Database Reference
In-Depth Information
d
,
-
f
ij
P
N
,
ij
N
(8.1)
¦¦
d
,
-
f
ij
i
j
where ˹ ˼˽ ˷ʿ T is the frequency of occurrence of gray levels i and j , separated by a
distance d and direction
$
$
$
$
T . The summation is over the total
number of pixel pairs N , given d , in the window.
We shall compute the following texture features from the co-occurrence matrix:
angular second moment (ASM), contrast (CON), inverse difference moment
(IDM), and entropy (ENT). These features are among the most commonly used
co-occurrence features in Section 8.2.2.4.
0
,
45
,
90
,
135
8.2.2.2 Improvement in Performance by Symmetric Linked List (SLL)
Because the number of operations required to compute any of the aforementioned
features is proportional to the number of resolution cells (gray values being used)
in the image block, co-occurrence matrices are time-consuming to compute and
are memory-intensive as well. For a typical gray-valued image, each
co-occurrence matrix computed from the image is a ˚ u matrix ( G = 256).
However, assuming that the window size is N and the gray level is G , then at most
there are ˡˡ
˄˅ matrix entries. So the redundancy computation is a
factor of ˚˚ˡˡ
ʻ
ʼ
u
u
ʻ ʼ˄˅ . To overcome this problem, the equal prob-
ability quantizing (EPQ) algorithm to reduce G is preferable. Although quantiza-
tion can remove the contrast sensitivity of textures, it will also remove the
first-order differences in the images. Also, it deeply destroys the relation of multi-
sources, especially input sources from multichannels. Furthermore, selection of
the gray level is required. The example in Fig. 8.3 shows three selected blocks
with the highest levels of gray values, so they will remain and the other gray val-
ues will be removed to reduce the dimension of co-occurrence matrix.
To take advantage of the characteristic of overlapped windows and symmetric
property, we can construct a symmetric linked list (SLL). Each node in SLL con-
sists of data i , data j , and a counter. Data i and j are indexes of the co-occurrence
matrix, and counter is used to count the frequency of occurrence of gray levels i
and j . To increase the efficiency, each entry in SLL should be sorted. Because the
co-occurrence matrix is symmetric, the memory store can be reduced at least by
half. Furthermore, as we can see, updating performance will be improved.
The update procedure is as follows. First, we construct a basic co-occurrence
matrix at the top-left corner of the image, and we compute the required features
from this matrix. Then we subtract elements from the last column. Second, we
move the window one column to the right. At the same time, we add elements
from the new inserted column and compute the required features. Repeat this
process column by column. When the window reaches the end of the row, we slide
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