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