Modified bacterial foraging algorithm based multilevel thresholding for image segmentation

Multilevel thresholding is one of the most popular image segmentation techniques. In order to determine the thresholds, most methods use the histogram of the image. This paper proposes multilevel thresholding for histogram-based image segmentation using modified bacterial foraging (MBF) algorithm. To improve the global searching ability and convergence speed of the bacterial foraging algorithm, the best bacteria among all the chemotactic steps are passed to the subsequent generations. The optimal thresholds are found by maximizing Kapur's (entropy criterion) and Otsu's (between-class variance) thresholding functions using MBF algorithm. The superiority of the proposed algorithm is demonstrated by considering fourteen benchmark images and compared with other existing approaches namely bacterial foraging (BF) algorithm, particle swarm optimization algorithm (PSO) and genetic algorithm (GA). The findings affirmed the robustness, fast convergence and proficiency of the proposed MBF over other existing techniques. Experimental results show that the Otsu based optimization method converges quickly as compared with Kapur's method.     

基于最大模糊熵和微粒群的双阈值图像分割

基于最大模糊熵准则和微粒群算法,提出了一种新的双阈值图像分割方法.该方法通过定义3种模糊隶属度函数,将图像模糊划分为暗、灰和亮3个不同的区域.同时采用微粒群算法搜索最大模糊准则下模糊参数的最优组合,进而确定图像的两个最佳分割阈值.仿真结果表明,该算法具有良好的分割效果和较强的实时处理能力.     

Multi-level image thresholding using Otsu and chaotic bat algorithm

Multi-level thresholding is a helpful tool for several image segmentation applications. Evaluating the optimal thresholds can be applied using a widely adopted extensive scheme called Otsu’s thresholding. In the current work, bi-level and multi-level threshold procedures are proposed based on their histogram using Otsu’s between-class variance and a novel chaotic bat algorithm (CBA). Maximization of between-class variance function in Otsu technique is used as the objective function to obtain the optimum thresholds for the considered grayscale images. The proposed procedure is applied on a standard test images set of sizes (512 × 512) and (481 × 321). Further, the proposed approach performance is compared with heuristic procedures, such as particle swarm optimization, bacterial foraging optimization, firefly algorithm and bat algorithm. The evaluation assessment between the proposed and existing algorithms is conceded using evaluation metrics, namely root-mean-square error, peak signal to noise ratio, structural similarity index, objective function, and CPU time/iteration number of the optimization-based search. The results established that the proposed CBA provided better outcome for maximum number cases compared to its alternatives. Therefore, it can be applied in complex image processing such as automatic target recognition.

     

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.     

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.     

A study on particle swarm optimization and artificial bee colony algorithms for multilevel thresholding

Segmentation is a critical task in image processing. Bi-level segmentation involves dividing the whole image into partitions based on a threshold value, whereas multilevel segmentation involves multiple threshold values. A successful segmentation assigns proper threshold values to optimise a criterion such as entropy or between-class variance. High computational cost and inefficiency of an exhaustive search for the optimal thresholds leads to the use of global search heuristics to set the optimal thresholds. An emerging area in global heuristics is swarm-intelligence, which models the collective behaviour of the organisms. In this paper, two successful swarm-intelligence-based global optimisation algorithms, particle swarm optimisation (PSO) and artificial bee colony (ABC), have been employed to find the optimal multilevel thresholds. Kapur's entropy, one of the maximum entropy techniques, and between-class variance have been investigated as fitness functions. Experiments have been performed on test images using various numbers of thresholds. The results were assessed using statistical tools and suggest that Otsu's technique, PSO and ABC show equal performance when the number of thresholds is two, while the ABC algorithm performs better than PSO and Otsu's technique when the number of thresholds is greater than two. Experiments based on Kapur's entropy indicate that the ABC algorithm can be efficiently used in multilevel thresholding. Moreover, segmentation methods are required to have a minimum running time in addition to high performance. Therefore, the CPU times of ABC and PSO have been investigated to check their validity in real-time. The CPU time results show that the algorithms are scalable and that the running times of the algorithms seem to grow at a linear rate as the problem size increases.     

