CHAPTER 3 TUMOR DETECTION BASED ON NEURO-FUZZY TECHNIQUE

Transcription

1 32 CHAPTER 3 TUMOR DETECTION BASED ON NEURO-FUZZY TECHNIQUE 3.1 INTRODUCTION In this chapter we present the real time implementation of an artificial neural network based on fuzzy segmentation process of the MRI data to detect various tissues like white matter, gray matter, CSF and tumor. The hierarchical self organizing map and fuzzy c means algorithms are used to classify the image layer by layer. The HSOM achieves multi-scale segmentation viewed at different levels of abstraction of the feature space. The multilayer segmentation results of this work are shown to have gray matter which will be represented at one level of abstraction, white matter at another and so forth which would make interesting consequences from the viewpoint of clinical diagnosis. MRI scan can be used as an extremely accurate method of disease detection throughout the body. It has rapidly evolved into an accepted modality for medical imaging of disease processes in the musculoskeletal system especially the foot and brain due to the use of non-ionizing radiation (Suchendra et al 1997, Suchendra et al 2001). MRI provides a digital representation of tissue characteristic that can be obtained in any tissue plane. The images produced by an MRI scanner are best described as slices through the brain. MRI has the added advantage of being able to produce images which slice through the brain in both horizontal and vertical planes.

2 33 Segmentation is an important process to extract information from complex medical images. Segmentation has wide application in medical field (Pal and Pal 1993). The main objective of the image segmentation is to partition an image into mutually exclusive and exhausted regions such that each region of interest is spatially contiguous and the pixels within the region are homogeneous with respect to a predefined criterion. Widely used homogeneity criteria include values of intensity, texture, color, range, surface normal and surface curvatures. During the past many researchers in the field of medical imaging and soft computing have made significant survey in the field of image segmentation (Haralick and Shapiro 1985, Fu and Mui 1981). Image segmentation techniques can be classified based on edge detection, region or surface growing, threshold level, classifier such as fuzzy, k-means, Self Organizing Map (SOM), and feature vector clustering or vector quantization. Vector quantization has proved to be a very effective model for image segmentation process. Vector quantization is a process of portioning an n-dimensional vector space into M regions so as to optimize a criterion function when all the points in each region are approximated by the representation vector associated with that region. There are two processes involved in the vector quantization: one is the training process which determines the set of codebook vector according to the probability of the input data, the other is the encoding process which assigns input vectors to the code book vectors. Vector quantization process has been implemented in terms of the competitive learning neural network (CLNN).

3 34 Figure 3.1 Structure for hierarchical SOM Self Organizing Map (SOM) is a member of the CLNNs and this can be the best choice when implementing vector quantization using neural network (Kohomen 1988). The importance of SOM for vector quantization is primarily due to the similarity between the competitive learning process employed in the SOM and the vector quantization procedure. The main shortcoming of the SOM is that the number of neural units in the competitive layer needs to be approximately equal to the number of regions desired in the segmented image. It is not however, possible to determine and priorities the correct number of regions M in the segmented image. This is the main

4 35 limitation of the conventional SOM for image segmentation. The input to the HSOM is a square image of size N X N, and the neural units in each competitive layer are organized as square arrays. One may further assume that the size of competitive layers are l X l,2 X 2,4 X 4... N X N, where N = 2 n = N/2 is the size of the first layer. This structure very much resembles the quad tree data structure (Bhandarkar 1997). The structure of the HSOM is illustrated in Figure 3.1. Here, 3D conversion of the input image means that the n dimensional vectors space of f(x, y). HSOM combines the idea of regarding the image segmentation process as one of the data abstractions where the segmented image is the final domain independent abstraction of the input image. The hierarchical segmentation process for a hierarchical structure is called abstraction tree. Figure 3.2 Abstraction tree containing all levels of abstraction The abstraction tree depicted in Figure 3.2 is similar to the quad tree data structure [Bhandarkar, 1997]. The root node in the quad tree represents the entire image. The image is divided into four quadrants which are represented by the four child nodes of the root node. The partitioning of a quadrant (i.e. a node) into four sub quadrants (i.e. four child nodes) is

