Dual Tree Complex Wavelet Transform, Probabilistic Neural Network and Fuzzy Clustering based on Medical Images Classification – A Study

International Journal of Advanced Engineering, Management and Science (IJAEMS) [Vol-4, Issue-12, Dec-2018]
https://dx.doi.org/10.22161/ijaems.4.12.2 ISSN: 2454-1311
www.ijaems.com Page | 793
Dual Tree Complex Wavelet Transform,
Probabilistic Neural Network and Fuzzy
Clustering based on Medical Images
Classification – A Study
Rajesh Sharma R, Akey Sungheetha
Department of Computer Science and Engineering, Adama Science and Technology University, Adama, Ethiopia.
Email: sharmaphd10@gmail.com,sun29it@gmail.com
Abstract— The venture suggests an Adhoc technique of
MRI brain image classification and image segmentation
tactic. It is a programmed structure for phase
classification using learning mechanism and to sense the
Brain Tumor through spatial fuzzy clustering methods for
bio medical applications. Automated classification and
recognition of tumors in diverse MRI images is enthused
for the high precision when dealing with human life. Our
proposal employs a segmentation technique, Spatial
Fuzzy Clustering Algorithm, for segmenting MRI images
to diagnose the Brain Tumor in its earlier phase for
scrutinizing the anatomical makeup.The Artificial Neural
Network (ANN) will be exploited to categorize the
pretentious tumor part in the brain. Dual Tree-CWT
decomposition scheme is utilized for texture scrutiny of an
image. Probabilistic Neural Network (PNN)-Radial Basis
Function (RBF) will be engaged to execute an automated
Brain Tumor classification. The preprocessing steps were
operated in two phases: feature mining by means of
classification via PNN-RBF network. The functioning of
the classifier was assessed with the training performance
and classification accuracies.
Keywords— fuzzy, neural network, computer aided
design, radial basis function.
I. INTRODUCTION
Automated classification and detection of tumors in
diverse Medical Resonance Image (MRI) is aggravated
for the requirement of high precision when dealing with a
human life. [1] In addition, the computer support is
employed in medical institutions due to the verity that it
might provide the outcomes of humans. It has been
established that double examination of medical images
outcomes acquired could direct to improved tumor
detection. But the double inspection procedure necessitate
high cost, that’s why fine software are employed to aid
humans in medical institutions for the advanced precision
as well as to diminish the operating cost. The requisite
schemes of monitoring and diagnosing the diseases assist
for detecting the occurrence of meticulous features by a
human observer. Because of many patients who come for
the treatment should have incessant surveillance, so that
quite a lot of practices for automated diagnostic systems
have been initiated to effort to resolve this crisis. Such
procedures offer qualitative fallouts for the diagnosis and
also the feature classification problem.
In this venture the automated classification of brain
Magnetic Resonance Images (MRI)[16],[17] by using
Learning Machine approach with Spatial Fuzzy
Segmentation technique are being exploited in this
proposal. The application of PNN for the classification of
MRI problems in the former scheme does not comprise
certain styles. In this proposed scheme, PNN embraces
the clustering and classification tactics in particular for
MR images possessing tribulations with huge training
notions. Thus subsequent to the complete pre-processing
phases, classification or clustering slants is indispensable
to the progress of Neural Network system predominantly
in medicine troubles.
Segmentation of brain tissues in GM, WM and tumor on
medical images is not only vital in serial treatment
monitoring of “disease burden” images but also acquiring
familiarity with the progress of image directed surgical
lines of attack[18]. Extorting the brain tumor part is the
chief step in setting up spatially localized radiotherapy
(e.g., Cyber knife, I MRT) which is more often than not
operated manually on contrast improved T1-weighted
magnetic resonance Images (MRI) in present clinical
laboratories. Where the T1 MR Images attained after
administration of any dissimilar agent like gadolinium,
blood vessels and part tumor pretentious parts, act as the
contrast that can pass to the Blood-Brain barrier which are
viewed as hyper intense regions. [19] There are assorted
endeavors for brain tumor segmentation in system which
employs a single modality which coalesces the multi

modalities and exploits priors acquired from population
atlases.
