Whale Optimization Algorithm and Moth-Flame Optimization for multilevel thresholding image segmentation

Determining the optimal thresholding for image segmentation has got more attention in recent years since it has many applications. There are several methods used to find the optimal thresholding values such as Otsu and Kapur based methods. These methods are suitable for bi-level thresholding case and they can be easily extended to the multilevel case, however, the process of determining the optimal thresholds in the case of multilevel thresholding is time-consuming. To avoid this problem, this paper examines the ability of two nature inspired algorithms namely: Whale Optimization Algorithm (WOA) and Moth-Flame Optimization (MFO) to determine the optimal multilevel thresholding for image segmentation. The MFO algorithm is inspired from the natural behavior of moths which have a special navigation style at night since they fly using the moonlight, whereas, the WOA algorithm emulates the natural cooperative behaviors of whales. The candidate solutions in the adapted algorithms were created using the image histogram, and then they were updated based on the characteristics of each algorithm. The solutions are assessed using the Otsu’s fitness function during the optimization operation. The performance of the proposed algorithms has been evaluated using several of benchmark images and has been compared with five different swarm algorithms. The results have been analyzed based on the best fitness values, PSNR, and SSIM measures, as well as time complexity and the ANOVA test. The experimental results showed that the proposed methods outperformed the other swarm algorithms; in addition, the MFO showed better results than WOA, as well as provided a good balance between exploration and exploitation in all images at small and high threshold numbers.     

Human mental search-based multilevel thresholding for image segmentation

Multilevel thresholding is one of the principal methods of image segmentation. These methods enjoy image histogram for segmentation. The quality of segmentation depends on the value of the selected thresholds. Since an exhaustive search is made for finding the optimum value of the objective function, the conventional methods of multilevel thresholding are time-consuming computationally, especially when the number of thresholds increases. Use of evolutionary algorithms has attracted a lot of attention under such circumstances. Human mental search algorithm is a population-based evolutionary algorithm inspired by the manner of human mental search in online auctions. This algorithm has three interesting operators: (1) clustering for finding the promising areas, (2) mental search for exploring the surrounding of every solution using Levy distribution, and (3) moving the solutions toward the promising area. In the present study, multilevel thresholding is proposed for image segmentation using human mental search algorithm. Kapur (entropy) and Otsu (between-class variance) criteria were used for this purpose. The advantages of the proposed method are described using twelve images and in comparison with other existing approaches, including genetic algorithm, particle swarm optimization, differential evolution, firefly algorithm, bat algorithm, gravitational search algorithm, and teaching-learning-based optimization. The obtained results indicated that the proposed method is highly efficient in multilevel image thresholding in terms of objective function value, peak signal to noise, structural similarity index, feature similarity index, and the curse of dimensionality. In addition, two nonparametric statistical tests verified the efficiency of the proposed algorithm, statistically.     

Fractional differentiation and non-Pareto multiobjective optimization for image thresholding

Various techniques have previously been proposed for single-stage thresholding of images to separate objects from the background. Although these global or local thresholding techniques have proven effective on particular types of images, none of them is able to produce consistently good results on a wide range of existing images. Here, a new image histogram thresholding method, called TDFD, based on digital fractional differentiation is presented for gray-level image thresholding. The proposed method exploits the properties of the digital fractional differentiation and is based on the assumption that the pixel appearance probabilities in the image are related. To select the best fractional differentiation order that corresponds to the best threshold, a new algorithm based on non-Pareto multiobjective optimization is presented. A new geometric regularity criterion is also proposed to select the best thresholded image. In order to illustrate the efficiency of our method, a comparison was performed with five competing methods: the Otsu method, the Kapur method, EM algorithm based method, valley emphasis method, and two-dimensional Tsallis entropy based method. With respect to the mode of visualization, object size and image contrast, the experimental results show that the segmentation method based on fractional differentiation is more robust than the other methods.     