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。     

Multilevel minimum cross entropy threshold selection based on the firefly algorithm

The minimum cross entropy thresholding (MCET) has been widely applied in image thresholding. The search mechanism of firefly algorithm inspired by the social behavior of the swarms of firefly and the phenomenon of bioluminescent communication, is used to search for multilevel thresholds for image segmentation in this paper. This new multilevel thresholding algorithm is called the firefly-based minimum cross entropy thresholding (FF-based MCET) algorithm. Four different methods that are the exhaustive search, the particle swarm optimization (PSO), the quantum particle swarm optimization (QPSO) and honey bee mating optimization (HBMO) methods are implemented for comparison with the results of the proposed method. The experimental results show that the proposed FF-based MCET algorithm can efficiently search for multiple thresholds which are very close to the optimal ones examined by the exhaustive search method when the number of thresholds is less than 5. The need of computation time of using the FF-based MCET algorithm is the least, meanwhile, the results using the FF-based MCET algorithm is superior to the ones of PSO-based and QPSO-based MCET algorithms but is not significantly different to the HBMO-based MCET algorithm.     

广义模糊熵阈值法中基于粒子群优化的参数选取

针对广义模糊熵图像阈值分割法中参数m的选取问题,提出一种利用优化算法自适应选取参数的广义模糊熵阔值分割方法.该方法通过粒子群优化算法,依据图像分割质量评价准则对参数m在(0,1)区间进行全局寻优,并依据广义模糊熵最大准则对S型隶属度函数中的3个参数(a,b,d)进行全局组合寻优,从而实现了广义模糊熵图像阈值分割方法的自动阈值选取.实验结果表明,该方法对光照不均匀图像具有更好的分割效果.     

An efficient method for multilevel color image thresholding using cuckoo search algorithm based on minimum cross entropy

Among various thresholding methods, minimum cross entropy is implemented for its effectiveness and simplicity. Although it is efficient and gives excellent result in case of bi-level thresholding, but its evaluation becomes computationally costly when extended to perform multilevel thresholding owing to the exhaustive search performed for the optimum threshold values. Therefore, in this paper, an efficient multilevel thresholding technique based on cuckoo search algorithm is adopted to render multilevel minimum cross entropy more practical and reduce the complexity. Experiments have been conducted over different color images including natural and satellite images exhibiting low resolution, complex backgrounds and poor illumination. The feasibility and efficiency of proposed approach is investigated through an extensive comparison with multilevel minimum cross entropy based methods that are optimized using artificial bee colony, bacterial foraging optimization, differential evolution, and wind driven optimization. In addition, the proposed approach is compared with thresholding techniques depending on between-class variance (Otsu) method and Tsalli’s entropy function. Experimental results based on qualitative results and different fidelity parameters depicts that the proposed approach selects optimum threshold values more efficiently and accurately as compared to other compared techniques and produces high quality of the segmented images.     

An improved biogeography based optimization approach for segmentation of human head CT-scan images employing fuzzy entropy

The present paper proposes the development of a three-level thresholding based image segmentation technique for real images obtained from CT scanning of a human head. The proposed method utilizes maximization of fuzzy entropy to determine the optimal thresholds. The optimization problem is solved by employing a very recently proposed population-based optimization technique, called biogeography based optimization (BBO) technique. In this work we have proposed some improvements over the basic BBO technique to implement nonlinear variation of immigration rate and emigration rate with number of species in a habitat. The proposed improved BBO based algorithm and the basic BBO algorithm are implemented for segmentation of fifteen real CT image slices. The results show that the proposed improved BBO variants could perform better than the basic BBO technique as well as genetic algorithm (GA) and particle swarm optimization (PSO) based segmentation of the same images using the principle of maximization of fuzzy entropy.     

