Features of GLCM

1. FEATURES OF GLCM

2. Feature Comment
F2: Contrast
- Have discriminating ability.
- Rotationally-variant.
F3: Entropy
- Have strong discriminating ability.
- Almost rotational-invariant.
F4: Variance
- Have discriminating ability.
- Rotational-invariant.
F5: Correlation
- Have strong discriminating ability.
- Rotational-dependent feature.
Features on co-occurrence matrix
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 2

3. Feature Comment
F7: Sum average
- Characteristics are similar to
‘variance’/F4
- Rotational-invariant.
F10: Information Measure
of Correlation–1
- It has almost similar pattern of ‘sum
average’/F7 but vary for various
classes
- Varies significantly with rotation
F11: Information Measure
of Correlation–2
- It is computationally expensive
compare to others.
- Rotation-variant
Features on co-occurrence matrix
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 3

4. Features on co-occurrence matrix
Feature Comment
F1: Angular Second
Moment / Energy
- No distinguishing ability
F6: Inverse Different
Moment
- Similar to ‘angular second
moment’/F1
F8: Sum Variance - Similar to ‘variance’/F4
F9: Sum Entropy - Similar to ‘entropy’/F3
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 4

5. Energy
Entropy
Correlation
Contrast
Inverse Difference Moment
Variance
Sum Mean
Co-occurrence matrices
13 Haralick texture descriptors
Inertia
Cluster Shade
Cluster Prominence
Max Probability
Inverse Variance
Mode Probability
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 5

6. GLCM texture descriptors
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 6
GLCM features Physical meaning Formula
Autocorrelation
An autocorrelation function measures the linear spatial relationships
between spatial sizes of texture primitives. )
.
(
)
,
(
1
1
1
1
j
i
P
j
i
ATION
AUTOCORREL
G
j
G
i







Contrast
Contrast is a measure of intensity or gray-level variations between the
reference pixel and its neighbor. n
j
i
j
i
P
n
CONTRAST
G
j
G
i
G
n


 

 



)},
.
(
{
1
1
1
0
2
Correlation-m Correlation is a measure of gray level linear dependence between the pixels
at the specified positions relative to each other.
Using MAT Lab built in function
Correlation-p 




 





1
0
1
0
}
{
)
,
(
}
{
G
j y
x
y
x
G
i
j
i
P
j
i
N
CORRELATIO




Cluster
prominence
A measure of the skewness and asymmetry of the GLCM. When the cluster
prominence value is high, the image is less symmetric. 










1
0
4
1
0
)
,
(
}
{
G
j
y
x
G
i
j
i
P
j
i
PROM 

Cluster shade
Cluster shade is a measure of the skewness of the matrix and is believed to
gauge the perceptual concepts of uniformity. 










1
0
3
1
0
)
,
(
}
{
G
j
y
x
G
i
j
i
P
j
i
SHADE 

Dissimilarity
Dissimilarity is a measure that defines the variation of grey level pairs in an
image j
i
j
i
P
ITY
DISSIMILAR
G
j
G
i

 





),
.
(
1
1
1
1
Energy
ASM returns the sum of squared elements in the GLCM. It measures the
uniformity of an image. When pixels are very similar, the ASM value will be
large.







1
0
2
1
0
)}
,
(
{
G
j
G
i
j
i
P
ASM
Entropy
Entropy is a measure of information content. It measures the randomness of
intensity distribution. 







1
0
1
0
))
,
(
log(
)
,
(
G
j
G
i
j
i
P
j
i
P
ENTROPY
Homogeneity-m
Homogeneity returns a value that measures the closeness of the distribution
of elements in the GLCM to the GLCM diagonal. 2
1
1
1
1 )
(
1
)
.
(
j
i
j
i
P
HOMOGENITY
G
j
G
i 

 





Homogeneity-p Using MAT Lab built in function
Maximum
probability
Maximum probability measures the maximum likelihood of producing the
pixels of interest.
)
,
(
max(
. j
i
P
Y
PROBABILIT
MAX 

7. GLCM texture descriptors
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 7
GLCM features
(Mean±SD)
Physical meaning Formula
Sum of squares:
variance
Variance is a measure of the dispersion of the values around the mean of
combinations of reference and neighbor pixels. 







1
0
2
1
0
)
,
(
)
(
G
j
G
i
j
i
P
i
VARIANCE 
Sum average
It refers to the average of gray-level. 




2
2
0
)
(
G
i
y
x i
iP
AVER
Sum variance
It refers to the gray-level variability of the pixel pairs and is a measurement
of heterogeneity. Variance increases when the gray-scale values differ from
their means.






)
1
(
2
0
2
)
(
)
(
G
i
Y
X i
P
AVER
i
E
SUMVARIANC
Sum entropy GLCM-based texture feature entropy obtained from sum of histograms. 






2
2
0
))
(
log
)
(
G
i
y
x
y
x i
P
i
P
SENT
Difference variance
GLCM-based texture feature variance obtained from difference of
histograms.
Variance of px-y







1
0
2
)
(
))
(
(
G
i
y
x
y
x i
P
i
iP
i
CE
DIFFVARIAN
Difference entropy
GLCM-based texture feature entropy obtained from difference of histograms.
Entropy of px-y







1
0
))
(
log
)
(
G
i
y
x
y
x i
P
i
P
DENT
Information
measure of
correlation1
Correlation between entropies
)
,
max(
1
1
HY
HX
HXY
HXY
INFMC


Information
measure of
correlation2
2
/
1
)])
2
(
2
exp[
1
(
2 HXY
HXY
INFMC 



Inverse difference
normalized (INN)
It is the measure of the local homogeneity of an image. Unlike Homogeneity
1, INN normalizes the difference between the values by dividing over the
total number of discrete values.





 


1
0
2
1
0
)
,
(
)
(
1
1
G
j
G
i
j
i
P
j
i
INN
Inverse difference
moment
normalized
A measure of the local homogeneity of an image. IDMN weights are the
inverse of the Contrast weights (decreasing exponentially from the diagonal
i=j in the GLCM). Unlike Homogeneity 2, IDMN normalizes the square of the
difference between values by dividing over the square of the total number of
discrete values.









1
0
2
1
0
)
,
(
)
(
1
/
1
G
j
G
i
j
i
P
j
i
IDM

8. Co-occurrence matrices
• Global
• Features extracted are for the entire cube
• 13 Directions
• Four original 2D directions
• Nine new 3D directions
• 4 Distances
• 1, 2, 4, and 8 pixels
• 13 features extracted per distance
per direction
• 13*4*13=676 features per cube
2/28/2024 Department of Biomedical Engineering, SRMIST, KTR 8