Combining Wavelet Texture Features and Deep Neural Network for Tumor Detection and Segmentation Over MRI

3.1 Noise Removal

The noise removal of a MR image is a significant process of MRI tumor detection and segmentation. Consider the gray-scale input image I_in, which has a few of the noises like Gaussian noises, etc. The noise image certainly disturbs the output. So noise removal is a necessary part. By removing the noise from the image, there is better accuracy for the classification stage. In this work, in the noise-removal stage, we utilized the Gaussian filter, which is used to remove the noise from image I_in. Finally, we obtain the noise-free image I, which is used for further processing.

3.2 Feature Extraction

After the noise removal, the image is given to the feature-extraction stage. Feature extraction is an important stage for medical image classification. The beneficial features of the images are extracted from the image for classification purposes. To extract a good feature from the images is a challenging task. There are many feature-extraction techniques that are available. In this work, we extract GLCM and wavelet-based GLCM features from the images.

3.3 Feature Selection Using OFPA

After calculating the features, we have to decrease the dimension of the feature vector because a high number of features are a great obstacle for classification. Consequently, a feature dimension-reduction technique is applied to reduce the features’ space without losing information. We decrease the number of features and take away the unrelated, redundant, or noisy information. In our work, we developed the OFPA algorithm for selecting the optimal features from the feature vector. The following steps are used to select the features.

Step 1: Solution Representation

To optimize the features, the OFPA algorithm initially creates an arbitrary population of the solution. Solution creation is an important step of the optimization algorithm that helps to identify the optimal solution quickly. Each image has the n number of features; among them, we select optimal features. The selected features are used for solution generation. Let us assume that there is M flower or solution in the entire population, and each flower contains N pollen. The whole flower population is represented as S=(F₁, F₂,…, F_M), where F_m is the m^th flower, and m∈[1, M] is the order number of the flower in the population. Each flower is represented as F_m=(P₁, P₂,…, P_N), where, P_n is the n^th pollen (feature) in the m^th flower, and n∈[1, N] is the pollen index. The initial solution representation is given in Table 2.

Step 2: Opposite Solution for FPA

Rendering to opposition-based learning (OBL) familiarized by Tizhoosh in 2005 [28], the current solution and its opposite solution are measured simultaneously to get a better approximation for the current solution. It is provided that an opposite pollen solution has a better chance to be closer to the worldwide optimal solution than random pollen solution. The opposite pollen positions (OS_i) are entirely defined by constituents of S_i.

where OP_i=L_i+U_i−P_i with OP_i ∈[L_i, U_i] is the position of the i^th opposite pollen OP_i. Now, we obtain two sets of initial solutions. These solutions are given in the next steps.

Step 3: Fitness Calculation

After generating the solution, the fitness function is evaluated. The selection of the fitness is a crucial aspect in the OFPA algorithm. It is used to evaluate the aptitude (goodness) of candidate solutions. Here, classification accuracy is the main criteria used to design a fitness function. The fitness computation is executed for each solution. For each iteration, the fitness is calculated using equation (2),

where TP represents the true positive, TN represents the true negative, FP represents the false positive, and FN represents the false negative.

Step 4: Update Solution Based on FPA

After the fitness calculation, we update the solution on the basis of flower pollen algorithm (FPA). The main target of a flower is basically reproduction by pollination. Flower pollination frequently associates with the transfer of pollen that frequently related to pollinators, like birds. The global pollination can be characterized mathematically as equation (3).

where, Fit is the pollen i or solution vector F_i at iteration t, and G_* is the current best solution found among all solutions at the current generation/iteration. The step size is controlled by a scaling agent γ. Here, L(λ) denotes the Levy flight-based step size that corresponds to the ability of pollination.

Γ(λ) is the standard γ function, and this distribution is precise for considerable steps (g>0). The local pollination and flower constancy can be represented as

where, Fjt and Fkt are pollen from various flowers of the same plant species mimicking the flower fastness in a confined neighborhood. For a local random walk, Fjt and Fkt derive from the same species, then ∈ is drawn from a uniform distribution as [0, 1].

Step 5: Termination Criteria

The algorithm discontinues its execution only if a maximum number of iterations is achieved, and the solution that is holding the best fitness value is selected. Once the best fitness is attained by means of the FPA algorithm, the selected feature is given to the classification stage.

3.3 Classification Stage

The selected features are given to the classification stage. In this classification, we used the DNN. An artificial neural network model with the multiple layers of the hidden units and outputs is termed DNNs. Moreover, it consists of both pre-training (using generative deep belief network or DBN) and fine-tuning stages in its parameter learning. The main aim of this paper is to train the features of images in the particular data set, i.e. to find the right weight that can be used to correctly classify the input features.

