Improving the segmentation of magnetic resonance brain images using the LSHADE optimization algorithm

Highlights

• The LSHADE algorithm is proposed for accurate MRBI segmentation.

• The minimum cross entropy is used by the LSHADE as objective function.

• The proposed segmentation method is tested over different datasets of MRBI.

• Segmentation metrics verify the quality of the LSHADE results in MRBI.

• By using LSHADE segmentation, it is possible to identify tumors in MRBI.

Abstract

Segmentation is an essential preprocessing step in techniques for image analysis. The automatic segmentation of brain magnetic resonance imaging has been exhaustively investigated since the accurate use of this kind of methods permits the diagnosis and identification of several diseases. Thresholding is a straightforward and efficient technique for image segmentation. Nonetheless, thresholding based approaches tend to increase the computational cost based on the number of thresholds used for the segmentation. Therefore, metaheuristic algorithms are an important tool that helps to find the optimal values in multilevel thresholding. The adaptive differential evolution, based in numerous successes through history, with linear population size reduction (LSHADE) is a robust metaheuristic algorithm that efficiently solves numerical optimization problems. The main advantage of LSHADE is its capability to adapt its internal parameters according to prior knowledge acquired along the evolutionary process. Meanwhile, the continuous reduction of the population improves the exploitation process. This article presents a multilevel thresholding approach based on the LSHADE method for the segmentation of magnetic resonance brain imaging. The proposed method has been tested using three groups of reference images— the first group consists of grayscale standard benchmark images, the second group consists of magnetic resonance T2-weighted brain images, and the third group is formed by images of unhealthy brains affected by tumors. In turn, the performance of the intended approach was compared with distinct metaheuristic algorithms and machine learning methods. The statistically verified results demonstrate that the suggested approach improves consistency and segmentation quality.

Introduction

Medical imaging has become essential in the field of medical diagnosis, treatment assessment, and surgical planning. Different modalities are used to acquire medical images, for example, Positron Emission Tomography, Ultrasonography, Magnetic Resonance, and Computed Tomography. Magnetic Resonance (MR) is a non-invasive system that provides high spatial resolution and detailed information of anatomical structures. Nevertheless, the analysis of MR images is complex since they are affected by artifacts due to the non-uniformity intensity, the voluntary or involuntary movements of the patient, and the partial volume effect [1].

On the other hand, segmentation plays an important role in preprocessing techniques for medical imaging [[2], [3], [4]]. Segmentation ensues through the division into non-overlapped consistent areas of an image that shares specific attributes such as texture, shape, or intensity. The segmentation of Magnetic Resonance Brain Images (MRBIs) has been broadly studied, considering that, with accurate segmentation of the brain, they can identify several brain illnesses such as multiple sclerosis, schizophrenia, Alzheimer's disease and dementia [5,6]. MRBIs are frequently analyzed based on the experience and visual capacity of the expert professional. However, it is a time-consuming, complex task limited by the human vision that cannot distinguish most of the gray levels in an MR image [5,6]. Therefore, computer-aided techniques are necessary to analyze and automatically segment MR images. In the field of MRBIs, it is possible to find different segmentation methodologies [[7], [8], [9], [10], [11]]. Such segmentation approaches can be classified into thresholding techniques, region growing methods, clustering approaches, and model-based techniques [12, 13].

Thresholding is a simple but efficient image segmentation technique, which aims to distribute the pixels of an image into different sets by setting a distinct threshold (th) to establish intensity values. Thresholding techniques are categorized according to the number of th levels as bilevel and multilevel thresholding (BTH and MTH, respectively). The BTH divides the pixel of the image into two classes by using a single th value; whereas in MTH, multiple th values are employed to separate the image into several significant classes. Numerous studies have been proposed to determine the optimum th values. Such as the works of Otsu [14], Kittler and Illingworth [15], Abutaleb [16], Pal [17], and Shanbhag [18], to name a few. Sezgin and Sankur [19] distributed the thresholding techniques into six categories according to the exploited data. Between these categories, the methods based on entropy attracted the attention of researchers and scholars considering that they have demonstrated to be more efficient in image segmentation [[20], [21], [22]].

Entropy establishes an index of statistic diversity on the intensity levels of an image. Several entropy-based methods have been proposed, such as the Shannon entropy [23], Kapur entropy [24], minimum cross-entropy (MCE) [25], Tsallis entropy [26], Renyi entropy [27], among others. The minimum cross-entropy formulated by Li and Lee [25] has been broadly employed for image segmentation. This method selects the optimum th value that minimizes the cross-entropy between the initial image and the output image. Initially, the MCE, like other entropy-based methods, was introduced for a BTH and later expanded to MTH. Whereas bi-level thresholding searches only for one optimal threshold value quickly and efficiently, the multilevel thresholding exhaustively calculates the best set of threshold values. This comprehensive process exponentially increases the computational cost [28]. To improve the search for optimal thresholds and reduce the computational effort of conventional methods, researchers have employed Metaheuristic Algorithms (MA) to settle the problem regarding MTH [29, 30].

