Aquilla Optimization Based K-Means Clustering for Brain Tumor Segmentation with Outlier Detection

A brain tumor is an aberrant, neoplastic growth of brain tissue. The two main kinds of brain tumors, sometimes referred to as lesions or neoplasia, are primary and metastatic tumors [1]. Primary brain cancers originate in the brain and its surrounding tissues. Brain tumors frequently have fatal effects due to its dangerous effects thus it is considered as a serious illness [2]. Hence, the study of brain tumor images has recently received increasing attention. Nowadays, a variety of modalities are employed to obtain various types of medical images, including positron emission tomography, magnetic resonance imaging (MRI), computed tomography (CT), and X-rays [3]. Among these distinct modalities MRI is suitable for brain imaging, because it can be done without providing radioisotopes [4]. MRI comprises a vast quantity of information and which is a multi-parameter-based imaging that can create diverse images through altering various parameters [5]. However, noise in MRI images sometimes results in low contrast, which makes it difficult to accurately identify lesion locations.

Tumor segmentation is effective and therefore crucial. A range of image segmentation methods are currently often used in medical image segmentation [6]. Because, in decision-oriented applications, image segmentation is an important and thorough way to accurately identify an image's pixel values. Several segmentation techniques, including edge-based, threshold-based, and neural network-based methods, are commonly employed in medical applications to aid in the diagnosis of various diseases [7]. However, these segmentation methods often yield suboptimal results, especially when applied to imaging of brain tumors. Segmentation based on threshold estimates the threshold based on particular properties of each pixel. Next, the pixel feature values are compared to the segmentation threshold in order to identify which regions of the features [8]. Using certain pixel boundary directions, edge-based segmentation establishes the boundaries [9]. One of the trickier parts of neural networks in neural network-based segmentation is creating the network [10]. The creation of neural networks is challenging since it takes a lot of time and calculation.

Techniques for clustering images are widely used in medical picture segmentation. Expectation maximization (EM), K-means clustering, fuzzy C-means clustering (FCM), and K-means++ clustering [11]. Fuzzy set theory makes soft segmentation possible, which is the foundation for how FCM-based segmentation operates. Data can be described as a collection of probability distributions in accordance with the EM technique [12]. The program then repeatedly computes the posterior probability and estimates the mean, covariance, and mixture coefficients by applying the maximum likelihood estimation method along with clustering criteria [13]. The majority of these clustering techniques are susceptible to noise [14]. The K-means clustering method presents several challenges, as it calculates the distances between the image's pixels and the cluster centroids. It then assigns each pixel to the class corresponding to the nearest centroid, updating the grayscale means of the clusters through iterative steps [15]. To address this concerns in this research proposed an Aquila optimization-based K-means clustering for selecting optimal cluster centroids. Consequently, an effective clustering segmentation method was presented in this research to improve unstable clustering and lessen noise sensitivity. The research work's primary contribution is listed below:

• An effective brain tumor segmentation model is presented utilizing an Aquila optimization-based K-means clustering algorithm.
• Preprocessing techniques are used to enhance the quality of the brain tumor image. Noise is removed from the brain image using both the median filter and the Wiener filter.
• An adaptive histogram equalization (AHE) technique, along with gamma correction, is applied to improve the contrast of the brain MRI pixels.
• Using the optimal K-means clustering algorithm for tumor segmentation which work based on the K-centroids, it divides or clusters the provided data into K-clusters or portions.
• In K-means clustering, the centroid is strategically selected to efficiently segment the region of interest from the background. The centroids of each cluster are determined using the Aquila optimization algorithm (AOA).

The structure of the remaining sections of the research is outlined as follows: Section 2 reviews several studies related to the current methodology. Section 3 provides a brief overview of the proposed brain tumor segmentation process. Section 4 presents the results and performance evaluation of the proposed framework. Finally, Section 5 concludes the study.

Aquila optimization-based K-means clustering for brain tumor segmentation is presented in this work. Image segmentation is considered as a significant process for properly identifying the pixel values of an image during classification. Generally, for segmentation, medical images are gathered from distinct modalities like X-ray, positron emission tomography CT, and MRI. Among these distinct modalities MRI is suitable for identifying the abnormal alternations in organs as well as tissues in the brain through segmentation. Thus, using clustering-based techniques that separate a range of similar sorts of components or colors into many clusters using gray and color intensity similarities, the tumors present in the MRI are segmented. Nevertheless, the majority of earlier clustering techniques are noise content sensitive. As a result, this study suggests an effective clustering segmentation technique to improve unstable clustering and lessen noise sensitivity. Figure 1 shows the architecture of the suggested brain tumor segmentation model.