多目标粒子群和人工蜂群混合优化的阈值图像分割算法

在图像分割中,为了准确地把目标和背景分离出来,提出了一种基于多目标粒子群和人工蜂群混合优化的阈值图像分割算法。在多目标优化的框架下,将改进的类间方差准则和最大熵准则作为适应度函数,通过粒子群和蜂群混合优化这2个适应度函数来获得1组非支配解。同时,为了提高全局和局部搜索能力,在蜂群进化时,将粒子群的全局最优解引入到人工蜂群算法的雇佣蜂阶段蜜源的更新中,并对搜索方程进行改进。最后通过类间差异和改进的类内差异的加权比值,从一组非支配解中选取最优阈值。实验结果表明,该算法能够取得理想的分割结果。     

Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy

The objective of image segmentation is to extract meaningful objects. A meaningful segmentation selects the proper threshold values to optimize a criterion using entropy. The conventional multilevel thresholding methods are efficient for bi-level thresholding. However, they are computationally expensive when extended to multilevel thresholding since they exhaustively search the optimal thresholds to optimize the objective functions. To overcome this problem, two successful swarm-intelligence-based global optimization algorithms, cuckoo search (CS) algorithm and wind driven optimization (WDO) for multilevel thresholding using Kapur’s entropy has been employed. For this purpose, best solution as fitness function is achieved through CS and WDO algorithm using Kapur’s entropy for optimal multilevel thresholding. A new approach of CS and WDO algorithm is used for selection of optimal threshold value. This algorithm is used to obtain the best solution or best fitness value from the initial random threshold values, and to evaluate the quality of a solution, correlation function is used. Experimental results have been examined on standard set of satellite images using various numbers of thresholds. The results based on Kapur’s entropy reveal that CS, ELR-CS and WDO method can be accurately and efficiently used in multilevel thresholding problem.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

Image segmentation using multilevel thresholding based on modified bird mating optimization

Multimedia Tools and Applications - Multilevel thresholding using Otsu or Kapur methods is widely used in the context of image segmentation. These methods select optimal thresholds in gray level...     

Cross entropy based thresholding for magnetic resonance brain images using Crow Search Algorithm

Segmentation is considered the central part of an image processing system due to its high influence on the posterior image analysis. In recent years, the segmentation of magnetic resonance (MR) images has attracted the attention of the scientific community with the objective of assisting the diagnosis in different brain diseases. From several techniques, thresholding represents one of the most popular methods for image segmentation. Currently, an extensive amount of contributions has been proposed in the literature, where thresholding values are obtained by optimizing relevant criteria such as the cross entropy. However, most of such approaches are computationally expensive, since they conduct an exhaustive search strategy for obtaining the optimal thresholding values. This paper presents a general method for image segmentation. To estimate the thresholding values, the proposed approach uses the recently published evolutionary method called the Crow Search Algorithm (CSA) which is based on the behavior in flocks of crows. Different to other optimization techniques used for segmentation proposes, CSA presents a better performance, avoiding critical flaws such as the premature convergence to sub-optimal solutions and the limited exploration-exploitation balance in the search strategy. Although the proposed method can be used as a generic segmentation algorithm, its characteristics allow obtaining excellent results in the automatic segmentation of complex MR images. Under such circumstances, our approach has been evaluated using two sets of benchmark images; the first set is composed of general images commonly used in the image processing literature, while the second set corresponds to MR brain images. Experimental results, statistically validated, demonstrate that the proposed technique obtains better results in terms of quality and consistency.     

基于鱼群算法的图像阈值分割*

本文提出了一种基于鱼群算法的二维阈值图像分割的新方法。传统的二维Otsu方法考虑了图像的灰度信息和像素间的空间邻域信息,是一种有效的图像分割方法。针对Ostu方法的计算量大、运行时间长的缺陷,采用鱼群算法来搜索最优二维阈值向量,通过鱼群追尾行为获得最优阈值。实验结果表明,所提出的方法不仅能得到理想的分割结果,而且分割速度快。     

灰度图像二维Otsu折线阈值分割法

Otsu法是一个应用较为广泛的阈值分割方法。为实现图像较为精确的分割,充分考虑边界的影响,从二维线阈值分割替代传统的点阈值分割思想出发,提出了折线阈值型Otsu法。该方法以对边界信息的迭代分割的手段获得实际用于分割的二维折线阈值。仿真结果表明,该方法能够获得优于原始Otsu法的分割效果,特别适用于边缘丰富的图像分割,具有较好的分割普适性。     

