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