Database Reference
In-Depth Information
¦¦
2
Contrast
(
i
,
j
)
p
(
i
,
j
).
(8.3)
i
j
The higher values of the contrast are, the sharper the structural variations in the
image.
z
Angular Second Moment (ASM). The angular second moment gives a strong
measurement of uniformity and can be defined as
¦¦
2
Angular
Second
Monent
{
p
(
i
,
j
)}
.
(8.4)
i
j
Higher nonuniformity values provide evidence of higher structural variations.
z
Inverse Difference Moment (IDM). The inverse difference moment is a meas-
ure of local homogeneity and is defined as
1
¦¦
Inverse
Difference
Monent
p
(
i
,
j
).
(8.5)
2
2
1
(
i
j
)
/
G
i
j
Features such as correlation cannot be used. If the variance becomes zero, the
correlation will go to infinity.
8.2.3 The Complete Procedure of Wavelet Decomposition
Wavelet decomposition [17] is a mathematical framework for constructing an or-
thonormal basis for the space of all finite energy signals. It can decompose input
signals into multiscale details, describing their power at each scale and position. It
can discriminate the locate properties corresponding to smooth and textured areas.
We will introduce the framework, implementation, and complete procedure of
wavelet decomposition in this section.
At each level, the coefficients
{h(n)}
and
{g(n)}
are squared, then summed, and
the square root is taken to generate a single feature for each approximation and
detail of that level. These sets of four numbers, i.e., the scaling function and the
wavelets for each level, are then used for classification. First, we perform one step
of horizontal pairwise averaging and differing on the pixel value in each row of
the image. Next, we apply vertical pairwise averaging and differing to each col-
umn of the result. To complete the transformation, we repeat this process recur-
sively only on the quadrant containing averages in both directions.
The complete procedure is shown in Fig. 8.5. First we select a point from the
top-left of the image and obtain a block from the gray values of its neighbors. Sec-
ond, we perform the wavelet decomposition row by row, including cases of low
pass and high pass. Finally, we apply the same process column by column. This is
the 2D wavelet decomposition. For the wavelet decomposition, we first extend the
size of the selected block to be a square block. Then we perform the convolution
and then downsampling the size of the block into half. Then we transpose the im-
age for the next wavelet decomposition. As an example shown in Fig. 8.6, the
top-left and bottom-right images are the result of wavelet decomposition from
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