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Segmentation is one of the most important image processing steps. It partitions an image into some meaningful regions or extracts its boundaries. It is often considered as the preprocessing step of other higher-level processing such as, image analysis and computer vision. There are numerous image segmentation techniques available in the literature. Thresholding is one of the simplest and popular image segmentation techniques available. Some comprehensive surveys over thresholding techniques can be found in (Sezgin, 2004; Nikhil, 1993; Sahoo & Soltani, 1988). Bi-level thresholding partitions an image into two classes- object and the background by using a global threshold. On the other hand, multilevel thresholding partitions an image into more than two classes using two or more number of thresholds. Otsu (Otsu, 1979), Kapur (Kapur et al., 1985), and minimum cross entropy (Li & Lee, 1993) are widely used nonparametric and unsupervised image thresholding techniques. Li and Lee (Li & Lee, 1993) first applied minimum cross entropy in image thresholding for bi-level thresholding. It selects a threshold that minimizes the cross entropy between the segmented image and the original image. When this method is extended to multilevel thresholding, computational complexity increases very rapidly. An iterative algorithm (Li & Tam, 1998) which uses one point iteration scheme is used to reduce the computational complexity of minimum cross entropy thresholding algorithm.
Several meta-heuristic algorithms are applied to reduce the computational complexity of multilevel thresholding. Evolutionary algorithm such as, genetic algorithm (Tang et al., 2011) is applied to reduce the computational cost of multilevel minimum cross entropy thresholding. This method substantially reduces the computation cost of multilevel thresholding. Differential evolution is applied in multilevel thresholding to segment grey level image as well as color image (Sarkar et al., 2015; Sarkar et al., 2011). This method also reduces computation cost substantially, but it is still high. Swarm intelligence algorithms such as, PSO (Yin, 2007) is applied to reduce the computational complexity of multilevel thresholding using minimum cross entropy as an objective function. This method is very fast in terms of computational time. BFO (Sathya & Kayalvizhi, 2011), cuckoo search (Roy et al., 2015), firefly algorithm and its modified versions (Horng & Liou, 2011), honey bee mating optimization (Horng, 2010), artificial bee colony algorithm (Cuevas et al., 2013) are also applied in multilevel thresholding. A hybrid BFO algorithm (Tang et al., 2017) has been applied to solve multilevel thresholding problem. This algorithm uses PSO to improve the global searching ability and convergence speed of the BFO algorithm. A modified PSO algorithm, which introduces adaptive inertia and also adaptive population size is applied in multilevel thresholding (Liu et al., 2015). A hybrid multilevel thresholding technique for brain MR image segmentation is proposed using PSO, Otsu’s function, and anisotropic diffusion (Khairuzzaman & Chaudhury, 2019). Moth-Flame Optimization (MFO) algorithm has been applied in a number of interesting applications. Most recently, Whale Optimization Algorithm (WOA) and MFO algorithm (Aziz et al., 2017) has been used in multilevel thresholding using Otsu’s function. MFO has also been applied to multilevel thresholding-based image segmentation using both Otsu’s function and Kapur’s entropy (Khairuzzaman & Chaudhury, 2017). Some other applications of MFO algorithm such as, in finding optimal machining parameters (Yildiz, 2017), solar module design (Allam et al., 2016), training multi-layer perceptrons (Yamani, 2015), Power system optimization (Mei et al., 2017) etc. Successful application of these meta-heuristic algorithms inspires us to investigate the merit of MFO algorithm in multilevel thresholding using minimum cross entropy as the objective function.