Figure 1. Architecture of the proposed brain tumor segmentation model

There are two stages in the suggested brain tumor segmentation model: image preprocessing and tumor segmentation. The first step is image preprocessing, which is done to improve the characteristics and quality of the image in order to obtain reliable results. In the preprocessing stage, gamma correction, AHE, and image denoising are used. For envision denoising, the wiener and median filters are employed. For the elimination of noise and normalization of color median is used. A Wiener filter is employed to control the additive noise and blurring. An AHE is used after noise reduction to improve the contrast of the images of brain tumors. Finally, in the preprocessing phase applied a gamma correction to control the entire brightness of the brain tumor image. Once completed preprocessing, the preprocessed brain tumor image is given as the input of the segmentation phase. Here, segmentation is performed with the aid of improved K-means clustering for effective segmentation. The K-means clustering is improved using an AOA which can select the optimal cluster centroids effectively this can remove the burdens of conventional K-means clustering algorithm and perform segmentation effectively. The segmented tumor regions are then used as input into the CNN model which is trained to classify the image into brain diseases categories to validate the proposed segmentation model. The process comprises in the proposed model is described as follows.

3.1 Image preprocessing

The primary goal of image preprocessing is to simplify complex calculations, leading to improved results. These preprocessing techniques are designed to enhance image quality while preserving its original features. The following outlines the various preprocessing strategies applied in this method.

3.1.1 Image de-noising

The image de-noising process effectively reduces the noise present in brain tumor images. The different intrinsic or extrinsic circumstances that lead to the noise in the images can be challenging to deal with further process. Therefore, the median filter and wiener filter are the two different de-noising techniques considered in this method.

1. Median Filter

It is a type of nonlinear filter which is used to reduce noise like "pepper" as well as "salt" noise i.e., impulse noise that exists in the image. These filters move through the various parts of the image in terms of pixels by pixels. Instead of average the grey levels in a pixel, the median filter replaces the grey level of each pixel with the median of the grey levels in its immediate vicinity. The following expression shows the median filter. The median filter is shown in the following expression:

$f(x, y)=\operatorname{median}_{(s, t) \in S_{x y}}\{g(s, t)\}$    (1)

The median is calculated based on the initial value of the pixels. Median filters are widely used for specific types of random noise because they effectively reduce noise while causing much less blurring compared to linear smoothing filters of similar size.

2. Wiener Filter

Wiener filters are widely used in image processing for restoration tasks, such as eliminating motion blur and optimizing image clarity. If a certain filter causes images to become blurry, inverse filtering can recover the original image. This technique lessens image degradation and enables the creation of restoration algorithms for each kind of degradation technique. Inverse filtering and noise smoothing are traded off in the Wiener filtering. When a color image is supplied to the wiener filter as an input. The channel with the greatest trade-off is used as the input image. Each channel's contrast was determined for the color channel selection. By utilizing a low pass filter, a wiener filter can measure the R, G, and B channels. It can be measured the contrast among the original images and the low pass filter image. The median and Wiener filters were selected for noise reduction, and the filter sizes were chosen to effectively handle impulse noise while minimizing blurring.

3.1.2 Adaptive histogram equalization

AHE is a technique similar to histogram equalization, but it further improves the contrast of input images by adjusting the enhancement process to local variations. The unique feature of AHE is its generation of multiple histograms, each of which represents a distinct part of the image. These histograms are then used to redistribute the brightness values, so strengthening the edges of each area of the image. Due to the extreme concentration of the histogram in fixed regions of the image, AHE may overestimate the contrast feature in the image. Utilizing AHE, it is possible to prevent the noise in neighbor-constant areas from being amplified. AHE can limit contrast amplification, hence which can resolve the issue of noise amplification. The AHE algorithm, which is based on probability theory recognizes the grey mapping of pixels present in the images by performing grey operations and which transforms the histogram to one that is uniformly smooth and has distinct grey levels in order to accomplish the goal of image enhancement.

