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
