Download - Academy Publisher

xi,
j
y' = εα ( (1 + tanh( )) − y ) (2)
ij , β ij ,
W
NDWI
(, i j; k, l)
=
N (, ij) + Nkl ( ,)
Nij (, ) − Nkl ( ,) + ε
(7)
S = ∑ , ( , ) ( ) ( )
, W ij kl Hx k l +
ij WHp −θ
−
p ij , p WHz − θ (3)
z z
kl , ∈Ni ( , j)
⎡
⎤
P' = (1 − P ) H ⎢ H( x , ) P
i, j i, j
∑ kl −θ
⎥
p −ε
⎢
⎥ i,
j
⎣kl , ∈NP
( i, j)
⎦
⎡
⎤
z ' = H ⎢∑
H ( x kl , ) −1⎥
−
⎢
⎥
z
⎣kl
, ⎦
where I i,
j is the stimulate input of pixel (, i j ). x i , j and
yi,
jare two oscillators on different temporal scale. And
ρ is the variance of Gaussian noise. S ij , was the couple
equation. Wij,
kl is the couple weight of pixel ( ij , ) and
pixel ( kl , ). H is the step function, W p , W z are the weight
coefficient correspond to P ij , , z is the globally
inhibition. P ij , is the later potential of pixel ( i, j ), and
θ
p,
θz
are the threshold of Pi,
jand z.
Equation (1), (2), (3) and (4) are differential equations.
The physical significance of these equations had been
analyzed particularly and comprehensively by Terman
and Wang in [12]. They had proposed a simplified
LEGION method in [18]. The couple weight coefficient
W ij , kl was the important factor, it decided what feature
will be chosen to cut the image.
III. THE LEGION BASE ON NDWI
A. The model of NDWI
The NDWI was defined as follow:
Green−NIR
NDWI =
(6)
Green+
NIR
Based on the NDWI, the distance between water and
other ground objects was enlarged. But because of the
pollution and the magnitude of sandiness, the coherence
on the water surface will be reduced and the NDWI
fluctuated above zero.
Fig.1 shows the spectrum change trend of water area,
vegetation area and building area around the river. Like
paper [5], the spectrum of building on the forth band
(TM4) and the second band (TM2) had the similarity
change trend, but with the different mean. Fifteen sample
points of NDWI were plotted in Fig. 2. The variance
within the water body and the building body were
smaller, and the variance between water and building
was larger.
B. The couple weight based on NDWI
From the above analysis, construct one couple weight
based on NDWI to describe the relationship of pixels:
(4)
(5)
Where N (, ij ) was the NDWI value of pixel Ii (, j. ) The
equation (2) could be rewritten as follow:
S = ∑ W (, ; ,) ( ) ( 0.5) ( 0.5)
, NDWI ijklHN + WHp − −WHz− (8)
ij ij , p ij , z
kl , ∈Ni (, j)
• C. LEGION based on NDWI
The special spectrum property was introduced into the
proposed extraction method which was found by Zhou.
The special spectrum property of water is:
B ( green) > B ( SW ) & B ( red ) > B ( IR)
(9)
3 4 2 1
So the equation (8) could be rewritten as follow:
S = ∑ (, ; ,) ( (, )) (( 3( ,) 2( ,))
ij ,
W NDWI i jkl H Ni j H I kl + I kl
kl , ∈Ni ( , j)
> ( I ( k, l) + I ( k, l))) + W H( p −0.5) −W H( z− 0.5) (10)
4 1 p i,
j z
Where I
1 ( k , l ) represent the spectrum luminance of
pixel I( k, l)
of the first band. H( x)
was the step function,
and H( N( i, j))
compared the NDWI value of pixel Ii (, j )
with zero. Adding H( N( i, j))
onto the second term was to
make the object to be remained which was with the
NDWI larger than zero.
spectrum value
Figure.1
NDWI
0.60
0.40
0.20
0.00
TM1 TM2 TM3 TM4 TM5
water 0.43 0.40 0.47 0.12 0.05
vegetation 0.33 0.28 0.21 0.52 0.48
building 0.48 0.42 0.47 0.31 0.47
0.60
0.50
0.40
0.30
0.20
0.10
0.00
b d
The spectrum change trend of water area, vegetation area
and building area around the river
0 2 4 6 8 10 12 14 16
sample points
NDWI of water and building
Figure.2
building
NDWI of water body and building body
water
259