Segmentation clustering analysis is to find the overall compactness

Segmentation of tumour
using K mean clustering algorithm

S Venkateswar Viswanath, Mrs. Sobha T S

We Will Write a Custom Essay Specifically
For You For Only $13.90/page!


order now

 

Abstract-In radiotherapy using 18-fluorodeoxyglucose
positron emission tomography (18F-FDG-PET), the accurate delineation of the
biological tumour volume (BTV) is a crucial step. In this study, the authors
suggest a new approach to segment the BTV in F-FDG-PET images. The technique is
based on the k-means clustering algorithm incorporating automatic optimal
cluster number estimation, using intrinsic positron emission tomography image
information.

Partitioning data into a finite number of k homogenous and
separate clusters (groups) without use of prior knowledge is carried out by
some unsupervised partitioning algorithm like the k-means clustering algorithm.
To evaluate these resultant clusters for finding optimal number of clusters,
properties such as cluster density, size, shape and separability are typically
examined by some cluster validation methods. Mainly the aim of clustering
analysis is to find the overall compactness of the clustering solution, for
example variance within cluster should be a minimum and separation between the
clusters should be a maximum.

 

I.                 
INTRODUCTION

There
are several approaches to validate the segmentation techniques such as phantom
studies and the macroscopic surgical specimen obtained from histology. The use
of macroscopic samples for validation of segmentation techniques in positron
emission tomography (PET) images is one of the most promising approaches
reported so far in clinical studies, the procedure consists of the comparison
of the tumour volumes defined on the PET data with actual tumour volumes
measured on the macroscopic samples recorded from histology (where PET was
performed prior to surgery). Segmentation using the cluster –based algorithms
is very popular, but the main problem in this case is the determination of the
optimal and desired number of clusters. In this, we have implemented an
approach based on k-means algorithm with an automatic estimation of the optimal
number of clusters, based on the maximum intensity ratio in a given volume of
interest (VOI).

 

 

II.               
METHEDOLOGY

 

Calculate
the VE for a range of k (2–50
clusters), and the

optimal
number which corresponds to the minimum of SVEs. This method gives good results

but
consumes a significant computation time by performing the clustering for a
large range

of
cluster values before selecting the optimal number of clusters. Several
approaches have

been
proposed in the literature to identify the optimal cluster number to better fit
the data,

three
of them are used.

Unfortunately,
the results are not promising because they are not adapted to PET image

segmentation.
So our goal in this study is to improve the k-means clustering method, by

incorporating
an automatic determination of the optimal number of clusters using a new

criterion
based on PET image features.

After
analysing the variation of the maximum activity (intensity) of the uptake  

() in the VOI by scanning all slices , we
conclude for all patients that the maximum

intensity
value decreases from middle to frontier slices, and the maximum intensity is
often

situated
almost at the centre of the BTV. The optimal cluster number has a minimum value

at
the centre of the BTV, and increases from central to frontier slices. This
correlation

between
the optimal number of clusters and the maximum intensity motivates our choice
of

the
following slice image feature:

 

 

where
 is
the maximum activity (intensity) of the uptake  in the

corresponding
slice,  is
the maximum activity in all slices that encompasses tumour

volume
BTV inside the  , and  is the difference between the

maximum
and the minimum values of (Imax (slice)/Imax (VOI)) in the .

Similarly
to , the new criterion , has a maximum value
for the middle slices and

decreases
for the frontiers of the BTV. Note that the r values range from ‘0’ to
‘1’ for all

patients.

3.3.2
Modelling: This section is dedicated to finding a
relationship between the optimal

number
of clusters k, and the new
criterion r. This relationship
could be used to determine

the
optimal cluster number for the segmentation of new PET images using only the
new

slice
image feature r. After analysing the variation of k in function
of r criterion (for all

patients
included in this study), we use two fitting models: an exponential and a power

function
given by below, respectively,

k
= ? ? e?. r + 1

k
= a ? + 1, (4.2)

Where
?, ?, a, b are coefficients of fitting models and r
is the proposed criterion. The fitting

accuracy
evaluation is based on the R-square criterion. Note that we added ‘1’ to
the

original
fitting equation to avoid clustering the image with one cluster for the high
values of

r.

3.3.3
Generalisation: The aim of this step is to automate the
choice of the optimal cluster

number
for all patients using one corresponding relationship function by defining a

generalised
model for all patients. For this reason, we have divided the database randomly

into
two parts of 50% each. The first part (validation set), contains three patients
is used for

optimising
the model coefficients and fixing the optimal power and exponential generalised

model.
The second part (test set), contains four patients, is used for testing the
accuracy of

the
fixed optimal model.

According
to the R-square criterion, the optimal exponential and power generalised
function

can
be rewritten as follows:

k
= 46.52e?5.918 × r
+ 1

k
= 1.683r?1.264 + 1

 

 

 

 

 

 

k
mean alogorithm 3 :

 

 

III.             
CONCLUSION

 

A  new unsupervised cluster-based
approach for segmenting the BTV in 18F-FDG-PET images is introduced. The system
is more reliable and has very less error. It can be improved by MMMindex technique used
in determining an optimal value of K in K-means
clustering1 , for which
k-means clustering it uses a method to find an optimal value of k number of
clusters, using the features and variables inherited from datasets. The new
proposed method is based on comparison of movement of objects forward/back from
k to k+1 and k+1 to k set of clusters to find the joint probability, which is
different from the other methods and indexes that are based on the distance.