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presence of microcalcification only, but determination of the type of carcinoma and benign breast cancer are not supported.The classifying types of Infiltrating Duktal Carcinoma and Infiltrating
Lobuler Carcinoma breast cancer histopathology using physical parameter in86,36 sensitivityin previous research are succeeded [11]. The determination of the level of the contra lateral breast health
using physical parameters in 93.75 sensitivity [12], the breast cancer stadium state in 86.67 sensitivity of [13]. Also, the readibility x-rays results of mammography on breast cancer
histopathological type determination using a special pattern croping through physical parameters in 97.5 sensitivity are succeeded too [14].
This paper organized as follows, section 2 discussing the radiation intensity on ca mammae, section 3 about physical quantities of the result of X-ray mammography images, the probability function in
section 4, section 5 about the multinomial linear regression function as an outcome types of carcinoma and benign, results and discussion in section 6 and the last section are conclusions.
2. The Radiation Intensity on Ca Mammae
Increase of the radiation absorption intensity depends on breast cancer density increasing due to pixel intensity values of carcinoma and benign types are different. So that the physical parameters between
the types of carcinoma and benign are different. The transmittance of the X-ray radiation intensity are written in equation 2.1 bellow [11][12][13][14].
I
1
= I e
–μd
2.1 where I
1
, I ,
μ, d are transmitted beam intensity, the intensity of light at first, absorption coefficient, breast cancer density, respectively.
3. Physical Quantities of X-Ray Mammography Results
The following physical parameters are nonuniformity, contrast, uniformity, local homogeneity, correlation, feature represents the nature, feature represents the density, nonuniformity of hdiff,
uniformity of hdiff and the feature represents the nature of hdiff derived from the x-ray mammography results. All the physical parameters are written as follows equations [11][12][13][14][15].
3.1 3.2
3.3
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3.4 for
3.5 where,
3.6 3.7
3.8
3.9 3.10
3.11 3.12
3.13 With Hy
q
, y
r
, d is distribution of probability of occurrence of a pair of gray-level value separated by a given displacemen vector d.
4. Probability Function
Consider probability functions bellows, and
dependent in , for
liniearly independent each others,
are fulfilled. For is output categories i.e for
, carcinoma,
, benign, and others. The logistic functions are written as follows: 3.13
further with
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for example, ,
The qualitative mapping the entropy to carcinoma and benign ca mammae are in abnormal Gaussian satisfied. So that,
, or ,
, ,
, and
as statistics model of logistics multinomial regression, for , will be
in all the cathegories are , furthermore:
For all the histopathology categories are fullfiled with,
5. The multinomial linear regression function as the outcome of carcinoma and benign types
Consider linear regression function bellows,
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where Zk is outcome for , entirely. Z
k0
as outcome initial values for ,
with .
is pertubation parameters for a number
are in linear form. For last term, as outcome correction factors for all
. For example:
Illustratively, the above expression are depicted in figure 1 as bellows.
Figure 1. Logistic and Linear Regression Model
6. Results and Discussion
Figures 2, 3, are types of carcinoma and benign mammogram images, respectively.
2 3 Figure 2. Carcinoma Type Figure 3. Benign Type
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Mammography images had been taken from radiology installations at Dr. Soetomo Hospital,Surabaya, RSUP Sanglah and RSU. Primamedika, Denpasar, supported by Sony Brand ICR type 3600M
apparatus. All the images in bmp format are stored which sample sized in 2 cm x 2 cm matrices. Table 1. Physical Quantity Intervals
No Physical Quantity
Benign Carcinoma
1 Anguler Secound Moment
0,00015 - 0.01013 0.00013 - 0.08280
2 Inverse Difference Moment
0.01527 - 0.08977 0.01106 - 0.39200
3 Mean
71.55468 - 195.80523 71.16284 - 220.92240
4 Deviation
18.84672 - 56.86512 11.06751 - 93.33126
5 Entropy of the Difference Second Order
Histogram 1.32977 - 2.05756
1.29424 - 2.14790 6
The Second Anguler Moment of the Difference Second Order Histogram
0.01051 - 0.05878 0.00806 - 0.11134
7 Mean of the Difference Second Order
Histogram 7.65163 - 43.77752
7.27355 - 55.92737 All the physical quantities above formulated bellows:
Z:= -17056.786 + 13939360.273MA[9] -14975532.439MA[10] + 79507.135MD[5]
+
123275.512MD[6] -52858.798 MD[7] -29317.721MD[8] -46033.962MD[9] - 84405.247MD[10] -2616.686MN[1] + 5924.284MN[2] -3119.844MN[3] -453.778MN[4] -
1114.523MN[5] + 3720.727MN[6] -3618.971MN[7] + 11.610MN[8] + 2152.569MN[9] - 885.095MN[10] -1327.391D[1] + 2202.098D[2] -3.143D[3] -3364.818D[4] + 7916.137D[5] -
10676.240D[6] + 6323.275D[7] + 415.555D[8] -1671.692D[9] + 197.645D[10] + 23576.501EH[1] + 7048.037EH[2] -98617.823EH[3] + 59177.808EH[4] -53465.845EH[5] +
81134.008EH[6] + 743.337EH[7] -81311.924EH[8] + 74475.699EH[9] -4742.767EH[10] + 169258.070MAH[1] + 31944.202MAH[2] -1083908.718MAH[3] + 826751.786MAH[4] +
888282.531MAH[5] -918006.126MAH[6] -487749.444MAH[7] -1455971.004MAH[8] + 1382311.075MAH[9] + 844659.147MAH[10] -124.008MHD[1] + 74.265MHD[2] -
744.240MHD[3] + 1741.103MHD[4] + 430.726MHD[5] -116.272MHD[6] -1461.422MHD[7] -1022.368MHD[8] + 894.912MHD[9] + 346.808MHD[10];
Probability for carcinoma and benign types each are formulated,
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The uniformity, local homogeneity, feature represents the nature, feature represents the density, nonuniformity of hdiff, uniformity of hdiff, feature represents the nature of hdiff parameters are
optimium to differ carcinoma and benign types in this research.
7. Conclusion