II. DUAL TREE COMPLEX WAVELET
TRANSFORM
The Complex Wavelet Transform (CWT) is
a complex-valued extension in normal Discrete Wavelet
Transform (DWT). It is a 2D wavelet transform which
offers multi resolution, sparse representation, and vital
description of the arrangement of an MRI image. [2]
Further, it affords a high scale of shift-invariance trait in
its magnitude. There is a downside to this transform is
that it exhibits 2d (where, d is the dimension of the signal
that is being transformed) redundancy in contrast to a
separable Discrete Wavelet Transform. The exploitation
of complex wavelets transforms in image processing was
initially done in 1995.
In the computer technologies, by employing the
perception of visual contexts, a person can effortlessly
focus on the candidate domains, where substances of
interest are be discovered, and then evaluates some more
features through the CWT method for those essential
regions. These features which are not required for global
regions, are of use in precise detection and recognition of
smaller objects. Likewise, the CWT is sometimes applied
to diagnose the activated voxels of cortex and in addition
the temporal Independent Component Analysis may be
employed to divide the fundamental independent bases
whose number is evaluated by Bayesian information
criterion.
2.1 Texture Analysis Overview
Texture is that inner property of all surfaces that
exhibits the visual patterns,with each having properties of
homogeneity. It comprises significant data about the
structural arrangement of the surface such as; clouds,
leaves, bricks etc. Texture portrays the association of the
surface to the adjacent environment. It is a feature that
shortly expresses about the analogous physical
composition of a surface.
Texture have their properties:
 Coarseness
 Contrast
 Directionality
 Line-likeness
 Regularity
 Roughness
Texture is one of the most imperative and absolute
narrative feature of an image, which is typified by the
spatial distribution of gray levels in a neighborhood. To
detain the spatial dependence of gray-level values that
donate to the acuity of texture a 2D dependence texture
scrutiny matrix is exploited. This 2D matrix is prepared
by decoding the image file.
2.2 Methods of Representation
There are 3 prime methods employed to explain the
texture as:
 Statistical schemes, depicts the textures employing
the statistical properties of the grey levels of the
pixels that embraces a surface image. These
properties are appraised using the Grey Level Co-
Occurrence Matrix (GLCM) or the wavelet
transformation of the surface.
 Structural schemes illustrate the textures as which
is being comprised of simple primitive structures
called “texels” or texture elements. These
rudiments are arranged consistently on a surface
on basis on some surface arrangement regulations.
 Spectral schemes have its foundation on some
properties of the Fourier spectrumand it expresses
the global periodicity of the grey levels of a
surface by calculating high-energy peaks in the
Fourier spectrum.
For optimal classification, the statistical slants of
portrayal are opted. Because it is in these practices that
effect in evaluating texture properties. The most
commonly practised statistical depictions of texture are:
 Co-occurrence Matrix
 Tamura Texture
 Wavelet Transform
2.3 Co-occurrence Matrix
It was projected by R.M. Haralick, the co-
occurrence matrix for the texture features offers the grey
level spatial dependence of texture of an image [3]. An
arithmetical definition of the co-occurrence matrix:
- Take the position operator as P(i,j),
- consider an n x n matrix A
- The element A[i][j] is the value of points with
grey level intensity g[i] occurs in the position
specified by P, with grey level g[j].
- Let C be the n x n matrix from A with the total
number of point pairs that satisfy P. C[i][j] is the
value of the joint probability that a pair of points
that is satisfying P will have values g[i], g[j].
- C is called as the co-occurrence matrix defined
by P.
For instance; consider an 8 grey-level image illustration
and a vector t that considers only one neighbor, we would
find:
Fig.1: Image example

Fig.2: Classical Co-occurrence matrix
Primarily the co-occurrence matrix is discovered, with the
orientation position and distance between image pixels.
Then consequential statistics are detached from the co-
occurrence matrix as the texture embodiment. Haralick
proposed the practical texture features
 Energy
 Contrast
 Correlation
 Homogeneity
 Entropy
For each Haralick texture feature, a co-occurrence matrix
is acquired. These co-occurrence matrices correspond to
the spatial distribution and the reliance of the grey levels
within a confined area. Each (i,j) th entry in the co-
occurrence matrices signify the probability of moving
from one pixel with a grey level of 'i' to another with a
grey level of 'j' under previously defined distance and
angle. From these outcomes in matrices, sets of statistical
courses are scrutinized, called as feature vectors.
Energy: It is a gray-scale image texture measure of
similar points that depicts the distribution of image gray-
scale homogeneity of weight and texture in equation 1.