MA provides high-quality solutions to different optimization problems. The MTH is an optimization problem whose fitness function is a thresholding technique. Over the years, various MA have been applied to solve the multilevel thresholding problem. For example, the Genetic Algorithm (GA) [31], motivated by the natural selection process, has been employed for the segmentation of general-purpose images, in which the GA was combined with the minimum cross-entropy criterion to find the optimal thresholds [32]. Swarm-based MA, such as the Particle Swarm Optimization (PSO) [33], and the Grey Wolf Optimizer (GWO) [34] have also been used for segmentation through MTH for general-purpose images in the works of Liu et al. and Khairuzzaman et al. [35,36], respectively. Likewise, the population-based Sine Cosine Algorithm (SCA) [37] has been applied for multilevel segmentation of real-time and medical images in the work by Kandan et al. [38]. Different MA have also been used in medical diagnosis [39]. For example, in [40] the authors combine machine learning techniques with MA for the diagnosis of breast cancer, diabetes, and erythemato-squamous. In [41,42] the support vector machines are evolved with MA for the classification of medical datasets. In this sense, one of the most popular MA is the Differential Evolution (DE), which is a simple and powerful vector-based optimization method proposed by R. Storn and K. Price [43]. DE has been successfully employed for the multilevel thresholding problem [[44], [45], [46]]; nevertheless, the control parameters and the learning strategies involved in DE are highly dependent on the field application. Different DE approaches have been proposed to solve these deficiencies, such as the Self Adaptive DE (SADE) [47], the Success-History based parameter adaptation for DE (SHADE) [48], and the Success-History based Adaptive DE with linear population size reduction (LSHADE) [49], to mention some of the most popular.

Significant contributions have also been made to the segmentation of MRBIs that employ MA, such as the method proposed by Kaur, Saini, and Gupta that segments brain tumors in MR images by using the PSO algorithm with a two-dimensional minimum cross-entropy [50]. Oliva et al. present a MRBI segmentation methodology based on the Crow Search Algorithm (CSA) with MCE as a fitness function [51]. T. Ramakrishnan and B. Sankaragomathi implemented the modified region growing algorithm with the GWO algorithm to segment MRBIs [52]. Sathya and Kayalvizhi applied an amended the Bacterial Foraging Optimization (BFO) algorithm for MTH of MR brain images [53]. Ali, Siarry, and Pant proposed the use of a hybrid DE algorithm aided with a Gaussian curve fitting to segment MR medical images [54]. Although the cited approaches can obtain acceptable results, the MA tends to present a deficiency of balance rate, among their exploration and exploitation skills. A metaheuristic algorithm can reach global optima depending on the adequate balance rate of exploration and exploitation. In turn, the MAs are not designed to solve all the problems; they are intended to significantly improve the solution of particular problems [55]. Each year, several new algorithms are proposed, which are assessed according to a generic comparison methodology that involves numerical benchmark problems whose results are statistically analyzed to define which algorithm surpasses others [56,57]. However, few studies assess the performance of MA according to a specific application; subsequently, it is essential to continue developing the application context assessments in this kind of methods.

Based on the related literature, it can be observed that the segmentation of MRBIs based on MA has provided appropriate and accurate solutions. This deduction inspired us to present a novel MTH image segmentation technique based on the Success-History based Adaptive Differential Evolution with a linear population size reduction (LSHADE) algorithm [49]. The proposed approach, called MCE-LSHADE, selects the optimal threshold values using the minimum cross-entropy (MCE) [25] criterion as a fitness function. In the experiments, three groups of reference images were used to verify the quality of segmentation. The first group is formed of sixteen standard test images broadly employed in the field of image processing. The second group consists of ten transaxial cut magnetic resonance brain images. Finally, the last set has three images of the brain affected by tumors, which allow verifying the performance of the MCE-LSHADE in solving a real segmentation problem. The robustness of MCE-LSHADE is appraised with the outcomes of five metaheuristic algorithms, Self-Adaptive Differential Evolution (SADE) [47], Differential Evolution (DE) [43], Particle Swarm Optimization (PSO) [33], Grey Wolf Optimizer (GWO) [34], and the Sine Cosine Algorithm (SCA) [32]. In turn, two machine learning methods are employed as well for comparative purposes. The first one is the K-means algorithm [64], which is a clustering-based method that operates with the image pixels. The second one is the fuzzy approach with an iterative average aggregation (IterAg) [59] that contemplates the histogram of the image to generate the optimal thresholds. The main contribution of this work is the application of LSHADE for MTH image segmentation by applying the minimum cross-entropy criterion on MRBIs. Statistically validated experimental results provide evidence that the MCE-LSHADE method achieves promising results for the MTH segmentation of both standard test images as well as complex MR brain images.

The remaining sections of this work are distributed as follows: Section 2 examines the entropy-based techniques and details the minimum cross-entropy. Section 3 introduces the Success-History based Adaptive Differential Evolution with a linear population size reduction algorithm. Section 4 describes the proposed multilevel thresholding technique based on LSHADE. All experimental results of MCE-LSHADE are exhibited in Section 5. Last but not least, in Section 6, the conclusions of the work are summarized.