Kapur’s entropy based optimal multilevel image segmentation using Crow Search Algorithm

Image segmentation is an essential part of image analysis, which has a direct impact on the quality of image analysis results. Thresholding is one of the simplest and widely used methods for image segmentation. Thresholding can be either bi-level, which involves partitioning of an image into two segments, or multilevel, which partitions an image into multiple segments using multiple thresholds values. This paper focuses on multilevel thresholding. A good segmentation scheme through multilevel thresholding identifies suitable threshold values to optimize between-class variance or entropy criterion. For such optimizations, nature inspired metaheuristic algorithms are commonly used. This paper presents a Kapur’s entropy based Crow Search Algorithm (CSA) to estimate optimal values of multilevel thresholds. Crow Search Algorithm is based on the intelligent behavior of crow flock. Crow Search Algorithm have shown better results because of less number of parameters, no premature convergence, and better exploration–exploitation balance in the search strategy. Kapur’s entropy is used as an objective function during the optimization process. The experiments have been performed on benchmarked images for different threshold values (i.e. 2, 4, 8, 16, 32 thresholds). The proposed method has been assessed and performance is compared with well-known metaheuristic optimization methods like Particle Swarm Optimization (PSO), Differential Evolution (DE), Grey Wolf Optimizer (GWO), Moth-Flame Optimization (MFO) and Cuckoo Search (CS). Experimental results have been evaluated qualitatively and quantitatively by using well-performed evaluation methods namely PSNR, SSIM, and FSIM. Computational time and Wilcoxon p-type value also compared. Experimental results show that proposed algorithm performed better than PSO, DE, GWO, MFO and CS in terms of quality and consistency.     

基于混沌布谷鸟优化的二维Tsallis交叉熵建筑物遥感图像分割

为了进一步提升建筑物遥感图像分割的准确性和运算速度,本文提出了基于混沌布谷鸟优化的二维Tsallis交叉熵的建筑物遥感图像分割方法。首先给出了二维Tsallis交叉熵的阈值选取公式,然后将Logistic混沌映射引入布谷鸟算法,进一步加快布谷鸟算法的收敛速度,最后通过该混沌布谷鸟算法优化基于二维Tsallis交叉熵的阈值寻找过程,并以得到的最优阈值分割建筑物遥感图像。大量实验结果表明,与二维倒数交叉熵法、二维Tsallis熵法、基于混沌粒子群优化的二维Tsallis灰度熵法等方法相比较,本文方法分割的目标更为准确,细节更为清晰,且运算时间更短。     

基于小生境粒子群算法的图像分割方法

为了得到分割图像的最佳阈值,提出了一种基于小生境粒子群算法的图像分割方法。小生境粒子群算法通过划分小生境的方法,保持了物种的多样性,克服了粒子群算法容易陷入局部解,后期收敛速度慢的缺点,提高了算法的全局寻优能力。该方法基于最大类间方差阈值分割技术,用小生境粒子群算法对适应度函数进行优化,得到最佳阈值,并用该阈值对图像进行分割。实验结果表明,与最大类间方差法,基于基本粒子群算法的最大类间方差分割法相比,所提出的方法不仅能得到理想的分割结果,而且分割速度也得到了提高。     

多种群联合的多目标进化自适应阈值图像分割算法*

多阈值图像分割算法的阈值数目大多需要用户指定,人为干预较大。本文提出多种群联合的多目标进化自适应阈值图像分割算法,本文提出多种群联合的多目标进化自适应阈值图像分割算法,在多个分组种群的联合进化框架下,通过同时优化类间方差准则和模糊熵准则获得图像阈值,并在进化过程中采用自调节的交叉和变异操作产生子代种群并自动确定阈值数目。实验结果表明,该算法不仅能自适应得到合适的阈值数目,而且阈值分割效果也是比较理想的。     

基于模糊Havrda-Charvát熵与混沌PSO算法的红外人体图像分割

针对红外人体图像成像质量较差的问题,提出一种基于模糊Havrda-Charvát熵的快速阈值分割方法.首先应用Z形及S形隶属度函数把图像灰度直方图信息转换到模糊域,定义图像背景与目标的模糊Havrda-Charvát熵;然后提出一种基于Tent映射的混沌粒子群优化算法,把隶属度函数参数组合作为粒子,根据最大熵原理确定参数的最佳组合,再由最佳隶属度函数参数计算得到图像的最佳分割阈值.在真实红外人体图像集上与几种经典的图像阈值方法进行对比实验的结果,说明了该方法的有效性和鲁棒性.     