-eq (1)
p(x,y) is the Grey Level Co-occurrence Matrix(GLCM)
Contrast: It is the key diagonal in near the moment of
Inertia that evaluates the value of the matrixconsisted and
the images of local changes in number values, exposes the
image clarity and texture of shadow depth in equation 2.
-eq (2)
Entropy: It quantifies image texture degree of
randomness, the space co-occurrence matrix for all values
are equivalent then it realizes the minimum value in
equation 3.
-eq (3)
Correlation Coefficient: It is the joint probability
occurrence of the specified pixel pairs.
Correlation: sum(sum ((x- μx) (y-μy) p(x, y)/σxσy))
Homogeneity: It computes the proximity of the
distribution of rudiments in the GLCM to its diagonal in
equation 4.
Homogeneity =sum (sum (p(x , y)/(1 + [x-y]))) –eq(4)
2.4 Probabilistic Neural Networks (PNN):
Probabilistic Neural Network (PNN) and
General Regression Neural Networks (GRNN) have their
analogous architectures, but there is a disparity:
Probabilistic Neural Network (PNN) executes
classification [4], where the object variable is classified,
whereas the General Regression Neural Network (GRNN)
[13] performs regression where the object variable is
incessant. If we opt for a PNN/GRNN network,[12]
DTREG will by design pick the precise type of network
in foundation on the category of target variable.
Fig.3: Architecture of a PNN
2.4.1 PNN networks layers:
1. Input layer — A single neuron is utilized for
each predictor variable. For the categorical
variables, N-1 neurons are employed, where N is
the number of categories. The input neurons
regulate the range of the values by calculation
process as subtracting the median and dividing
by the interquartile range.
2. Hidden layer —The neuron amasses the values
of the predictor variables for the case along with
the object value. When expressed with the x
vector of input values from the input layer, a
hidden neuron evaluates the Euclidean distance
of the test case from the neuron’s center point
and then smears the RBF kernel function by use
of the sigma value(s). The consequent value is
then moved on to the neurons in the pattern
layer.
3. Pattern layer / Summation layer — the
subsequent layer in the network is dissimilar for
PNN networks and for GRNN networks. The

definite target category of each training case is
accumulated with each hidden neuron; the
weighted value emerging out of a hidden neuron
is fed only to the pattern neuron that is
compatible to the hidden neuron’s category. The
pattern neurons add the values for the class they
signify (hence, it is a weighted vote for that
category). Former neuron is the denominator
summation unit the latter is the numerator
summation unit. The denominator summation
unit adds up the weight values resulting from
each of the hidden neurons. The numerator
summation unit adds up the weight values
multiplied by the definite object value for each
hidden neuron.
4. Decision layer — The decision layer is unlike
from PNN and GRNN networks. For PNN
networks, the decision layer contrasts the
weighted votes for each target category amassed
in the pattern layer and exploits the largest vote
to forecast the target category. For GRNN
networks, the decision layer partitions the value
stored in the numerator summation unit by use of
the value in the denominator summation unit and
employs the outcome as the predicted target
value.
The subsequent diagram is a concrete embodiment or
projected network employed in our venture:
Fig.4: Projected network employed in PNN
2.4.2 Functional flow of PNN
The function flow of the PNN which includes
major three layers [5] input, radial basis and competitive
layers.
III. WORKING PRINCIPLES OF PNN NETWORK
Although the execution is very dissimilar,
Probabilistic Neural Networks are conceptually similar to
K-Nearest Neighbor (k-NN) models. The fundamental
notion is that a foreseen target value of an article is
probable to be about the similar as other articles that have
close values of the predictor variables. Consider this
figure 5.
Fig.5: Working Model
Now, suppose we are putting effort to forecast the value
of a novel case signified by the triangle with predictor
values x=6, y=5.1. Should we foresee the target as
positive or negative? Observe that the triangle is position
approximately precisely on top of a dash depicting a
negative value. But that dash is in a quite strange position
contrasted to the other dashes which are clustered
underneath the squares and left of center. So it could be
that the fundamental negative value is an odd case.The
adjacent neighbor classification operated for this instance
depends on how many neighboring points are thought of.
If 1-NN is exploited and only the closest point is
considered, then obviously the novel point should be
categorized as negative since it is on top of a known
negative point. Conversely, if 9-NN classification is
employed and the closest 9 points are considered, then the
consequence of the surrounding 8 positive points may
overbalance the close negative point.A Probabilistic
Neural Network builds on this base and simplifies it to
consider all of the other points. The distance is calculated
from the point being analyzed to each of the other points,
and a radial basis function (RBF) [11] (also called a
kernel function) is put into the distance to compute the
weight (influence) for each point.
