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compute the probabilities P ( C A i
L ij =
true )where C A i and C B j are the classes of regions A i and B j , respectively.
Given our class definition in (2), we can easily model these relations through a
causal independence model using the logical OR. The Bayesian network RegNet
models this scheme.
At the second stage of our Bayesian network framework we combine the com-
puted region probabilities from RegNet by using a causal independence model
with the logical OR to obtain the probability for cancer of the respective view.
Thus we represent the knowledge that the detection of at least one cancerous re-
gion is sucient to classify the whole view as cancerous whereas the detection of
more cancerous regions will increase the probability of the view being cancerous.
We call this Bayesian network ViewNet .
At the third stage, we combine the view probabilities obtained from ViewNet
into a single probabilistic measure for the breast as a whole. As additional inputs
we use the likelihoods for cancer (NSc) for each view computed by the single-view
CAD system, which are already indicators for the level of suspiciousness of the
view. To explicitly account for the view dependences we model the probabilities
obtained from ViewNet and the single-view measure by two v-structures, whose
outputs are combined using the logical OR function. We refer to this Bayesian
network model as to BreastNet .
In the last, fourth, stage, we compute the probability for a case being cancer-
ous using two combining schemes. Since in the screening programs breast cancer
occurs mostly in one of the breasts then the first simple combining technique
is to take the maximum of both breast probabilities obtained from BreastNet .
As a second more advanced scheme we use a causal independence model and
the MAX function to combine the breast probabilities from BreastNet and the
single-view likelihoods for cancer for each breast. We refer to the latter as to
CaseNet and to the whole multi-view detection scheme as to MV-CAD-Causal .
= true
|
L ij
= true )and P ( C B j
= true
|
6 Application to Breast Cancer Data
6.1 Data Description
The proposed model was evaluated using a data set containing 1063 screening
exams from which 383 are cancerous. All exams contained both MLO and CC
views. The total number of breasts were 2126 from which 385 had cancer. All
cancerous breasts had one visible lesion in at least one view, which was verified
by pathology reports to be malignant. Lesion contours were marked by, or under
supervision of, a mammogram reader.
For each image (mammogram) we selected the first 5 most suspicious regions
detected by the single-view CAD system. In total there were 10478 MLO re-
gions and 10343 CC regions. Every region is described by 11 continuous features
automatically extracted by the system, which tend to be relatively correlated
across the views. These features include the neural network's output from the
single-view CAD and lesion characteristics such as spiculation, focal mass, size,
contrast, linear texture and location coordinates. Every region from MLO view
 
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