广义模糊熵图像阈值分割参数选取的ADE方法

针对广义模糊熵图像阈值分割参数不能自动选取,提出自适应差分进化（Adaptive Differential Evolution,ADE）的广义模糊熵图像阈值分割方法。利用自适应差分进化算法作为优化工具来选取广义模糊熵阈值分割所需要的最佳参数,引入自适应变异算子和提出交叉概率自适应函数对优化过程进行控制,通过把参数带入广义模糊熵的补函数得到图像的阈值,进而得到图像最优分割。为验证其有效性与可行性,分别同基本图像质量评价准则的模糊熵图像阈值分割算法和粒子群优化广义模糊熵图像阈值分割算法相比较,实验表明,针对不同细节的图片,该算法所得分割结果多数情况下背景信息更少,目标信息更清晰,用时更短,分割更稳定且效果良好。     

A novel local contrast fusion-based fuzzy model for color image multilevel thresholding using grasshopper optimization

The segmentation process is considered the significant step of an image processing system due to its extreme inspiration on the subsequent image analysis. Out of various approaches, thresholding is one of the most popular schemes for image segmentation. In segmentation, image pixels are arranged in various regions based on their intensity levels. In this paper, a straightforward and efficient fusion-based fuzzy model for multilevel color image segmentation using grasshopper optimization algorithm (GOA) has been proposed. Thresholding based segmentation lacks accuracy in segmenting the ambiguous images due to their complex characteristics, uncertainties and inherent fuzziness. However, the fuzzy entropy resolves these problems, but it is unable for segmenting at higher levels and also the complexity level for selecting suitable thresholds is high. The selection of metaheuristic GOA reduces this problem by selecting optimal threshold values. Therefore, to increase the quality of the segmented image, a simple and effective multilevel thresholding method is exploited by using the concept of fusion which is based on the local contrast. Experimental outputs demonstrate that fusion-based multilevel thresholding is better than most specific segmentation methods and can be validated by comparing the different numerical parameters. Experiments on standard daily-life color and satellite images are conducted to prove the effectiveness of the proposed scheme.     

Efficient multilevel image segmentation through fuzzy entropy maximization and graph cut optimization

The fuzzy c-partition entropy has been widely adopted as a global optimization technique for finding the optimized thresholds for multilevel image segmentation. However, it involves expensive computation as the number of thresholds increases and often yields noisy segmentation results since spatial coherence is not enforced. In this paper, an iterative calculation scheme is presented for reducing redundant computations in entropy evaluation. The efficiency of threshold selection is further improved through utilizing the artificial bee colony algorithm as the optimization technique. Finally, instead of performing thresholding for each pixel independently, the presented algorithm oversegments the input image into small regions and uses the probabilities of fuzzy events to define the costs of different label assignments for each region. The final segmentation results is computed using graph cut, which produces smooth segmentation results. The experimental results demonstrate the presented iterative calculation scheme can greatly reduce the running time and keep it stable as the number of required thresholds increases. Quantitative evaluations over 20 classic images also show that the presented algorithm outperforms existing multilevel segmentation approaches.     

基于粒子群优化算法和模糊熵的多级阈值图像分割算法

针对现有阈值分割算法利用穷举搜索寻找最优阈值而造成的计算成本较大的问题,提出了一种基于粒子群优化算法和模糊熵的多级阈值图像分割算法。图像分割是图像分析中非常重要的预处理步骤,在提出的方法中,首先选择香农熵和模糊熵作为优化技术的目标函数;然后建立一种基于粒子群优化算法的多层次图像阈值分割,通过最大化香农熵或模糊熵进行图像分割。最后从图像分割数据库中选取Lena、baboon和airplane作为测试图像进行性能分析（包括鲁棒性、效率和收敛性）,并与现有的几种阈值分割算法进行比较。结果显示,提出的算法得到了更高PSNR值和更少的分类误差,证明了该算法是一种高效的多级阈值图像分割算法。