(i) Pre-training Stage Using a Deep Belief Network (DBN)

In the training stage, we use a DBN that is a deep architecture and a feed forward neural network, i.e. with numerous hidden layers. The instance of the DBN network is shown in Figure 2. At this time, the abridged features are provided to the input of the DBN. At this time, we implement the learned weights as the initial weights of the DBN; this weight is engaged for generatively pre-training a DNN. The DBN model permits the network to produce visible activations on the basis of its hidden units’ states, which characterizes the network belief. This layer comprises an input layer that encircles the input units (called visible unit v), L number of hidden layers, and at last, an output layer that has one unit for each class is measured. The parameters of a DBN are the weights W_i among the units of layers i−1 and i, the biases B(i) of layer i (note that there are no biases in the input layer). To prepare the parameters is one among the chief difficulties for training DNN. Currently, the random initialization results in an optimization algorithm to determine the poor local minima of the fault function resulting in low generalization. We implemented the restricted Boltzmann machine (RBM) to work out the above issue. A DBN can be investigated as a composition of simple learning modules by stacking them. This uncomplicated learning module is known as the RBMs.

Figure 2:

Proposed DBN with Three Hidden Layers.

Restricted Boltzmann Machine: An RBM is an exclusive type of Markov random field that has one layer of (typically Bernoulli) stochastic hidden units and one layer of (typically Bernoulli or Gaussian) stochastic visible or observable units. RBMs can be indicated as bipartite graphs, in which all visible units are connected to all hidden units, and there are no visible–visible or hidden–hidden connections. The important structure of RBM is quantified in Figure 3.

Figure 3:

RBM Architecture.

In the training phase, primarily we analyze the energy performance of the visible layer v and the hidden layer h. A joint configuration (v, h) of the visible (Bernoulli) and hidden (Bernoulli) units of an RBM has an energy provided by:

where:

• w_ij→ is the symmetric interaction term between the visible unit v_i and the hidden unit h_j,

• a_i, b_j→ is the bias term,

• I, J→ is the number of visible and hidden units.

By modifying the weights and biases to lower the energy of that information and to raise the energy of other information, the possibility that the network assigns to a training information can be raised principally for those that have low energies and, hence, make a big contribution to the partition function. The derivative of the log probability of a training vector concerning a weight is erratically easy. Between hidden units in an RBM, there are no direct influences; it is enormously easy to get an impartial sample of 〈vihj〉data. Known as an arbitrarily chosen training data v, the binary state h_j, of each hidden unit j, is set to 1 with probability:

where:

• σ(x) → is the logistic sigmoid function 1(1+exp(x)),

• v_ih_j → is the unbiased sample.

In addition, there are no direct connections among the visible units in an RBM. It is, furthermore, extremely uncomplicated to get an unbiased sample of the state of a visible unit, specified in a hidden vector

Then, the binary states of the hidden units are all computed in parallel using equation (7). Once the binary states have been chosen for the hidden units, a “reconstruction” is produced by setting each v_i to 1 with a probability given by equation (8). Finally, the states of the hidden units are updated again. The change in a weight is then given by

where, under the distribution specified, the angle brackets are employed to indicate the expectations by the subscript that follows. For executing the stochastic steepest ascent in the log probability of the training data, this shows the way to a very uncomplicated learning rule

where:

  η → is the learning rate.

  Procedure for training the DNN:

• Primarily we initialize the visible units v to the training vector.

• After that, we update the hidden units in parallel in the provided visible units using equation (7).

• In a similar manner, we update the visible units in parallel given the hidden units with the help of equation (8).

• Then, we re-update the hidden units in parallel given the reconstructed visible unit with the help of the same equation utilized in step (9).

• We accomplish the weight updates Δwijα〈vihj〉data−〈vihj〉reconstruction.

When the RBM is trained, a dissimilar RBM can be “stacked” on top of it to form a multilayer model. Each time a dissimilar RBM is stacked, the input visible layer is a primed vector, and values for the units in the already-trained RBM layers are apportioned by means of the current weights and biases. The concluding layer of the already-trained layers is engaged as input to the novel RBM. The new RBM is then trained with the method above, and then, this complete procedure can be simulated until some needed stopping standard is met. We change the weight in each RBM for the purpose of declining the multi-objective function. The accomplished deep network weights are engaged in priming a fine-tuning phase.

