2.3: Log gabor
filter:
The Gabor filter was originally introduced
by Dennis Gabor[5] and the concept has been extended for two
dimension by Daugman as follows
(1)
--(2)
Where 
and 
defines the center
frequency and 
denotes the spread of
the Gaussian window. The maximum bandwidth of the gabor filter is limited to
one octave, hence gabor filter is not suitable if the application demands broad
spectral information[18]. Log Gabor filter introduced by Field can
be constructed with arbitrary bandwidth. Log gabor filter consist of logarithmic
transformation of the gabor domain[3], which eliminates the DC
component in medium and high pass filter.
Log gabor has a transfer function of
the form G(w) = ---
------------------------(3)
Log gabor does not form orthogonal basis
set, hence there are many options for arranging filter[4]. Two
contradictory requirements, while selecting the filters are even coverage of
the part of the spectrum that application demands, and the output of each of
the filter in the bank should be as independent as possible. Filters are
constructed by taking in to consideration of radial component and angular
component. Radial component controls the frequency band that the filter
responds and the angular component, controls the orientation of the filter. The
specification of the log gabor filter used in this work are:
Number
of wavelet scale = 8
Number
of filter orientation = 6
Wavelength
of the smallest scale filter(Min wavelength)=2
Scaling
factor between successive filter = 1.18-3.28
Ratio of the standard deviation of the
Gaussian describing the log gabor filter’s transfer function in the frequency
domain to the filter center frequency = 0.65.
Lnorm=1
Feedback
=0
(a) (b)
Figure(4)
a. Original image(Green Channel) b. Output after pre processing and after
applying log gabor
Figure(4) indicates the log gabor filter
output which gives high energy only in the case drusen presence. In the drusen
area local energy is maximum and we get high value of energy for the images
with drusens.
2.3.1: Gray Level Cooccurance matrix:
It depicts how frequently different
combination pixel values appear in image. The set of features derived from the
matrix are called as Haralick features[16]. Symmetrical and normalized
GLCM is used for the feature extraction at angle of 135degree. Ten features are
extracted namely energy, contrast, correlation, homogeneity, entropy,
autocorrelation, dissimilarity, cluster shade, cluster prominence and maximum
probability.
2.4: Feature
Selection Technique:
Feature selection algorithms (FSA) consist
of four steps namely, subset generation, subset evaluation, stopping criterion
and result validation. Feature selection methods can be grouped under three
headings namely embedded, filter and wrapper. In embedded techniques, feature
selection can be considered to be part of the learning. The filter approach
evaluates and choose feature subsets based on general characteristics of data.
In the present work, Fuzzy Entropy thresholding technique is used to select the
most discriminative feature which will be use full for classification purpose.
Fuzzy entropy concept is introduced in the year 1972[27] and further
refinement is done [10],[14].
A new method of weighted fuzzy entropy is
introduced in[15]. Calculate the ideal vector corresponding to the
class one. Calculate the similarity between test class feature vector and the
ideal vector. The decision to which class the feature vector belongs is made
according to the similarity value. In Ideal case, we get one if the test
feature vector belongs to the same class as ideal feature vector else zero.
While calculating the fuzzy entropy values, low entropy value is obtained for
high similarity value. Hence the features with lowest entropy values are
retained, which alone will be useful for classification purpose. By using this
technique, eight features are removed and two features namely autocorrelation
and contrast is chosen.
Table 1: Feature vector values for normal and AMD images
|
Feature
vector type
|
Normal
fundus image
|
AMD
|
|
|
|
Mean
± SD
|
Mean
±SD
|
|
|
Energy
of the log gabor
|
15±5
|
200±50
|
|
|
filter
|
|
|
|
Contrast
from GLCM
|
0.5
±0.1
|
0.1
±0.05
|
|
Autocorrelation
from
|
61±2
|
71±2
|
|
GlCM
|
|
|
|
|
|
|
|
|
|
2.5: Classification:
In this stage, after pre processing for
all the training images features are extracted and feature database is formed.
The test feature vector extracted from test image is compared with the feature
database and the label has been assigned by the classifier. The classifier
performance is evaluated in terms of sensitivity, specificity and positive
predictive accuracy provided in table[3]. Locating the neighbours in instance
space and classifying the unknown instance with the same class label as that of
the located neighbour is used in k-nearest neighbour classifier. Random
forest classifier is constructed by using the 1000 decision trees. Decision
tree learning is the best method comes under supervised learning approaches.
SVM seeks normally a hyper plane to separate data. Using Kernel trick SVM
performs efficiently non linear classification. In the present work radial
basis function is used as kernel.
Table
2: Number of Images used for training and testing
|
Number of images
|
Normal
|
Abnormal
|
|
Training
|
70
|
30
|
|
Testing
|
80
|
70
|
2.6 Experimental
Results and Discussion:
Three different classifiers are used to do
the classification of the test images. One hundred and fifty normal image and
hundred images with AMD are used in this work..Ten fold cross validation is
done by partitioning the images. Nine subset used for training and one subset
used for testing. The cross validation procedure is repeated for ten times by
keeping exactly one subset once for testing. Then averaging is done to get
single estimated value. Table (2) gives the total number of images for validating
the proposed method.. It is imperative from table(1) large interclass variation
is present in selected feature vector which makes the classification process
simple and accurate. Performance of the classifier is represented in table(3)
and random classifier outperforms the other two classifier chosen in the
present work.
-------------------- (4)
Specificity = 
-------------------- (5)
Positive predictive accuracy = 
------- (6)
CONCLUSION:
A new method for the detection of Age
related Macular degeneration is proposed with the novel feature vector namely
energy from log Gabor filter, autocorrelation and contrast computed from GLCM
after applying feature selection technique namely Fuzzy entropy thresholding.
After removal of blood vessel and optic disk, log Gabor filter bank is applied
to compute energy and autocorrelation, contrast from GLCM. Higher
classification rate is obtained in the case of random forest classifier. The
proposed method achieves higher classification rate compared to the existing
techniques in literature.
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