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Top1. Introduction
Recent works on image segmentation are interested in segmentation of brain Magnetic Resonance Images (MRI), which consists in detecting the three types of tissue: white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF). In (Ivana et al., 2015), several methods for brain MRI segmentation are described such as the intensity-based segmentation methods, thresholding methods, atlas-based methods, surface-based methods and hybrid segmentation methods. All of these segmentation methods present advantages as well as disadvantages. As an example of recent research works, (Sanromaa et al., 2018) consists one of the newest methods of brain MRI segmentation. Concerning image thresholding, it includes bi-level and multilevel thresholding. The bi-level thresholding classifies the pixels into two categories; pixels, with gray levels above a determined threshold, belong to the first group; the other pixels belong to the second one. However, the multilevel thresholding divides the pixels into a number of groups or classes. Every class contains pixels having gray levels within a specific range defined by several thresholds.
Image thresholding approaches can be parametric or nonparametric. In this current work, we are interested in the nonparametric approaches, in which, we search thresholds that optimize an objective function mainly like the Otsu’s function (also named the between-class variance) (Otsu, 1979), the Kapur’s function (also named the entropy) (Kapur et al., 1985) and the cross entropy (Li and Lee, 1993). Hence, we propose to ensure the brain MRI segmentation by the use of a new multilevel thresholding approach. It consists in applying the Variable Neighborhood Search metaheuristic to optimize brain MRI segmentation. In fact, the Variable Neighbourhood Search is one of the most successful optimization algorithms thanks to its flourishing implementation in various applications. In the literature, the VNS metaheuristic is first developed by (Mladenovic and Hansen, 1997) where the basic idea is a systematic change of a neighbourhood within a local search.
So, the main idea of this paper is to apply the Variable Neighbourhood Search (VNS) metaheuristic to solve the problem of multilevel thresholding for brain MRI segmentation. Two maximizing thresholding functions, the between-class variance (the Otsu’s function) and the entropy (the Kapur’s function), are developed to find the optimal thresholds. Consequently, two versions of the VNS metaheuristic are given for the two objective functions: the VNS-Otsu metaheuristic uses the between-class variance objective function whereas the VNS-Kapur metaheuristic implements the entropy thresholding one.
In order to prove the performance of the two proposed multilevel thresholding methods (based on the VNS metaheuristic), eleven benchmark brain MRI slices are used.
This paper is structured as follows. In section 2, we present an overview about the brain MRI segmentation. In section 3, we describe the Variable Neighbourhood Search metaheuristic and its applications. Section 4 is dedicated for giving all details about applying the VNS metaheuristic on the brain MRI segmentation. Section 5 defines the Optimal Global Thresholding using Otsu’s then Kapur’s functions. Experimental results, on eleven benchmark brain MRI slices, are reported and analyzed in section 6. Finally, in section 7, we conclude this paper and suggest further research directions.