(ii) Fine-Tuning Stage

After the network is pre-trained as the RBM–stack model, the weights are further attuned using back propagation for the purpose of upsurging the accuracy of the scheme. The fine-tuning phase is simply the ordinary back propagation algorithm. To categorize the tumor image, an output layer is intended (tumor or not) in the top of the DNN. Also, there are N number of input neurons (depending upon the features), and three hidden layers are utilized in our DNN. The optimized weight is intended through the training stage with the help of the training data set D^T, where back propagation starts the weights attained in the pre-training phase. Primarily, the reduced features are provided to the DNN, though the weight is arbitrarily adjusted. The chief contribution of our DNN is to detect the minimum error function with the help of equation (6). Also, the training dataset is skilled until the optimized weight is grasped, or maximum accuracy is attained with the help of equation (6). Finally, on the basis of the optimal weight (w), the images are categorized in the testing stage by testing the data set D^T.

3.5 Segmentation Stage

After the image classification stage, the tumor images are selected, and the selected images are given to the segmentation stage. In this work, for the segmentation stage, we utilize the PFCM. The application of the PFCM methods will improve the clustering process and the accuracy of the segmentation. The vital motive of the PFCM module is devoted to the segmentation of a specified set of data into clusters. The PFCM constitutes a data clustering technique, where each data point is a part of the cluster to a level indicated by the membership grade. In the clustering module, it is dependent on the reduction of the objective function, which is illustrated in the following equation (11):

where,

• U → is the membership matrix,

• T → is the possibilistic matrix,

• C → is the resultant cluster center,

• X → is the set of all data points.

The constants a and b represent the comparative significance of the fuzzy membership and typicality values in the objective function. The gradual procedure of the PFCM is effectively elucidated below.

Step 1: Calculation of Distance Matrix

At first, the number of clusters (C) is furnished by the user, which is identical with respect to every segment. When the number of clusters is determined, the evaluation of the distance between the centroids and data point for each segment is carried out. In this work, the Euclidian distance function is used for distance calculation. Further, the distance matrix is determined with respect to each and every cluster:

where c_i is the centroid, and x_k is the data point. Here, the distance function is effectively utilized to estimate the distance between every data point x_k with every centroid v_i value.

Step 2: Calculation of Typicality Matrix

After the estimation of the distance matrix, the typicality matrix is evaluated. The typicality matrix T_ik is obtained from the possibilistic c-means (PCM) [20]. As illustrated in equation (13), the probability value of each data point in relation to every centroid is completed:

Step 3: Calculation of Membership Matrix

The evaluation of the membership matrix U_ik is performed by means of assessing the membership value of the data point, which is gathered from the fuzzy c-means (FCM) [21]. As illustrated with the help of the following equation (14), the membership value of each data point in relation to each centroid is completed.

Step 4: Update of Centroid

After the generation of the clusters, the modernization of the centroids is performed in accordance with equation (15) shown below.

Subsequent to the modernization of the centroids with respect to each and every cluster, the task of evaluating the distance with the lately modernized centroids is started and continued until the evaluation of the modernization of the centroids. The relative procedure is performed again and again until the efficient centroids of each and every cluster become identical and similar in successive iterations.

Step 5: Stop the Whole Process

Using this PFCM, the input images are getting segmented. All the images are segmented, which means that we will stop the process.

4.1. Evaluation Metrics

We need various assessment metric values to be calculated in order to analyze our proposed technique for the efficient MRI brain tumor classification. The metric values are found based on true positive (TP), true negative (TN), false positive (FP), and false negative (FN) with the option of segmentation and grading. The usefulness of our proposed work is analyzed by three metrics such as Accuracy, Sensitivity, and Specificity. The demonstration of these assessment metrics is specified in the equations that given below.

Sensitivity: The sensitivity of brain tumor detection is determined by taking the ratio of a number of true positives to the sum of true positive and false negatives. This relation can be expressed as:

St=TpTp+Fn

Specificity: The specificity of the brain tumor detection can be evaluated by taking the relation of a number of true negatives to the combined true negative and the false positive. The specificity can be expressed as:

Sp=TnTn+Fp

Accuracy: The accuracy of brain tumor detection can be calculated by taking the ratio of the true values present in the population. The accuracy can be described by the following equation:

A=Tp+TnTp+Fp+Fn+Tn

4.2 MRI Data Set Description

The MRI brain image data set is effectively employed in the innovative image segmentation and classification techniques, which are obtained from the publicly accessible sources. The corresponding image data set contains 20 brain MRI images of which 15 brain images are with tumor and the remaining five brain images are without tumor. The brain image data set is subdivided into two distinct sets such as the training data set and the testing data set. The training data set is effectively utilized to segment the brain tumor images, and the testing data set is employed to evaluate the performance of the novel approach. Here, 10 images are elegantly employed for the training purpose, and the residual 10 images are effectively used for the testing purpose. Figure 4 illustrates certain sample MRI images with tumor and without tumor.

