Full text: Mapping without the sun

89 
that the novel approach is very effective for extracting the block 
objects in remote sensing images. 
2. DIRECTIONAL WAVELET GROUP AND REMOTE 
SENSING IMAGES FEATURE VECTORS 
CONSTRUCTING 
2.1 2-D Gaussian directional wavelet group 
Define a smooth function 3 2 ) in the direction of a of 2- 
D directional wavelet [13,14 ] 
at \ dô(x,y) . d0(x,y) m 
if/ (x, y) = cos a - + sin a — U) 
dx dy 
If equation (1) chooses Gaussian function as a smooth function, 
it has 
y/ a 0, y, cr) = cosa • i//(x, cr)0(y, cr) + sina • 0(x, a)y/(y, o) (2) 
Gaussian function and first order derivative are 
(/)(2co x ,2(0 y ,cr) « H((D X ,CO y ,cr)• (¡)(co x ,(0 V ,CT) 
y/ a {2(0 x ,2(0 y ,cr) « G((0 X ,(0 y ,cr) ■ </>(o) x ,(o v ,cr) 
(6) 
X ’ y ■ 
Due to 
(f){(0, cr)-e 2 ,y/{(o,cr) = -j(o e 2 
3 a 1 co 1 3 a 2 a> 2 
H{(o,<j) = e 2 ,G((o,<j) = -j2(o e 2 
We can get 
fH{(q,oj,d)=li(q,d)H^,d) 
(7) 
h(m,n,a) = -^j£ ( [IH(co x ,co x ,<j)-e jma 'dco x )• e jn< °'dco y ( 8 ) 
Chooses 
0{x, (j) = -~L e 
V 2;r cr 
d6{x, cr) - x 
2a 
2 a 1 
dx 
<7 
y[27T 
(j){x, cr) = 0{x, cr) 
y/{x,(j) = 
X 
2a 
cr 
’ VZtt 
(3) 
g(m, n, a) = —^ f ' ( [ x G(ûj x , co , cr) • e jmco ' dco ) • e jnWy dco ( 9 ) 
4 k x 
Namely 
h(m, n, cr) = h(m, <j)h(n, cr) (10) 
g a (m, n, cr) = cosa • g(m, cr)h(n, a) + sina • g(n, o)h(m, a) ( 11 ) 
Let Ao f (wi, n) approximate to the original image 
f(m,n) , dispersed wavelet transform fast Algorithm is 
In this equation a is the parameter related to scale. Fourier 
transform of (/){x, y, cr) and y/ “ (x, y, <j) are 
iK(O x ,(O y ,Cj) = (j){(O x ,G)-(j){(O y ,G) (4) 
¥ a {<o x ,co y ,cf)=cosay/ (a> x ,cr)-0(co y ,<j) + sina-0(c0 x ,o-)-i// (a> y ,cr) (3) 
Limited \_—7t,jz\, approximately there are two scale equations 
A 2 j +1 /(/, k) = A 2 j f(m, n) * h{m, n, cr) 
f(U k) = A 2 j f(m, n) * g a (m, n, cr) 
(12) 
Where A^ f is the low-frequency image information when 
the scale is j, and { D^j f} is the high-frequency information 
related to the (X . For example, respectively select (X 
as (30,60,120,150 ) , corresponding directional 
1 . .-1 „30° 60° 120° 150° 
wavelet spatial filter are g , g , g , g .By 
equation (12), high-frequency features information of 
corresponding four directions image are extracted, the results
	        
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