A Novel Model Determination of Breast Cancer Stage … 25
3. Physical Parameters
Each level of malignancy disease has different patterns of pixel intensities. Of these patterns are probabilities pair gray-level at a certain
distance. Pair of gray-level probability at any distance can be determined by lack of uniformity entropy, sharpness structural variations contrast,
structural uniformity angular second moment, the local homogeneity inverse difference moment, linear dependence correlation, authenticity
properties mean, density deviation, lack of uniformity of the distribution of probability of occurrence gray-level pair at a certain distance entropy of
,
diff
H structural uniformity of the distribution of probability of occurrence
gray-level pair at a certain distance angular second moment of
diff
H and
the nature of the authenticity of the pair probability distribution of gray-level events at a certain distance mean
diff
H as follows [24, 25]:
[ ] [
]
, ,
, log
, ,
1 1
∑ ∑
= =
− =
t q
t r
y y
y y
y y
r q
r q
d y
y H
d y
y H
E Entropy
3.1 ,
, ,
1 1
2
∑ ∑
= =
− =
t q
t r
y y
y y
y y
r t
r q
d y
y H
y y
C Contrast
3.2 Angular second moment
ASM
[ ]
, ,
,
1 1
2
∑ ∑
= =
=
t q
t r
y y
y y
y y
r q
d y
y H
3.3 Moment differential inverse
MDI
∑ ∑
= =
⎥ ⎥
⎦ ⎤
⎢ ⎢
⎣ ⎡
− +
=
t q
t r
y y
y y
y y
r q
r q
y y
d y
y H
1 1
2
1 ,
, 3.4
for ,
q r
y y
≠
Correlation Corr
d y
H d
y H
d y
H d
y H
d y
y H
y y
r m
q m
y y
y y
y y
r m
q m
r q
r q
t q
t r
, ,
, ,
, ,
1 1
σ σ
μ μ
− =
∑ ∑
= =
3.5
Anak Agung Ngurah Gunawan 26
with ,
, ,
,
1
∑
=
=
t r
y y
y r
q q
m
d y
y H
d y
H 3.6
, ,
, ,
1
∑
=
=
t q
y y
y r
q r
m
d y
y H
d y
H 3.7
∑
=
=
t q
y y
y q
m q
d y
H y
M Mean
1
, ,
3.8
, ,
,
1 1
2
∑ ∑
= =
⎥⎦ ⎤
⎢⎣ ⎡
− =
t q
t p
y y
y q
m y
y y
p m
p q
d y
H d
y H
y y
D Deviation
3.9
∑ ∑
= −
= =
=
t r
q q
t r
y y
y y
y y
y r
q diff
d y
y H
d i
H
1
, ,
, ,
1
3.10
Entropy of ,
, log
,
1
∑
=
− =
t
i i
i diff
diff diff
d i
H d
i H
EHD H
3.11 ASM of
[ ]
, ,
,
1
2
∑
=
=
t
i i
i diff
diff
d i
H ASMHD
d i
H 3.12
Mean of
∑
=
=
t
i i
i diff
diff
d i
iH MHD
H
1
, ,
3.13 where
d y
y
r q
, ,
are the gray-level pixel value of unity, the value of the second pixel gray-level and the distance between the two pixels with pixels
unity, respectively. d
y y
H
r q
, ,
is a second-order histogram that describes the distribution of probability of occurrence of a pair of gray-level.
4. Logistic Regression Mapping Function
Kategori