自适应最小误差阈值分割算法

对二维最小误差法进行三维推广, 并结合三维直方图重建和降维思想提出了一种鲁 棒的最小误差阈值分割算法. 但该方法为全局算法, 仅适用于分割均匀光照图像. 为 提高其自适应性, 本文采用Water flow模型对非均匀光照图像进行背景估计, 以此获 得原始图像与背景图像的差值图像, 达到降低非均匀光照对图像分割造成干扰的目的. 为进 一步提高分割性能, 本文对差值图像采用γ 矫正进行增强, 然后采用鲁棒最小误差 法进行全局分割, 从而完成目标提取. 最后本文对均匀光照下以及非均匀光照下图像进行了 实验, 并与一维最小误差法、二维最小误差法、三维直方图重建和降维的Otsu阈值分割 算法、灰度波动变换自适应阈值方法以及一种改进的FCM方法在错误分割率和运行时间上进 行了对比. 实验结果表明, 相对于以上方法, 本算法的分割性能均有明显提升.     

A Local Contrast Fusion Based 3D Otsu Algorithm for Multilevel Image Segmentation

To overcome the shortcomings of 1D and 2D Otsu’s thresholding techniques, the 3D Otsu method has been developed. Among all Otsu’s methods, 3D Otsu technique provides the best threshold values for the multi-level thresholding processes. In this paper, to improve the quality of segmented images, a simple and effective multilevel thresholding method is introduced. The proposed approach focuses on preserving edge detail by computing the 3D Otsu along the fusion phenomena. The advantages of the presented scheme include higher quality outcomes, better preservation of tiny details and boundaries and reduced execution time with rising threshold levels. The fusion approach depends upon the differences between pixel intensity values within a small local space of an image; it aims to improve localized information after the thresholding process. The fusion of images based on local contrast can improve image segmentation performance by minimizing the loss of local contrast, loss of details and gray-level distributions. Results show that the proposed method yields more promising segmentation results when compared to conventional 1D Otsu, 2D Otsu and 3D Otsu methods, as evident from the objective and subjective evaluations.      

A multi-scale 3D Otsu thresholding algorithm for medical image segmentation

Thresholding technique is one of the most imperative practices to accomplish image segmentation. In this paper, a novel thresholding algorithm based on 3D Otsu and multi-scale image representation is proposed for medical image segmentation. Considering the high time complexity of 3D Otsu algorithm, an acceleration variant is invented using dimension decomposition rule. In order to reduce the effects of noises and weak edges, multi-scale image representation is brought into the segmentation algorithm. The whole segmentation algorithm is designed as an iteration procedure. In each iteration, the image is segmented by the efficient 3D Otsu, and then it is filtered by a fast local Laplacian filtering to get a smoothed image which will be input into the next iteration. Finally, the segmentation results are pooled to get a final segmentation using majority voting rules. The attractive features of the algorithm are that its segmentation results are stable, it is robust to noises and it holds for both bi-level and multi-level thresholding cases. Experiments on medical MR brain images are conducted to demonstrate the effectiveness of the proposed method. The experimental results indicate that the proposed algorithm is superior to the other multilevel thresholding algorithms consistently.     

工业检测图像灰度波动变换自适应阈值分割算法

工业检测图像经常受到不均光照的影响,对该类图像局部自适应分割算法比全局算法能产生更好的分割效果. 但局部算法中基于分块的算法对分块方法缺乏指导,而基于邻域的算法容易在背景或前景内部产生误分. 针对上述缺点,本文提出了一种多方向灰度波动变换的自适应阈值分割算法. 该算法先从多个方向依照灰度波动对图像进行转换,构造以多维向量为基础的灰度波动变换矩阵, 然后利用主成分分析法(Principal component analysis, PCA)将高维向量压缩至一维并生成变换图像,最后运用Otsu算法分割变换图像. 该算法无需分块,并且仅需波动幅度阈值和布尔型背景色两个参数. 实验结果表明,该算法能够有效减少不均光照对工业检测图像分割的影响, 与Niblack法、Sauvola法等几种局部算法相比,该法在分割效果上具有了明显的提升.     