Figure 4:

Sample Experimental Used Images.

4.3 Experimental Results on Proposed Approach

The performance of the proposed brain tumor classification and segmentation is analyzed with the help of sensitivity, specificity, and accuracy, which are the most significant performance parameters. The effectiveness of the proposed technique is demonstrated by performing a comparison between the matching results of the proposed method with other approaches. The result section is split into two phases, the classification phase and the segmentation phase. We first, verify the improvement of the classification phase. In the classification phase, we used the DNN classifier to recognize the tumor present in the image. In segmentation, we obtain the ROI and background region separately, and also, we measure the accuracy of the proposed approach with other segmentation approaches.

• Performance of Classification Phase

  The basic idea of our research is efficient MRI brain tumor detection and classification based on the combining wavelet texture feature and DNN. In the classification stage, at first, we extract the texture features from the image using GLCM and wavelet GLCM. After that, we reduce the features based on OFPA. Then, the relevant features are given to the DNN classifier for classification. Our proposed classification approach is compared with other well-known classifiers such as NN, RNN, and KNN. The performance of the approach is shown in Figures 5–7.

  Figure 5 shows the performance of the accuracy plot based on the classification stage by varying hidden neuron sizes; as per the analysis, the accuracy gradually increases when compared to the other approaches. Here, in the classification stage, we used the DNN. In Figure 5, the hidden neuron size is 20. We obtain the maximum accuracy of 92% for using the proposed DNN, 70% for using NN, 70% for using RNN, and 60% for using KNN. Moreover, NN and RNN are producing almost the same output value. Moreover, Figure 6 shows the performance of the proposed approach based on sensitivity. Here, we also obtain the maximum accuracy compared to the other approaches. Similarly, Figure 7 shows the performance of the proposed approach based on specificity. In analyzing Figure 7, we obtain the maximum specificity of 100. From the three figures, we clearly understand that our proposed approach obtained better results compared to the existing approaches. Moreover, in this classification stage, we obtain the maximum accuracy because of the optimal feature selection using the OFPA methods. A large number of features are great obstacles for the classification stage. Here, oppositional based learning (OBL) is combined with the FPA algorithm to improve the performance.

• Performance of Segmentation Phase

  Segmentation is an important stage for tumor detection system. After the classification stage, the tumor images are given to the PFCM for segmentation. The explanation of the PFCM algorithm is explained in Section 3.5. The experimental results are illustrated in Table 3.

  In this proposed methodology, for segmentation, we used the PFCM algorithm. This algorithm is a combination of the FCM and the PCM. Here, we compare our proposed PFCM algorithm with the FCM algorithm-based segmentation. Figure 8 shows the performance of the segmentation stage. Here, our proposed PFCM algorithm obtains the maximum output of 99.3%, 96.1%, and 99.5% for accuracy, sensitivity, and specificity, respectively. Moreover, the FCM-based segmentation approach achieves the output of 95.9%, 86%, and 87.2% for accuracy, sensitivity, and specificity, respectively. From the results, we clearly understand that our proposed PFCM algorithm outperforms the FCM algorithm. Moreover, Figure 9 shows the performance of the accuracy plot by varying the cluster size. Here, we obtain the maximum accuracy of 99.6%.

• Compared with Published Paper

  In this paper, we compare our proposed work with already published papers. Here, our proposed work was compared with the work of Kumar and Vijayakumar [17]. In Ref. [17], the author explained a tumor image segmentation and classification using the principal component analysis (PCA) and RBF kernel-based support vector machine. Here, the combined edge- and texture-based features are extricated using a histogram and the co-occurrence matrix, then, the PCA was depleted to demote the dimensionality of the feature space, which results in a more efficient and accurate classification. Finally, in the classification stage, a kernel-based SVM classifier was utilized to classify the image.

  Table 4 shows the comparative analysis of the proposed methodology. Here, our proposed approach achieves the maximum accuracy of 92%, sensitivity of 865, and specificity of 91%. Similarly, using the work of Kumar and Vijayakumar [17], we obtain the accuracy of 88%, the sensitivity of 84%, and the specificity of 90%. From the discussion, we clearly understand that our proposed approach is better than the existing results.

Figure 5:

Performance of Proposed Approach Based on Accuracy.

Figure 6:

Performance of Proposed Approach Based on Sensitivity.

Figure 7:

Performance of Proposed Approach Based on Specificity.

Table 3:

Experimental Results of Segmentation Stage.

Figure 8:

Performance of Segmentation Phase Using Different Measures.

Figure 9:

Performance of Accuracy Plot by Varying Cluster Size.