Determination of physical parameter model 2237
2. MATERIALS AND METHODS
A. Data Acquitions
This study was approved by the ethics committee of health research at the Dr Soetomo Surabaya Hospital, focused on number 07 Panke KKEI2012 and the
patient informed consent are signed alltogether. All the mammographic images are collected from the data base computer at radiodiagnostic Dr. Soetomo
Surabaya Hospital, these images of mammographic labelling Kodak brand, type 6900 laser imager dryview data prints of mammographic films and its placed in
the direct view 975 CR. The reason importing mammographic image data from a computer data base caused theese images is not deformed by the external scratch
influences. Images saved in bmp format and sampled with a matrix size of 5 cm x 5 cm.
B. Radiation Interaction in The Breast Cancer Mater.
If the x-ray enters a material in this case breast cancer, can result in ionization, but ionization is produced mainly through the process of secondary
ionization. Thus, the x-rays interact with breast cancer just a few pairs of primary ions are formed. Primary ions were subsequently conducted in order to obtain the
secondary ionization ion pair more than which had been formed in the primary ionization process.
When x-rays electromagnetic waves into the breast tumor, the radiation intensity will decrease, while the energy remains unchanged. The relationship
between the radiation intensity of a material can be written, With I, I
, , and L is the intensity of each of the transmitted radiation, the radiation intensity at first, the linear absorption coefficient of materials, and
material thickness. There are three main processes that can occur when x-rays pass through
breast cancer, namely photoelectric effect, Compton scattering and pair production. The third process is the next release electrons that can ionize other
atoms in the material. Opportunities for interaction between the x-ray with breast cancer, is determined by the linear absorption coefficient . Because the
absorption intensity of the electromagnetic wave through three main processes, the value of is also defined by opportunities for all three processes, ie f for
photoelectric,
c for Compton scattering and pair production pp. Total
absorption coefficient t of the three coefficients are
t
=
f
+
c
+
pp
C. The physical scale film mammographic X-ray photos.
There are ten films that have physical scale on the x-ray mammographic images is [1]:
Entropy is a measure of unequal and defined as
2238 Anak Agung Ngurah Gunawan et al
∑ ∑
, , log
, ,
+
, -
, , +
. 01 2 3 4 5
, , +
,
6 7899 3 5 5
, , + 1 ;
+
,
for y
r
≠ y
q
1 8 ∑
∑ , ,
=
,
=
, +
=
,
=
, + with
=
, , , +
=
, + , , +
4
=
, +
7 68 8 ?
=
,
, =
, +
A
BCDD
8, + , , +
E EC
9
BCDD BCDD
8, + log
BCDD
8, +
C CC
Determination of physical parameter model 2239
. 01 2 3 4 5
9
BCDD
8, +
BCDD
8, +
, C
CC
4 9
BCDD
8
BCDD
8, +
C CC
With Y
Q
, yr, d, are respectively pixel gray-level value of unity, the value of the pixel gray-level and the distance between pixels of unity with the second pixel. H
Y
Q
, yr, d is the second-order histogram illustrating the distribution of likelihood of occurrence of a pair of gray-level.
High uniformity will show a lower structural variation. Conversely if the value is low it can be concluded that the sign of possible events related microcalsification
greater. Y
Q
- yr
2
is the unequal size. These measurements provide evidence of how sharp variations in the structure of the image [1].
D. Logistic mapping function
Review the following probability function: F G and G 9H+ where the dependent variable that is bound to free variables
IH
C
J, and H
C
linearly independent with X
j
that is H
C
K ∑
L L
H
L
Where Y, is output category, eg: y=0, normal category, y = 1, The category is rather normal, and so
on, y=k, particular category. This form is multinomial, or multiple linear rate.
Review the logistic function logit the following:
1 8 IF G 1|HJ 1 N F G 1|H+
1 F G 1|H+O ≅ 1 N F G 1|H+
1 F G 1|H+O G Further
G: IR
S
, R
,
, R
T
, R
U
J with X ∶ Iall of EntropyJ For example the category Y = Z
k
1 c
d eS|f+
S d eS|f+
g R
h
, Note: Use of functional ln natural logarithm related to qualitative mapping
Entropy to qualitative histological types of breast cancer, which is not satisfy the normal Gaussian, statistically
d eS|f+
S d eS|f+
i
j
or
S d eS|f+
d eS|f+
i
j
to obtain: 1 F G 1|H+ F G 1|H+
i
j
, F G 1|H+I1 ;
i
j
J 1,
2240 Anak Agung Ngurah Gunawan et al
F G 1|H+
S kSlm
noj
p
, And
F G 1|H+ as a multinomial logistic regression of statistical model. eg for
IG R
h
J
hS,,,
, it will be found in all categories ∑
F
, hS
R
h
1|H+ 1, to
IR
h
1J NR
S
1, 7, 3
R
,
1, q, 3
O F R
,
1|H+
S kSlm
nor
p
, And because the fulfillment of all categories infiltrating into force,
F
U hS
R
h
1|H+ 1 F R
S
1|H+ ; F R
,
1|H+ 1, so that F R
S
1|H+ 1 F R
,
1|H+ F R
S
1|H+ 1 s 1
I1 ;
i
r
Jt E.
Linear Regression Multinomial Function as Outcome of The Histological Type
Review the following linear regression: R
h
R
h
; u v
hL L
w h,LS
x ; Bkn. MeanHd10 Z
k
is the outcome impact of a number of k
L
p Z
k0
is the intersection intersection of the axis, or the initial value of outcome, R
h
R
h
For the tribe k∑
v
hL L
w h,LS
p ; Bkn. MeanHd10 0 ∑
v
hL L
w h,LS
is a nuisance parameter variable-free number k
L
p the rank of 1 one or linear.
Bkn. MeanHd10 is the correction factor by the number of outcome k
L
p For example:
Determination of physical parameter model 2241
R
,
R
,
; u v
,L L
w ,,LS
x ; B2n. MeanHd10 R
T
R
T
; u v
TL L
w T,LS
x ; B3n. MeanHd10 R
U
R
U
; u v
UL L
w U,LS
x ; B4n. MeanHd10 There are illustrated as bellows:
Figure 1. Linear Regression Model
3. RESULTS AND DISCUSSION
