In the modern world, early tumor detection is crucial for the best course of therapy. We have introduced a novel medical image segmentation technique with this propose algorithm, which could be helpful for accurately orienting the size and form of brain tumors from MRI brain images. With the aid of the K-means and FCM algorithms already in use, the initial segmentation result was obtained. It has been recognized that the FCM approach is better suited for medical picture analysis. Next, as demonstrated in Figure2, we employed fuzzy c means thresholding to enhance the multilevel thresholding method. This suggested FCMMT technique produces superior results with better segmentation.
1.1 Fuzzy C- Means Thresholding
This research paper introduces 3-class FCM based thresholding to be used for initializing the multilevel thresholding and LS evolution and regulating the controlling parameters. C classes are created by dividing N objects using FCM clustering. N in our approach is the number of pixels in the image, therefore for 3-class FCM clustering, C=3 and N=Nx x Ny. An objective function based on a weighted similarity measure between each of the c-cluster centers and the image's pixels is iteratively optimized by the FCM algorithm. The FCM algorithm uses iterative optimization of an objective function based on a weighted similarity measure between the pixels in the image and each of the C-cluster centers. A local extremism of the objective function indicates an optimal clustering of the input data. The objective function that is minimized is given by formula (1)
(1) where
zj∈
Z;
v={
v1,
v2,…,
vc} and
z={
z1,
z2,
z,…,zN} &
vi∈
V and where||*|| is a norm expressing the similarity between any measured data value and the cluster centre; m is [1, ∞] is a weighting exponent and can be any real number greater than 1.
Calculations suggest that best choice of m is in the interval [1.5, 2.5], so m=2 is used here as it is widely accepted as a good choice of fuzzification parameter.
The fuzzy c-partition of given data set is the fuzzy partition matrix U= with i=1, 2….C and j=1, 2, 3…N, uij indicate the degree of membership of jth pixel to ith cluster.
The membership functions are subject to satisfy the following conditions.
for j=1,2,3,…
N;
for i=1,2,…,C; 0≤
uij ≤1
The aim of FCM algorithm is to find an optimal fuzzy c-partition by evolving the fuzzy partition matrix U= [uij] iteratively and computing the cluster centers. In order to achieve this, the algorithm tries to minimize the objective function Q by iteratively updating the cluster centres and the membership functions using the following equations. FCM clustering is used to partition N objects into C classes. In this method, N is equal to the number of pixels as formula 2
(2)Each pixel is ultimately assigned to the cluster for which its membership value is maximum after completing FCM clustering. The threshold value is determined by taking the mean of the maximum of cluster 1 and the minimum of cluster 2, or the maximum of cluster 2 and the minimum of cluster 3, based on the intensity distribution produced from the picture histogram. The image's intensity distribution is taken into consideration while using this threshold selection technique. This method of threshold selection takes into account the intensity distribution in the image. This choice helps in obtaining optimum threshold values for different images obtained under different conditions (Masood, 2013).