Biomedical Engineering Reference
In-Depth Information
In many medical image applications, texture plays a major role in the task of
segmentation of regions of interest. Associated with texture features are numerous
techniques. Basically, the different methods of feature extraction emphasize dif-
ferent fundamental properties of the texture, such as scale, statistics, or structure.
In a very rough way, we can subdivide the texture feature extractors into: complex
statistics, with techniques as co-occurrence methods [21] or higher-order statistics
represented by moments [22]; multi-resolution strategies, such as derivatives of a
gaussian model [23], Gabor filters [24], or Wavelet techniques [25]; and structure
related measures, such as Fractal Dimension [26] and Local Binary Patterns [27].
Probably, one of the most well-known techniques is the co-occurrence matrices
measures. Due to the popularity of this technique, we have selected it to illus-
trate the filter approach. The following paragraphs are devoted to give a brief
introduction and examples of the co-occurrence matrices measures technique.
The graylevel co-occurrence matrix [28] is a well-known statistical tool for
extracting second-order texture information from images [21]. The creation of the
matrix involves the computation of the relative frequencies of graylevel pairs of
pixels at certain relative displacement. We can look at the co-occurrence matrix
as an estimate of the joint probability density function of graylevel pairs in an
image for a given angle and distance. For
N
different gray levels in the image,
the co-occurrence matrix
M
is of size
N
N
. Usually, the image is quantified
so that the total number of gray levels is smaller than the original image. This is
done in order to increase the appearance of pixel pairs contributing to each position
of the co-occurrence matrix. Take into account that, if the number of pixel pairs
contributing to each element of the matrix
M
i,j
is low, the statistical significance
will be poor. On the other hand, if
N
is small, much of the texture information
may be lost in the image quantization.
Given a pixel
p
(
l,m
)
at position
×
{
l, m
}
of the image
I
, and two parameters
{
D, θ
}
, a distance and an angle respectively, each element of the co-occurrence
matrix is defined as follows:
M
(
i, j
)=
|{
p
(
l,m
)
|
I
(
l, m
)=
i
and
I
(
l
+
D
cos(
θ
)
,m
+
D
sin(
θ
)) =
j
}|
∀
p
(
l,m
)
∈
I
(8)
The parameter
θ
is commonly set at
θ
=
{
0
0
,
45
0
,
90
0
,
135
0
}
. And the distance
D
is a scale parameter of the texture we are looking for. This set of four matrices
for each distance
D
is considered to be the minimal set in order to describe texture
second-order statistic measures [29].
The co-occurrence matrix is a tool for representing the appearance of the
pixel pairs; however, the matrix, as it is, is difficult to use as a descriptor of the
texture. Therefore, several measures describing the matrix can be used instead.
The most common measures are: Energy, Entropy, Inverse Difference Moment
(IDM), Shade, Inertia, and Prominence [29].
