# [PERSON]'s Entropy Based Multilevel Thresholding Using a Novel Meta-Heuristics Algorithm
## 1 Introduction  
With the rapid development of computers, technologies of image processing were applied widely in many areas, including quality estimation [1; 2], infrared detection [3; 4], disease recognition [5; 6], agricultural identification [7; 8], fingerprint identification [9], and many other aspects [10; 11]. Especially, image analysis has become a very useful method in the study of cement microstructure based on the cement SEM (scanning electron microscope) image [12], as it is possible to analyze the mechanism of cement hydration reaction by observing the microstructure of cement in cement stone materials [13]. Image segmentation is the first step of image understanding, and any other steps (such as feature extraction and recognition) largely depend on its results, it is to partition an image into interrelated parts or regions, which are composed of image pixels with related data eigenvalues. Threshold technology is considered as the most popular image segmentation algorithm, which has the advantages of small storage space, fast processing speed, and easy operation. Some successful thresholding approaches have been proposed for image segmentation, including inter class variance method (OTSU) [14], the maximum entropy-based thresholding method [15], [PERSON]'s entropy-based thresholding method [16], [PERSON] entropy based thresholding method [17], and so on. Due to the complexity of the real world, multi-level thresholding-based partition methods have become morebroadly used for practical work [18; 19; 20]. When the one-dimensional threshold algorithm is extended to multiple dimensions, they may show high computational cost and do not meet real-time requirements when the number of classes to be detected increases. In essence, this problem could be viewed as a combinatorial optimization problem, and meta-heuristics algorithms are often employed to deal with this kind of problem. For instance, [PERSON], [PERSON], et al. combined improved fruit fly optimization algorithm with support vector machine and used it to classify pancreatic cancer [21], ant colony optimization were utilized for the selection of accounting models, graph anonymization and robot rescue mission [22; 23; 24], [PERSON], [PERSON] et al. applied hybrid genetic algorithms to the diagnosis of heart disease [25], and many other evolutionary algorithms have been applied to solve optimization problems in various fields [26; 27; 28]. There is no doubt that a lot of researches have been conducted around the multi-threshold segmentation handled with evolutionary algorithms, such as hybrid whale optimization algorithm is employed in Kapur entropy for multi-threshold segmentation [29], combine particle swarm optimization algorithm with Tsallis entropy for multi-threshold segmentation [30], ant colony optimization algorithm is employed in OTSU to quickly search for multiple thresholds in images [31], some other optimization algorithms are also used for multi-threshold segmentation, such as water cycle algorithm [32], cuckoo search algorithm [33], knee evolutionary algorithm [34], differential evolution algorithm [35], and bat algorithm [36]. These efforts have achieved good results; however, it is hard for meta-heuristic optimization algorithms to obtain the same optimal solution as the exhaustive method with the increment of the number of thresholds in seconds. Inspired by the breeding mechanism of Chinese hybrid rice, a novel meta-heuristics algorithm is proposed [37], for simplicity, it is called hybrid rice optimization algorithm (HRO). HRO has the advantages of strong stability, large search range, and strong optimization. In [37], it is shown that HRO prevails over particle swarm optimization (PSO), differential evolution algorithms (DE), genetic algorithm (GA), artificial bee colony (ABC) on the basis of six benchmark functions. At the same time, HRO has also been used for security situation prediction in [38]. Preliminary studies show that it is very prospective and competition for the problem with low or middle dimension.