Image Processing Reference

In-Depth Information

Edge Value

In MR imaging, the histogram of the given image is in general unimodal. One side of the

peak may display a shoulder or slope change, or one side may be less steep than the other,

reflecting the presence of two peaks that are close together or that differ greatly in height.

The histogram may also contain a third, usually smaller, population corresponding to points

on the object-background border. These points have gray levels intermediate between those

of the object and background; their presence raises the level of the valley floor between the

two peaks, or if the peaks are already close together, makes it harder to detect the fact that

they are not a single peak.

As the histogram peaks are close together and very unequal in size, it may be di
cult

to detect the valley between them. In determining how each point of the image should

contribute to the segmentation method, the current method takes into account the rate of

change of gray level at the point, as well as the point's gray level (edge value); that is, the

maximum of differences of average gray levels in pairs of horizontally and vertically adjacent

2×2 neighborhoods (Maji et al., 2008; Weszka and Rosenfeld, 1979). If ∆ is the edge value

at a given point I
m,n
, then

1

4
max{|I
m−1,n
+ I
m−1,n+1
+ I
m,n
+ I
m,n+1
−I
m+1,n
−I
m+1,n+1
−I
m+2,n
−I
m+2,n+1
|,

|I
m,n−1

∆ =

+ I
m,n
+ I
m+1,n−1

+ I
m+1,n
−I
m,n+1

−I
m,n+2

−I
m+1,n+1

−I
m+1,n+2

|}

According to the image model, points interior to the object and background should gen-

erally have low edge values, since they are highly correlated with their neighbors, while

those on the object-background border should have high edge values (Maji et al., 2008).

Haralick's Textural Feature

Texture is one of the important features used in identifying objects or regions of interest in

an image. It is often described as a set of statistical measures of the spatial distribution of

gray levels in an image. This scheme has been found to provide a powerful input feature

representation for various recognition problems. Haralick et al. (Haralick et al., 1973)

proposed different textural properties for image classification. Haralick's textural measures

are based upon the moments of a joint probability density function that is estimated as

the joint co-occurrence matrix or gray level co-occurrence matrix (Haralick et al., 1973;

Rangayyan, 2004). It reflects the distribution of the probability of occurrence of a pair

of gray levels separated by a given distance d at angle θ. Based upon normalized gray

level co-occurrence matrix, Haralick proposed several quantities as measure of texture like

energy, contrast, correlation, sum of squares, inverse difference moments, sum average,

sum variance, sum entropy, entropy, difference variance, difference entropy, information

measure of correlation 1, and correlation 2. In (Haralick et al., 1973), these properties were

calculated for large blocks in aerial photographs. Every pixel within these each large block

was then assigned the same texture values. This leads to a significant loss of resolution that

is unacceptable in medical imaging.

In the present work, the texture values are assigned to a pixel by using a 3×3 sliding

window centered about that pixel. The gray level co-occurrence matrix is constructed by

mapping the gray level co-occurrence probabilities based on spatial relations of pixels in

different angular directions (θ = 0
◦
, 45
◦
, 90
◦
, 135
◦
) with unit pixel distance, while scanning

the window (centered about a pixel) from left-to-right and top-to-bottom (Haralick et al.,

1973; Rangayyan, 2004). Ten texture measures - angular second moment, contrast, corre-

lation, inverse difference moment, sum average, sum variance, sum entropy, second order

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