Multilevel threshold selection for image segmentation using soft computing techniques

Multilevel thresholding is the method applied to segment the given image into unique sub-regions when the gray value distribution of the pixels is not distinct. The segmentation results are affected by factors such as number of threshold and threshold values. Hence, this paper proposes different methods for determining optimal thresholds using optimization techniques namely GA, PSO and hybrid model. Parallel algorithms are also proposed and implemented for these methods to reduce the execution time. From the experimental results, it is inferred that proposed methods take less time for determining the optimal thresholds when compared with existing methods such as Otsu and Kapur methods.     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

Multilevel thresholding selection based on the artificial bee colony algorithm for image segmentation

Multilevel thresholding is an important technique for image processing and pattern recognition. The maximum entropy thresholding (MET) has been widely applied in the literature. In this paper, a new multilevel MET algorithm based on the technology of the artificial bee colony (ABC) algorithm is proposed: the maximum entropy based artificial bee colony thresholding (MEABCT) method. Four different methods are compared to this proposed method: the particle swarm optimization (PSO), the hybrid cooperative-comprehensive learning based PSO algorithm (HCOCLPSO), the Fast Otsu’s method and the honey bee mating optimization (HBMO). The experimental results demonstrate that the proposed MEABCT algorithm can search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method. Compared to the other four thresholding methods, the segmentation results of using the MEABCT algorithm is the most, however, the computation time by using the MEABCT algorithm is shorter than that of the other four methods.     

细胞膜机制萤火虫算法优化多阈值Otsu图像分割

图像阈值分割是将灰度图像转换为二值图像的常用图像分割方式.经典多阈值Otsu算法对复杂图像进行分割取得了很好的效果,但是其采用穷举方法来寻找最优阈值是非常耗时的.针对这一问题,本文提出了一种基于细胞膜和自适应步长萤火虫混合优化算法的多阈值Otsu图像分割方法.利用萤火虫算法的启发式搜索来寻找图像分割的最优阈值很好地降低了算法的时间复杂度,并且在萤火虫算法中混合细胞膜算法很好地解决了萤火虫算法的"早熟"现象.实验结果表明,与经典多阈值Otsu法和萤火虫算法优化多阈值Otsu法相比,本文提出的算法具有更高的收敛速度和更好的图像分割效果,并且有效解决了萤火虫算法易陷入局部最优的问题.     

混合择优的多目标免疫粒子群优化算法

为解决多目标粒子群优化算法存在解的多样性差、分布不均等问题,提出一种混合择优机制：在迭代过程中每个粒子依概率,根据解集信息熵或Sigma值确定其全局极值;并直接对解集进行基于信息熵的克隆选择,根据支配关系更新解集,充分发掘分布性更好的解。测试函数的仿真实验结果表明,该算法在保持较好的收敛性能的同时,其求解的分布性指标要明显优于其他算法,这说明混合择优机制能够有效地提升多目标粒子群优化算法求解的多样性和分布性。     

Hybrid marine predators algorithm for image segmentation: analysis and validations

Naturally, to analyze an image accurately, all the similar objects within it should be separated to pay attention to the most important object for reaching more details and hence achieving better accuracy. Therefore, multilevel thresholding is an indispensable image processing technique in the field of image segmentation and is employed widely to separate those similar objects. However, with increasing thresholds, the existing image segmentation techniques might suffer from exponentially-grown computational cost and low accuracy due to local optima shortage. Therefore, in this paper, a new image segmentation algorithm based on the improved marine predators algorithm (MPA) is proposed. MPA is improved using a strategy to find a number of the worst solutions within the population then tries to search for other better ones for those solutions by moving them gradually towards the best solutions to avoid accelerating to local optima and randomly within the search space based on a certain probability. In addition, this number of the worst solutions is increased with the iteration. This strategy is known as the linearly increased worst solutions improvement strategy (LIS). Also, we suggested that apply the ranking strategy based on a novel updating scheme, namely ranking-based updating strategy (RUS), on the solutions that could find better solutions in the last number iterations, perIter, in the hope of finding better solutions near it. RUS updates the particles/solutions which could not find better solutions than the best-local one in a number of consecutive iterations, with those that are generated based on a novel updating strategy. LIS is integrated with MPA to produce a new segmentation meta-heuristic algorithm abbreviated as MPALS. Also, MPALS and RUS are combined to tackle ISP in a strong variant abbreviated as HMPA for overcoming the image segmentation problem. The two proposed algorithms are validated on 14 test images and compared with seven state-of-the-arts meta-heuristic algorithms. The experimental results show the effectiveness of HMPA with increasing the threshold levels compared to the seven state-of-the-arts algorithms when segmenting an image, while their performance is roughly the same for the image with a small threshold level.