5 36 repeated until the leaf nodes (which represent the individual pixels of the input image) are reached, resulting in a pyramidal data structure. The quad tree is used extensively in image segmentation algorithms based on the splitand-merge technique. Clustering is the process of grouping a data set in a way that the similarity between data within a cluster is maximized while the similarity between data of different clusters is maximized and is used for pattern recognition in image processing. To recognize a given pattern in an image various techniques have been utilized but in general two broad categories of classifications have been made: unsupervised techniques and supervised techniques. In the unsupervised method, data items that are to be clustered are not preclassified while in supervised clustering the data points are preclassified. One of the well-known unsupervised algorithms that can be applied to many applications such as image segmentation, fuzzy c means (FCM) etc. FCM algorithm is one of the popular fuzzy clustering algorithms which are classified as constrained soft clustering algorithm. A soft clustering algorithm finds a soft partition of a given data set by which an element in the data set may partially belong to multiple clusters. Moreover, there is a constraint on the function that the membership degree of a point in all the clusters adds up to 1. The researchers in this field have used SOM or HSOM or FCM separately as one of the tool for the image segmentation of MRI brain for the tumor analysis. In this chapter, we propose a hybrid technique combining the advantages of HSOM and FCM and implemented for the MRI image segmentation process to detect various tissues like white matter, gray matter, CSF and tumor.

6 IMPLEMENTATION OF HSOM AND FCM ALGORITHM In this section we discussed the implementation of the HSOM and FCM algorithm in detail. First, we described the HSOM structure, learning procedure and then FCM with abstraction tree. The pseudo code for the above neuro fuzzy technique is also presented at the end of this section. The HSOM is organized as pyramidal structure consisting of multiple layers where each layer resembles the single layer SOM. The detailed explanations and the structure of the HSOM were presented by Bhandarkar et al 1996, Bhandarkar et al 1997, Bhandarkar and Nammalwar Learning process consists of sequential corrections of the vectors representing neurons. In every step of the learning process a random vector is chosen from the initial data set and then the best-matching (the most similar to it) neuron coefficient vector is identified. The winner is selected, which is more similar to the input vector and we have used energy, entropy, standard deviation features for feature extraction in existing work they have chosen commonly features like mean, median standard deviation. The distance between the vectors is measured by two methods, euclidean and mahalanobis metrics and is given by i i x w min x w (3.1) c where x is the neuron, w is the winning neuron vector and w c i is the weight vector. The modified weight vector coefficients can be calculated by t w t h t xt wt w i 1 i ci (3.2) where t is the epoch number (discrete-time index), x (t) is the vector and is obtained by selecting a sample randomly for iteration t. The function h ci (t) is called neighborhood function and it represents a non-increasing function of

7 38 time and the distance between the winning neuron and its neighbors on the grid. The function h ci (t) consists of two parts: the proper distance function and the learning rate function and is given by h t h r r t at, (3.3) c i where, r determines neuron position on the grid. Cluster is a group of vectors with the distance between any two of them shorter than that between this group and the neighboring ones. With the SOM algorithm the clusters structure can be represented by visualizing the distance between the reference vectors (neurons weight coefficients). Clustering of SOM is motivated by the fact that it achieves a nonlinear projection of the input distribution to a two dimensional grid. This mapping has the property that it can be used to visualize and explore properties of multidimensional data in a very effective manner. Hence, a properly trained SOM would be a good sampling of the data sample. The result of neighborhood function h(t) is an initial cluster center (centroids) for fuzzy c means algorithms Fuzzy C-Means Algorithm (FCM) FCM algorithm based on the concept of fuzzy C- partition which was introduced by various researcher in this field Ruspini (1970), developed by Dunn (1973 and 1974) and generalized by Bezdek (1974, 1980 and 1981) The aim of FCM is to find cluster centers (centroids) that minimize dissimilarity functions. In order to accommodate the fuzzy partitioning technique, the membership matrix (U) is randomly initialized as c i 1 U ij 1, j 1,..., n (3.4)