3.1. Advantages and disadvantages of PNN
networks:
1) It is typically much quicker to train a
PNN/GRNN network than a multilayer
perceptron network.
2) PNN/GRNN networks often are more precise
than multilayer perceptron networks.
3) PNN/GRNN networks are comparatively numb
to outliers (wild points).
4) PNN networks generate precise predicted target
probability scores.
5) PNN networks come up to Bayes optimal
classification.
6) PNN/GRNN networks are slower than multilayer
perceptron networks at categorizing new cases.

7) PNN/GRNN networks necessitate more memory
space to amass the model.
3.2.1. Removing unnecessary neurons
One of the drawbacks of PNN models contrasted
to multilayer perceptron networks is that PNN models are
huge because of the fact that there is one neuron for each
training row. [14] This effects the model to run slower
than multilayer perceptron networks when employing
scoring to predict values for new rows. DTREG offers an
alternative to cause it get rid of redundant neurons from
the model after the model has been constructed.
Eliminating needless neurons has three reimbursements:
1. The size of the amassed sculpt is diminished.
2. The time necessary to apply the model during
scoring is lessened.
3. Detaching neurons often enhances the accuracy
of the model.
The process of eliminating pointless neurons is an
iterative process. Leave-one-out validation is employed to
measure the blunder of the model with each neuron being
eliminated. The neuron that effects the least increase in
error (or possibly the largest reduction in error) is then
eliminated from the model. The process is recurred with
the residual neurons until the stopping criterion is
achieved.When superfluous neurons are rejected, the
“Model Size” section of the scrutiny report illustrates how
the error varies with various numbers of neurons. You can
view a graphical chart of this by clicking Chart/Model
size.There are three criteria that can be chosen to steer the
exclusion of neurons:
1. Minimize error – If this option is preferred, then
DTREG eliminates neurons as long as the leave-
one-out error remains steady or decreases. It
stops when it discovers a neuron whose
exclusion would cause the error to increase
above the minimum found.
2. Minimize neurons – If this option is preferred,
DTREG excludes neurons until the leave-one-
out error would surpass the error for the model
with all neurons.
3. Number of neurons – If this option is preferred,
DTREG diminishes the least significant neurons
until only the specified number of neurons
remain.
3.3 PNN:
NEWPNN generates a two layer network [6].
The first layer has RADBAS neurons, and computes its
weighted inputs with DIST, and its net input with
NETPROD. The second layer has COMPET neurons,
and computes its weighted input with DOTPROD and its
net inputs with NETSUM. Only the first layer has
prejudices. NEWPNN sets the first layer weights to P',
and the first layer biases are all set to 0.8326/SPREAD
effecting in radial basis functions that cross 0.5 at
weighted inputs% of +/- SPREAD.
3.4 Methodology:
An elucidation of the derivation of the PNN
classifier was provided. PNNs had been utilized for
categorization issues.[15] The PNN classifier offered
good precision, very small training time, robustness to
weight changes, and negligible retraining time. There are
6 stages involved in the projected prototype which are
initiating from the data input to output. The initial stage is
should be the image processing system. Principally in
image processing system, image acquisition and image
enhancement are the steps that have to do. In this
manuscript, these two steps are skipped and all the images
are composed from accessible resource. The proposed
model necessitates transforming the image into a format
capable of being influenced by the computer. The MR
images are transformed into matrices form by using
MATLAB. Then, the PNN is exploited to categorize the
MR images. Finally, performance based on the outcome
will be scrutinized at the end of the development stage.
IV. FUZZY CLUSTERING MODEL
Fuzzy clustering plays a vital position in resolving
crisis in the domains of pattern identification and fuzzy
model recognition [7]. A diversity of fuzzy clustering
techniques have been projected and most of them are
pertaining to the distance criteria. One predominantly
employed algorithm is the Fuzzy C-Means (FCM)
algorithm. It exploits reciprocal distance to evaluate fuzzy
weights. A more competent algorithm is the new FCFM.