Assume that the pixel in the original denoised brain tumor image has the grey value is denoted as $r(0 \leq r \leq 1)$ and $p(r)$ specifies the probability of its density. The pixel in the enhanced image has the grey value is specified as $s(0 \leq s \leq$ 1), $p(s)$ signifies the probability of its density and $s=T(r)$ represents the mapping function. Every point on the equalized histogram is of the same height, which is evident from the histogram's physics interpretation:

$p_{\mathrm{s}}(s) d s=p_r(r) d r$     (2)

Assuming that the interval of the monotonically growing function is considered as $s=T(r)$ and its monotonically increasing inverse function is taken as $r=T^{-1}(s)$. According to Eq. (2), written the following Eq. (3) for both these functions:

$p_s(s)=\left[p_r(r) \frac{1}{d s / d r}\right]_{r=T^{-1}(s)}=p_r(r) \frac{1}{p_r(r)}=1$    (3)

The mapping relationship of $i$, which indicates that a pixel in the original image has a grey value, and $f_i$, which shows that a pixel in the enhanced image has a grey value, is the next discrete condition. Eq. (4) gives the mapping connection:

$f_i=(m-1) T(r)=(m-1) \sum_{k=0}^i \frac{q_k}{Q}$    (4)

where, $q_k$ represents the number of pixels with the $k t h$ grey level, $m$ specifies the number of grey levels contained in the original image, and $Q$ represents the overall number of pixels in the image. If an image has $n$ different grey levels and $p_i$ represent the $i$ th gray level occurrence probability, then the entropy of that level can be described as the following Eq. (5):

$e(i)=-p_i \log p_i$   (5)

The entropy of the complete image is estimated using Eq. (6):

$E=\sum_{i=0}^{n-1} e(i)=-\sum_{i=0}^{n-1} p_i \log p_i$    (6)

Eq. (6) shows that $E$ will grow to its greatest value if $p_0= p_{12}=\cdots p_{n-1}=\frac{1}{n} \cdot$ In other words, when the AHE of the image has a uniform distribution, the entropy of the entire image is at its highest. The findings of AHE are given in the gamma correction for further processing of the brain tumor image.

3.1.3 Gamma correction

The gamma correction procedure that can be utilized to control the overall brightness of the brain tumor image incorporates the AHE findings. It can be used on images that are overly contrasted or dark. Expanding and compressing pixel intensity levels is necessary for images that are fading and darker. Every pixel value undergoes gamma correction, a nonlinear adjustment. The majority of the time, subtraction, addition, and multiplication are applied to every pixel. The process of applying nonlinear algorithms to the input image's pixels and adjusting the image's saturation as a consequence is known as gamma correction. It is crucial to keep the gamma value constant because it shouldn't be too high or too low. The gamma correction parameter was selected based on its ability to adjust the enhance the image without overexposing or underexposing important features while it provided a good balance for the brain MRI images in our dataset.

3.2 Brain tumor segmentation using Aquila optimization-based K-means clustering

After preprocessing the brain tumor image, it undergoes segmentation to isolate the affected region in the brain. In this proposed model, an enhanced version of the K-means clustering algorithm is introduced, optimized using Aquila optimization. The segmentation strategy has been suggested to enhance unstable clustering and lessen its noise sensitivity. The Aquila optimization is applied to select the effective cluster centroids in the image, which is done by maximum the PSNR value of the pixel present in the brain images. The process involved in the proposed segmentation algorithm is described as follows.

3.2.1 K-means clustering

The unsupervised learning model known as K-means is used to describe clustering. Models based on unsupervised learning are used for data sets that have never been labeled or categorized. Every data point is processed in line with these identical points, which are recorded in the data set. The model, which uses either a distance-based approach or a centroid-based technique, assigns points to each cluster in order to estimate the distance. After calculating a K value, divide the data into K categories to make it easier to distinguish between them. This will improve the data's similarity within each group. The distance is estimated using the Euclidean distance formula that is described below:

1. Euclidean Distance

Typically, Euclidean distance is used as an index to estimate the similarity among two sets of data. The Euclidean distance is the length of time in three dimensions between two places. The following equation gives a three-dimensional Eq. (7):