8 39 where, i is the number of cluster and j is the image data points. The dissimilarity function can be computed as c c n m 2 J ( U, c, c,..., c J u d (3.5) 1 2 c ) i1 i ij i1 j1 where, U ij is between 0 and 1, c i is the centroid of cluster i, d ij is the Euclidian distance between i th centroid (c i ) and j th data point, m is a weighting exponent and the value is greater than one. The minimum of dissimilarity function can be computed as ij U ij c k 1 1 d d ij kj 2 /( m1) (3.6) where, d ij = x i -c j, d kj = x i -c k, x i is the i th of d-dimensional data, c j is the d-dimension center of the cluster and * is any norm expressing the similarity between any measured data and center. This iteration will stop when Max ij { u (k+1) ij -u (k) ij } < ε, where ε is a termination criterion between 0 and 1, whereas k are the iteration steps. The steps of the FCM algorithm has been listed as follows 1. Initialize U=[u ij ] matrix, U (0) 2. At k-step: Initialize centers vectors C (k) = [c j ] taken from HSOM mapping clustering algorithm 3. Update U (k), U (k+1), then compute the dissimilarity function U ij c k 1 1 d d ij kj 2 /( m1) (3.7) 4. If U (k+1) - U (k) < ε then STOP; otherwise return to step 3.

9 40 In the first step, the algorithm selects the initial cluster centers from SOM clustering algorithm. Then, in later steps after several iterations of the algorithm, the final result converges to actual cluster center. Therefore a good set of initial cluster is achieved and it is very important for an FCM algorithm. If a good set of initial cluster centers is chosen, the algorithm make less iterations to find the actual cluster centers. The winning neural units and their corresponding weight vectors from each layer result in a hierarchical structure termed as an abstraction tree. Each node in the abstraction tree represents the region of the image at a specified level of abstraction. A segmented image is generated on demand by traversing the abstraction tree in the breadth first manner starting from the root node until some criterion is met. The size of the abstraction tree (weight vector) is expanded if the sum of the variances of weight vector is divided by the size of the weight vector which is less than element of weight vector. Otherwise the node is labeled as a closed node and none of its descendants are visited. Regions corresponding to the closed nodes constitute a segmented image and the resulting segmented image usually contains the regions from different abstraction levels Pseudo code of the neuro fuzzy technique Procedure seg (image) im=imread(image); /* Read the input image*/ /*Find the Feature value for the input image (Features are Energy MN Entropy 1 M N M i1 j1 i1 j1 N X b Standard Deviation*/ 2 i, j i, j*logx, i, j feature(1,1)=energy(im) feature(1,2)=entropy(im)

10 41 feature(1,3)=std(im) /* Segmented result using abstraction tree*/ for each layer of segmentation( 1 to k)) map=2; /*initialize som map value*/ /*find the winner neuron*/ [win,wx,wy]=winner(map,im) /*find the som mapping vector*/ mw(x,y,a)=mw(x,y,a)+gain*(mw(wx,wy,a)-mw(x,y,a)) /*find the abstraction tree*/ sum=sum(var(mw))/map if(sum>mw(i,j)) e(i,j)=mw(i,j) ; /*find the cluster center*/ hc=hclucter( e ) c=hc /*inverse transformation*/ [m,n]=size(c) ; /*segmentation using fuzzy c means*/ clustfcm(im,c,n) else /* expand the som mapping*/ map=map+2; k=k+1; end; end seg; 3.3 RESULTS AND DISCUSSION The results of the implementation of the hybrid neuro fuzzy segmentation process are discussed in this section. Any computer aided analysis; the execution time and accuracy are important parameters for analyzing medical images. The number of tumor pixel is detected by various methods with the execution time is presented in Table 3.1. In these results, we

