Figure 2. Gray Level Co-occurrence Matrix
Gray level co-occurrence matrix can be expressed by
mathematical formula as follows:
P(iJ,S,0) = {[(x,y), (x+Ax,y+Ay)] / f(x,y) = i
f(x+Ax, y+Ay) -j; x = 0,1,2, ..., Nx-1; y-0,1,2, ...,Ny-l}
In the formula, i, j=0, 1, 2... L-l; x, y is pixels coordinates in
the image; L means gray progression of the image; Nx and Ny
respectively enumerate the number of image line.
According to the above definition, P (i,j,d,0) expressed
elements with Line i and Row j of the gray level co-occurrence
matrix. It also indicated appearance frequencies on all the pixel
point pairs with the direction as 9 and distance as S. In addition,
a pair of pixel point includes one gray i value and gray j value.
9 here included angle created by two pixels and x axis
according to the clockwise direction. 9 value is 0°, 45°, 90°and
135°. Definitions on different 9 matrix element are as follows:
P(i, j, 5, 0°) = # / ((k,l),(m,n)) E(Ly*Lx) x(Ly*Lx) / k-m=0,
/ l-n / =S; I(k, z)=i,I(m, n)=j /
P(i,j,d,45°)=# / ((k,l),(m,n))
n=-S); Or(k-m=-d,l-n=S), l(k, l)=i,l(m, n)=j /
P(iJ,S, 90°) = # / ((k,l),(m,n)) E(LyxLx) x(Ly*Lx)//le
nt / =d,l-n-0; I(k, l)=i,I(m, n)=j /
P(i,j,d,135°)=# / ((k,l),(m,n)) (E(LyxLx)x(LyxLx) /(k-m=d,l-
n=d); or (k-m=-S,l-n=-d), I(k, l)=i,I(m, n)=j /
In the formula, symbol # / X / expresses elements numbers of
gathers X.
The gray level co-occurrence matrix reflects integrated
information image gray on direction and adjacent interval and
change scope, which is the base to analyze partial model
structure and array rule of image. Feature quantity as texture
analysis is not usually gray level co-occurrence matrix applying
computing directly. It extracts texture feature quantity based on
gray level co-occurrence matrix which is called second statistic
summation.
Using the gray level co-occurrence matrix, amount of
texture feature can be defined whose aim is to assistant
classification of sensing image texture. Haralick(1973)
proposed 14 textural eigenvalue. However, Barald thought that
computation quantity of grey level co-occurrence is great and
following four features are often adopted to extract texture
feature of image. For sensing image, four kinds of statistic
quantity what follows will have the best effects[Guo, 2005].
These are four mentioned textural features
ASM-XX A/,./) 2 ;
i j
C0N= XX<''-iTW,./) ;
' j
CORRLN=
II ((ij)p(Uj))~M x M y
!
y '
EMT=- X X PO’j) log pi}, j) ■■
3.2 Extraction of the textures features image based on the
gray level co-occurrence matrix
3.2.1 The technical plan about extraction of texture
feature image
The extraction algorithm of textures feature image based on
gray level co-occurrence matrix is as follows:
1) Transform the colored image into the gray image and pick
single band of the gray image.
The texture feature of the image is extracted in term of the
single band. Therefore, the first step of computing texture
feature is that single band standing for R or G or B are
extracted from multi-band and then one of the bands are chosen
to compute the texture feature. Because the texture feature is
one kind of structure feature, using the texture feature image
with different bands will produce the same texture features.
Thus we choose the R band to take the research. In figure 3,
remote sensing image with the single band is picked through
matlab.
Figure 3. The remote sensing image of R band
2) Gray level quantification. Since computing quantity is great,
we should cut down the gray levels under maintaining primary
shape of the image to save time. So, when computing gray level
co-occurrence matrix, the gray levels of original image is
reduced to smaller scope. We usually extract level 8 or level 16
to decrease co-occurrence matrix and save time. In this paper,
the image is compressed into 8 gray levels. Although quantified
image has some distortion, its influence for the texture feature
is not too great.
3) Computation requests of texture feature value
a) Choice of sliding window
Texture analysis method of the gray level co-occurrence matrix
need choose the sliding window. That is the image is divided
into several sub-images computing the gray co-occurrence
matrices with size as windows. In this paper, we use two kinds
of sliding windows with 5x5 and 7x7 to compute the texture
feature value.
b) Step of distance choice
Use step d=l is appropriate through the experiment and the
comparison.
c) Direction choice
The direction of compute gray level co-occurrence matrix
always adopt 0°, 45°, 90° and 135°. We should handle the
value of the four directions otherwise there are too many
texture features which is not propitious to use. Average value
of four directions is used as final texture feature value in the
paper.
4) Transform calculated texture characteristic value into the
image, namely texture feature image.