It calculates the cluster center using Gaussian weights,
utilizes large initial prototypes, and adds processes of
eliminating, clustering and merging. In the subsequent
sections we confer and contrast the FCM algorithm and
FCFM algorithm.Spatial Fuzzy C Means method inte
grates spatial data, and the membership weighting of each
cluster is manipulated after the cluster distribution in the
neighborhood is considered. The first pass is similar as
that in standard FCM to compute the membership
function in the spectral domain. In the second pass, the
membership data of each pixel is mapped to the spatial
domain and the spatial function is evaluated from that.
The FCM iteration proceeds with the new membership
that is integrated with the spatial function. The iteration is
stopped when the maximum difference flanked by cluster
centers or membership functions at two successive
iterations is less than a least threshold value.
The Fuzzy C-Means (FCM) algorithm was initiated. The
notion of FCM is employing the weights that diminishes
the total weighted mean-square error by equation 6:
J(wqk, z(k)) = (k=1,K) (k=1,K) (wqk)|| x(q)- z(k)||2
(k=1,K) (wqk) = 1 -eq(5)

wqk = (1/(Dqk)2)1/(p-1) / (k=1,K) (1/(Dqk)2)1/(p-1) ,
p > 1 –eq(6)
The FCM permits each feature vector to fit in to every
cluster with a fuzzy truth value (between 0 and 1), which
is evaluated using Equation (6). The algorithm allocates a
feature vector to a cluster in accordance to the maximum
weight of the feature vector over all clusters [8].
4.1 A New Fuzzy c-means Implementation
Algorithm Flow
Fig. 6: Fuzzy C-means Algorithm Flow.
In order to weigh against the FCM with FCFM, our
execution permits the user to opt for initializing the
weights using feature vectors or arbitrarily. The process
of initializing the weights using feature vectors allocates
the first Kinit (user-given) feature vectors to prototypes
then calculates the weights.
4.2 Standardize the Weights over Q.
During the FCM iteration, the evaluated cluster
centers get closer and closer. To prevent the quick
convergence and always clustering into one cluster as in
equation 7.
w[q,k] = (w[q,k] – wmin)/( wmax – wmin) –eq(7)
before normalizing the weights over Q. Where
wmax, wmin are maximum or minimum weights over the
weights of all feature vectors for the scrupulous class
prototype.
4.3 Eliminating Empty Clusters.
In consequence to the fuzzy clustering loop we
add a step to exclude the empty clusters. This step is put
outside the fuzzy clustering loop and before computation
of tailored XB validity. Without the abolition, the
minimum distance of prototype pair utilized in Equation9
may be the distance of empty cluster pair. We entitle the
method of abolishing small clusters by passing 0 to the
process so it will only remove the empty clusters. In
consequence to the fuzzy c-means iteration, for the
rationale of contrast and to choose the optimal outcome,
we add Step 9 to compute the group centers and the
customized Xie-Beni clustering validity  :
The Xie-Beni validity is a product of compactness and
separation measures [9],[10]. The compactness-to-
separation ratio  is defined by Equation( 8) and (9).
 = {(1/K)(k=1,K)k
2}/Dmin
2 -eq(8)
k
2 =(q=1,Q) wqk || x(q) – c(k) ||2 -eq(9)
Dmin is the minimum distance between the cluster centers.
The Modified Xie-Beni validity  is defined in equation
(10).
= Dmin
2/ {(k=1,K)k
2 } –eq(10)
The variance of each cluster is computed by summing
over only the members of each cluster rather than over all
Q for each cluster, which compares with the unique Xie-
Beni validity measure.
k
2 ={q: q is in cluster k} wqk || x(q) – c(k) ||2 –eq(11)
The spatial function is comprised into membership
function as given in Equation (11).
V. CONCLUSION
A new-fangled algorithm for Brain Tumor
Classification is proposed. This novel scheme is a blend
of Dual tree Wavelet Transform, Probabilistic Neural
Network and the fuzzy clustering with the implementation
of GLCM. By employing these algorithms a competent
Brain Tumor Classification technique was built with
maximum recognition rate. Simulation outcomes
exploiting Brain Tumor database illustrated the capability
of the projected method for most favorable feature
extortion and proficient Brain Tumor classification. The
capability of our proposed Brain Tumor Classification
system is established on the basis of acquired outcomes
on Brain Tumor image database. On other Brain Tumor
image databases the other grouping are there for training
and test samples. In this proposal only 5 classes of Brain
tumors are considered, with regard to an instance of 15
test images for example, but this technique can be
extensive to more classes of Brain tumors.
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