Image Processing Reference
In-Depth Information
=− X
P L (k) log
p L (k)
=− X
P R (l) log
p R (l)
= X
P LR (k, l) log
p L,R (k, l)
x k,l / X
p LR (k, l)
x(k, l)
= X
p L (k)
p LR (k, l)
= X
p R (k)
p LR (k, l)
and is employed as a further descriptor employ.
Fourier analysis
As last feature descriptors we calculate the Fourier spectrum and use the difference of
absolute values of the ROI spectra. The features we adopt are the difference maximum and
the distance of this maximum from the centre.
To summarise we characterise each breast thermogram using the following set of features:
4 basic statisical features, 8 histogram features, 8 cross co-occurrence features, mutual
information and 2 Fourier descriptors. We further apply a Laplacian filter to enhance the
contrast and calculate another subset of features from the resulting images. In total we
end up with 38 descriptors per breast thermogram which describe the asymmetry between
the two sides. We normalise each feature to the interval [0;1] to arrive at comparable units
between descriptors.
For our experiment we gathered a dataset of 146 thermograms of which the correct
diagnosis (i.e. malignant or benign) is known. It should be noted that this dataset is
significantly larger than those used in previous studies (e.g. (Qi et al., 2000)). For all
thermograms we calculate a feature vector of length 38 as outlined above. We then train
the fuzzy classifier explained in the previous section using this data to obtain a classifier
that is capable of distinguishing cancer patients from healthy individuals.
As a first test we wish to examine how the classifier is able to separate the two classes
and hence train the classification system on all data available (i.e. on all 146 cases) and then
test it on all samples, that is for this experiment the training and test data are identical.
We experiment with different number of fuzzy partitions per attribute, from 2 to 15, and
show the results in Table 6.4 in terms of classification rate, i.e. the percentage of correctly
classified patterns.
Looking at Table 6.4 we see that in general classification performance increases with
an increase in the number of fuzzy partitions used. A classification rate of above 90% is
reached only based on partitioning the attribute values into 9 or more intervals; the best
performance is achieved with 15 partitions resulting in a classification rate close to 98%. We
notice that even though the classifiers are tested on the same data that was used for training
we do not achieve perfect classification. This suggests that we have indeed a challenging
data set to deal with as the two classes cannot even be separated by the non-linear division
our fuzzy classifier is capable of.
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