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# Full text

Title
Mapping without the sun
Author
Zhang, Jixian

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, We can get
fH{(q,oj,d)=li(q,d)H^,d)
(7)
h(m,n,a) = -^j£ ( [IH(co x ,co x , 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, 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, iK(O x ,(O y ,Cj) = (j){(O x ,G)-(j){(O y ,G) (4)
¥ a { x ,cr)-0(co y , 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