11 42 have calculated the number of pixels that are affected by the tumor cells and the results have been compared with the ground truth and existing results. For the 256x256 MRI brain tumor image we have calculated ground truth tumor pixels are Our proposed neuro fuzzy based segmentation technique detects accurate tumor pixels. We have also studied the execution time for different segmentation techniques. SOM k-means and HSOM k-means require less time than the proposed one. The weight vector value obtained for the proposed method is less compared to the existing results. This is due to the clustering process and abstraction level technique. The number of map value, number of cluster and cluster values are detected by various methods with the execution time is presented in Table 3.2. Our proposed method gives accurate cluster values than the existing methods. This is due to the mahalanobis distance and fuzzy c-means method. Table 3.1 Weight vector value, tumor pixels and execution time of HSOM-Fuzzy compared with existing methods Sl.No Types of segmentation 1. SOM-kmean [Suchendra 2001] Value of weight vector Total No. of Tumor pixels for proposed work Execution Time (seconds) SOM fuzzy SOM fuzzy HSOM-kmean [Suchendra 2001] 5. HSOM-fuzzy (Our result)

12 43 Table 3.2 Execution Time and cluster values (256x256 synthetic images) of HSOM-Fuzzy compared with existing methods Eucli. Distance Map No. of cluster Cluster values SOM-kmeans HSOM-kmeans HSOM-Fuzzy Execution Time (seconds) SOM HSOM Mahal. Distance The variation of the weight vector values for the different types of segmentation process is depicted in Figure 3.3. The weight vector for the SOM with fuzzy is 8x8. The weight vector for the SOM with k-means is about 12 x 12. This weight vector value for the SOM with fuzzy is higher but it is less in our method. The weight vector for the HSOM with k-means and HSOM with fuzzy are also depicted in the above Figure 3.3. The weight vector for the HSOM with k-means is also 12 x 12. Here, we have achieved the lowest value of weight vector as 6x6 for the HSOM with c means. The input features for the calculation of the weight vector for the HSOM with fuzzy c means includes some new feature like energy, entropy and standard deviation. We have used three new features but we have achieved the lowest value of weight vector values. This is due to the fuzzy clustering technique and the abstraction level.

13 Value of weight vector SOM-kmean SOM-fuzzy SOM-fuzzy HSOM-kmean HSOM-fuzzy Types of Segmentation Figure 3.3 Relationship between the weights vectors with the types of segmentation techniques Figure 3.4 shows the variation of the total number of tumor pixels detected of an image with various segmentation techniques. The value of the tumor cells detected with our proposed implementation is about 3223 for the both HSOM and SOM with fuzzy but the value of the tumor pixel detected for the SOM k means and HSOM k means is only The used standard input features are mean, median and standard deviation for the SOM and HSOM with k means. In our proposed implementation of the neuro fuzzy technique the input features are entropy, energy, standard deviation. The increase in the value of the detected tumor cells is due to the abstraction level and fuzzy clustering process.

14 No.of tumor pixels SOM-kmean SOM-fuzzy SOM-fuzzy HSOM-kmean HSOM-fuzzy Types of segmentation Figure 3.4 Variation of total number of tumor pixels with types of segmentation techniques Execution time (sec) SOM-kmean SOM-fuzzy SOM-fuzzy HSOM-kmean HSOM-fuzzy Types of segmentation Figure 3.5 Variation of execution time with types of segmentation In image processing, execution time is an important parameter to analyze any image in general and in medical image is particular. Variation of the execution time for various segmentation processes is depicted in

15 46 Figure 3.5. The execution time for the SOM-FCM is seconds as against seconds in SOM-kmeans and HSOM - FCM is seconds as against seconds in HSOM kmeans. The increase in the execution time for the proposed implementation is due to the layer-by-layer abstraction level and fuzzy clustering techniques. (a) (b) The (c) (d) Figure 3.6 (a) Input image (256x256) (b) Gray matter segmented at level 1 (2x2) (c) GM, WM with tumor cell segmented at level 2 (4x4) (d) WM, GM, tumor and CSF segmented at level 3 (6x6) Figure 3.6 shows the tested segmented images with various levels of abstractions of the MRI brain image. The original image (256 x 256) is shown in Figure 3.6.a. Figure 3.6.b-d shows the segmented image generated