$d=\sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2+\left(z_1-z_2\right)^3}$   (7)

Additionally, it can be used for n-dimensional space, as given in the following Eq. (8):

$d=\sqrt{\sum\left(x_{i 1}-x_{i 2}\right)^2}$     (8)

The $i$ th dimensions coordinate of the first point is given as $x_{i 1}$, and the $i$th dimensional coordinate of the second point is given as $x_{i 2}$, where $i=1,2, \ldots, n$. Each point in the n dimensional Euclidean space can be written as, $x(i)= (x(1), x(2), \ldots x(n)$, where $i=1,2, \ldots n$ is a real number and is referred to as the $i$th coordinate of $x$. Eq. (8) is used to calculate the distance between two points x and y.

As the Euclidean distance between two sets of data decreases, so does the degree of similarity. Furthermore, each cluster is associated with one of the initial K centroids, and data points close to the centroid are classified as being a part of a cluster for classification purposes. To cluster the points as near to their respective cluster centroids as possible is the main goal of the iterative K-means algorithm. These perform three different processes. The first process is to choose K items to serve as the initial cluster's center in accordance with our study goal. Calculating the Euclidean distance between the data and the cluster center after classifying the data that are close together into one category. Recalculating the cluster centers of the recently split clusters is the second step, after which the clusters are divided once more using the initial divisions. The third process, the method can be terminated once this iterative process is completed and the cluster center no longer changes. The process can be stopped under three different conditions: first, the newly created cluster's centroid must remain intact; second, all of the points must remain in the same cluster; and third, it must complete the maximum number of iterations. Another indication that training should be expressly ended if, even after performing several iterations, these points are still in the same cluster. In this case, training should be terminated. When the allotted number of iterations has been reached, it can finally terminate the training.

3.2.2 Aquila optimization

Aquila optimization is a relatively new nature-inspired algorithm. The Aquila, a widely known species of bird of prey, is one of the most studied birds due to its hunting behavior. Males of the species are particularly efficient hunters, often capturing more prey when hunting alone. Aquilas rely on their speed and sharp talons to hunt animals such as rabbits, squirrels, and other creatures. They employ four distinct hunting techniques to capture their prey, demonstrating their ability to swiftly adapt their methods based on the situation. The four hunting techniques are described as follows.

• In the first method, the Aquila hunts by soaring at a great height before diving vertically towards its prey. After spotting its target, it executes a long, shallow glide, gradually increasing its speed as its wings fold. For this strategy to succeed, the Aquila must maintain a height advantage over its prey.
• In the second hunting method, the Aquila starts at a low altitude and relentlessly chases its target, whether it's flying or running. This approach is particularly effective for hunting seabirds, breeding grouse, or ground squirrels.
• The third hunting technique involves the Aquila flying at a low altitude, gradually descending as it approaches its prey. Once near the ground, the Aquila closes in on its target, aiming to land on the neck and back of the animal.
• The fourth technique, known as "walking and grabbing prey," sees the Aquila moving on the ground while using its beak to attract and seize its target.

The following is the mathematical expression of Aquila optimization. The Aquila method starts with N agents and a starting population of X, like other nature-inspired metaheuristic optimization algorithms in Eq. (9)

$\begin{aligned} X_i(t+1) & =X_b(t) \times\left(\frac{1-t}{T}\right)+\left(X_M(t)-X_b(t) * \text { rand }\right)\end{aligned}$    (9)

where, $T$ signifies the total number of iterations, $\left(\frac{1-t}{T}\right)$ is used to control the search process. The agent's exploration is updated based on the Levy flight distribution that is specified as $(\operatorname{Levy}(D))$ and $X_b$ in the second process. The following mathematical Eq. (10) defines this process:

$\begin{aligned} X_i(t+1) & =X_b(t) \times \operatorname{Levy}(D)+X_R(t)+(y-x) * \operatorname{rand}\end{aligned}$    (10)

The randomly selected agent is represented as $X_R$. Also, the spiral tracking shape are specified as $x$ and $y$, which is mathematically formulated aa below:

$\begin{aligned} X_i(t+1) & =\left(X_b(t)-X_M(t)\right) \times \alpha-\text { rand }+((U B-L B) \times \text { rand }+L B) \times \delta\end{aligned}$      (11)

