Modified update U2:
2 _j25d? +a),i = 0
a ‘ "{¿(¿, 2 + dU) + a),i = 1,2,..., Af/2-1
Modified update P1:
joc(x 2 i + X 2 i+2 ) ^ 2/+1 ’ * — 0,1,2,..., «/2-1
fl| = {2ax 2i + x 2l+1 ,i = N / 2-1
Modified update P2:
2 _ f Y(a) + a l M ) + d),i = 0,1,2,..., N/2-2
a ‘ [lya]+dj,i = N/2-1
There are some parameters: a = -1.586134342 , 3 = -
0.05298011854, ¥= 0.88291107662, 6 = 0.4435068522,
4 =1.149604398.
L*L image 3 resolution levels decomposing procedure as
follows:
112
HL2
HL1
m2
1+12
LH1
HH1
LL
LH
HL
HH
(b)one-level decomposition
LL,
HL,
HL,
HL,,
LH X
HH 3
lh 2
HH 3
LH l
HH X
(c) second level decomposition (d)third level decomposition
Figure 1. 2-d DWT subband decomposition ( 3 resolution levels)
Thereinto: LL: approximation part
HL: plane details
LH: vertical details
HH: diagonal details
3. EXTRACTING TEXTURE STRUCTURE IMAGE
FEATURE BASED ON WAVELET TRANSFORM AND
GRAY LEVEL COOCCURRENCE MATRIX
Generally, the result of wavelet transform can not be used for
character measure, just statistics result from the result of
wavelet transform can be showed the texture character. And
texture is characterized by the spatial distribution of the gray in
a knighthood, the local image region, statistics or property that
is repeated over the textured region, is called a texture element
or texel. Selecting texture structure image character based on
wavelet transform and Gray Level Co-occurrence Matrix is
useful.
Gray Level Co-occurrence Matrix is the commonly texture
statistics analysis method, which is implied the roughness and
repetition of texture image, and can distill the texture character
quantity, such as contrast , energy , entropy , local
homogeneity, cluster shade, cluster prominence, maximum
probability, etc.
Second order moment (energy)
ASM = X P(i,j,d,6f 0)
¡=0,j=0
where
P(i.j, d, 6) =# {[(*, y), (x + Ax, y + AjO] | /U, .y) = i,
f(x + Ax, y +Ay) = j; x = 0,1,- ■■N x ~l;y = 0,1,- • -N y -1}
i, j: row and column of image
d: distance
0: angle
Energy index is used for the study of image texture in our paper
here.
In the test, we use bi second generation wavelet transform,
selecting CDF97 wavelet basis processing textural image, as
low-filter can keep the low frequency weight of original
information , and not result in blur effects. In general, when
N=3,we find it that the effect is better, so defining third
resolution character distilling from the textural sub-image .and
extracting texture structure image character method is as follow:
Firstly, we got one low frequency sub-image and three
high frequency (such as E8, E9 and E10) through the wavelet
transform of image L*L;
Secondly, we can got one low frequency sub-image and
three high frequency (such as E5, E6 and E7) through the
wavelet transform of image L/2*L/2;
Thirdly, we got one low frequency sub-image and three
high frequency (such as E8, E9 and E10) through the wavelet
transform of image L/4*L/4.
Sub-images blocks coding in various scales as follows:
L.' 4
El
E2
E5
EK
E>
E4
E6
E7
E9
EtO
L
Figure 2. Sub-images blocks coding in various scales
E2: vertical direction texture sub-image of third scale
E3: plane direction texture sub-image of third scale
E4: diagonal direction texture sub-image of third scale
E5: vertical direction texture sub-image of second scale
E6: plane direction texture sub-image of second scale
E7: diagonal direction texture sub-image of second scale
E8: vertical direction texture sub-image of first scale
E9: plane direction texture sub-image of first scale