16 47 by neuro fuzzy technique with the level of abstraction. Here, we have achieved the white matter segmentation at level 1 of abstraction. Various tissues like white matter, gray matter and some small portions of tumor cells are segmented at level 2. As level of abstraction increases, the visibility of the different tissues also increases. In our implementation the segmentation of white matter, gray matter, tumor and CSF are achieved at level Validation of HSOM-Fuzzy Vs. Ground Truth Validation of magnetic resonance image segmentations is an important but difficult problem. We have tested the algorithm on more than 100 patients each patient has 3 views, were within the view range of the system and known to contain tumor. After processing by the system, the views were compared with ground-truth tumor segmentations that were created by radiologist hand labeling (Velthuizen 1994). Error was found between the two segmentations, both false positives (where the system indicated tumor pixels where ground truth did not) and false negatives (where ground truth indicated tumor pixels that the system did not). To compare how well (on a pixel level) the HSOM-Fuzzy method corresponded with ground truth. Accuracy is calculated from the number of true positives divided by the total tumor size. Table 3.3 lists the results of the HSOM-Fuzzy system on tumor volume basis. The results show that the HSOM-Fuzzy system performs well overall. Totally, we have experienced 4 patients each patient has 3 views that has a percent match rating of 91% or higher. Views of that show considerable false negative presences which are primarily the result of one situation. Overall, the HSOM-Fuzzy approach tended to significantly overestimate the tumor volume. Only one volume in Table 3.3 shows

17 48 underestimation (Patient 4 view 1), and that tumor pixel can be viewed as an edema so we can not predict tumor volume accurately. The tendency to overestimate is consistent with the system's paradigm, since only those pixels positively believed to be non-tumor are removed, defaulting areas of uncertainty to be labeled as tumor. Table 3.3 Comparison of HSOM-Fuzzy Tumor Segmentation vs. Hand Labeled Segmentation per Volume Patient(P) Scan Views Tumor size True positive False positive False negative Accuracy P1-4 yrs/male P1-4 yrs/male P1-4 yrs/male P2-46 yrs/male P2-46 yrs/male P2-46 yrs/male P3-8 yrs/female P3-8 yrs/female P3-8 yrs/female P4-58 yrs/male P4-58 yrs/male P4-58yrs/male

18 49 Total tumor volume for ground truth, the HSOM-Fuzzy method, HSOM-kmeans, Fuzzy and kmeans are compared in Table 3.4. When compared to other methods, HSOM-Fuzzy volumes showed closer to the ground truth volume in 6 of the 12 views. More importantly, comparing their respective performances in Tables 3.4, HSOM-Fuzzy has a higher number of true positive than the other two methods, suggesting the HSOM-Fuzzy method more closely matched ground truth than all methods. Table 3.4 Tumor Volume Comparison for (GT = Ground Truth Volume) Patient(P) Scan Views GT/ Tumor size Fuzzy Fuzzy HSOM- HSOMkmeans P1-4 yrs/male P1-4 yrs/male P1-4 yrs/male P2-46 yrs/male P2-46 yrs/male P2-46 yrs/male P3-8 yrs/female P3-8 yrs/female P3-8 yrs/female P4-58 yrs/male P4-58 yrs/male P4-58yrs/male

19 50 (a) (b) (c) (d) (e) (f) Figure 3.7 (a)-(c) (d)-(f) Raw images for 4 yrs/male in different views (512x512) and is corresponding final segmented results using HSOM-Fuzzy method Figure 3.7. Shows that, 512x512 raw images for 4 years boy with 3 views of MRI scan, and its correspondence segmented results with gray matter, white matter, CSF and tumor. Here red color indicates tumor volume.

20 CONCLUSION A neuro-fuzzy based segmentation process to detect brain tumor was implemented. We studied the performance of the MRI image in terms of weight vector, execution time and tumor samples detected and compared the results with the existing ones. A layer by layer abstraction level with fuzzy clustering technique was implemented to detect various tissues like white matter, gray matter, CSF and tumor. We have achieved a higher value of detected tumor pixels than any other segmentation techniques. We have also achieved the weight vector value for the neuro fuzzy is (6x6) with the additional input features. The weight vector value, the number of tumor cells and the execution time will also be studied with different distance classifier technique. The change of growth rate of the tumor of the same patient analyses may also be undertaken.