The first process updates the agents based on $X_M$ and $X_b$ during the exploitation process and which is mathematically expressed as the following Eq. (11). During the exploitation process the adjustment parameters are considered as $\delta$ and $\alpha$. Also, the randomly created parameters are specified as rand $\in[0,1]$. The agent is updated in the second strategy during the exploitation process according to the quality functions such as, $Q F, X_b$ and Levy. The second process is mathematically expressed in the following Eq. (12):

$\begin{aligned} X_i(t+1) & =Q F \times X_b(t)-\left(G_1 \times X(t) \times \text { rand }\right)-G_2 \times \operatorname{Levy}(D)+\operatorname{rand} \times G_1\end{aligned}$      (12)

3.2.3 Selecting optimal cluster centroids through aquila optimization

By optimizing the PSNR value of the brain tumor imaging pixels, the ideal cluster centroids are chosen. PSNR is measured in decibels (dB). As the PSNR value increases, the quality of the reconstructed or compressed image improves. The MSE and PSNR are used to compare the quality of image compression. The most common application of the PSNR is to evaluate loss compression codes for recovered data. Here, the error caused by compression is the noise, while the original data is the signal.

$P S N R=10 \log _{10}\left(\frac{M A X_I^2}{M S E}\right)$    (13)

$M S E=\frac{1}{m n} \sum_{i=0}^{m-1} \sum_{j=0}^{n-1}[I(i, j)-K(i, j)]^2$         (14)

where, $M A X_I^2$ signified the maximum value of the pixel is in the original image, $m$ represent the number of rows in the original image and $n$ specifies the number of columns in the original image. With a size of $m \times n, ~I$ and $K$ denote original and contrast-enhanced images, respectively.

Step 1: Initialization

The pixels in the preprocessed images are considered for the problem in this research which is used to discover the optimal cluster centroid. The population is initialized using the following mathematical formula.

$P=\left\{p_1, p_2, p_3, \ldots p_n\right\}$    (15)

From Eq. (15), $p_n$ specifies the number of pixels initialized in the population.

Step 2: Fitness function

The best centers for clustering in the brain tumor image are chosen using the fitness function. The maximum PSNR value of the pixel determines the ideal cluster center.

Fitness $=\max \left(P S N R=10 \log _{10}\left(\frac{M A X_I^2}{M S E}\right)\right)$    (16)

Based on the above Eq. (16), the optimal cluster centroids are selected.

Step 3: Updating

To find the optimal cluster center within the pixels of the tumor image, the value of PSNR gets updated in each iteration.

Step 4: Termination

The optimal cluster centroid is discovered the process is ended.

3.2.4 Procedure of the proposed Aquila optimization-based K-means clustering

The following is the procedure that the suggested Aquila optimization-based K-means clustering (AOKC) algorithm uses.

Step 1: Select the value for the number of clusters, k

In this step, the specified number of clusters, denoted as k, are created.

Step 2: Using AOKC, select k random points from the data to serve as centroids

Then choosing the cluster centroids in the considered k number of clusters. The conventional K-means algorithm randomly selects the cluster centroids that is the major concern in the conventional algorithm. In order to address these concerns, the proposed model selects the optimal cluster centroid through Aquila optimization using Eq. (16).

Step 3: Assign all the points to the closest cluster centroid

Assign each point to the closest cluster centroid after the centroids have been initialized using the Aquila optimization method.

Step 4: Recomputed the centroids of newly formed clusters

After all the points have been allocated to a cluster, the next step is to compute the centroids of newly formed clusters.

Step 5: Repeat steps 3 and 4

The process is repeated using steps 3 and 4. Figure 2 shows the overall process of selecting the pixel for K-means clustering.

One iteration is required to compute the centroid and allocate each point to the cluster based on far away it is from the centroid. Three criteria are used to terminate an improved K-means clustering process: The maximum number of iterations is reached, points remain in the same cluster, and the centroids of newly created clusters remain unchanged. According to the proposed segmentation algorithm the tumor tissues present in the brain images are effectively segmented which can used to the physicians for taking proper decision to save the patient's life. The segmented images are fed into CNN to validate the segmented image for diseases prediction. The pseudo code for the proposed algorithm is presented in Algorithm 1.

Figure 2. Flow chart of proposed Aquila optimization-based K-means clustering