
n„2 = LW„al (8)
(4) The final output vector a2 ; is computed as follows. Only two
kinds of value (0& 1) are found in the output vector, and serial
number of element 1 is that of classification of input data.
