A multilevel color image segmentation technique based on cuckoo search algorithm and energy curve

Amongst all the multilevel thresholding techniques, standard histogram based thresholding approaches are very impressive for bi-level thresholding. But, it is not effective to select spatial contextual information of the image for choosing optimal thresholds. In this paper, a new color image thresholding technique is presented by using an energy function to generate the energy curve of an image by considering spatial contextual information of the image. The property of this energy curve is very much similar to histogram of the image. To estimate the spatial contextual information for thresholding practice, in place of histogram, the energy curve function is used as an input. A new energy curve based color image segmentation approach using three well known objective functions named Kapur’s entropy, between-class-variance, and Tsalli’s entropy is proposed. In this paper, cuckoo search (CS) and egg lying radius-cuckoo search (ELR-CS) optimization algorithms with different parameter analysis have been used for solving the color image multilevel thresholding problem. The experimental results demonstrate that the proposed CS-Kapur’s energy curve based segmentation can powerfully and accurately search the multilevel thresholds.     

Oppositional symbiotic organisms search optimization for multilevel thresholding of color image

Selection of optimal threshold is the most crucial issue in threshold-based segmentation. In case of color image, this task is become challenging, because conventional color image segmentation has computational complexity and also it suffers from lack of accuracy. Various techniques such as threshold based, region growing, edge detection, graph cut, pixel classification, neural network, active contour, gray level co-occurrence matrix are proposed so far for image segmentation in the literature. Out of them, threshold-based segmentation is popular for its simplicity. To address the problem of color image segmentation, we propose an enhanced version of metaheuristic optimization algorithm called Opposition based Symbiotic Organisms Search (OSOS) to solve multilevel image thresholding technique for color image segmentation by introducing opposition based learning concepts to accelerate the convergence rate and enhance the performance of standard symbiotic organisms search (SOS). The performance of the proposed OSOS based algorithm is investigated thoroughly and compared with some existing techniques like Cuckoo Search (CS), BAT algorithm (BAT), artificial bee colony (ABC) and particle swarm optimization (PSO). The comparison is made by applying the algorithm to a set of color images taken from a well-known benchmark dataset (Berkeley Segmentation Dataset (BSDS)) and some of the color images collected for the COCO dataset. It is observed from the results that the performance of the OSOS based algorithm is promising with respect to standards SOS and others in terms of the values of objective functions as well as the values of some well-defined quality metrics such as peak signal-to-noise ratio (PSNR), structure similarity index (SSIM) and feature similarity index (FSIM). The results of the proposed algorithm may encourage the scientists and engineers to apply it into pattern recognition problems.     

Edge magnitude based multilevel thresholding using Cuckoo search technique

Multilevel thresholding technique is popular and extensively used in the field of image processing. In this paper, a multilevel threshold selection is proposed based on edge magnitude of an image. The gray level co-occurrence matrix (second order statistics) of the image is used for obtaining multilevel thresholds by optimizing the edge magnitude using Cuckoo search technique. New theoretical formulation for objective functions is introduced. Key to our success is to exploit the correlation among gray levels in an image for improved thresholding performance. Apart from qualitative improvements the method also provides us optimal threshold values. Results are compared with histogram (first order statistics) based between-class variance method for multilevel thresholding. It is observed that the results of our proposed method are encouraging both qualitatively and quantitatively.     

二维类内最小交叉熵的图像分割快速方法

熵是基于图像的一维灰度直方图得到的,仅利用了像素的灰度信息。最小交叉熵就是要寻找最优阈值使原始图像和分割图像之间的信息量的差异最小,在交叉熵的基础上,通过引入图像的空间信息,定义了二维类内交叉熵,并提出了基于二维类内最小交叉熵的图像分割方法。实验结果表明,充分利用图像的灰度信息和空间信息后,二维类内交叉熵取得了比交叉熵更好的分割效果。为了提高运算效率,提出了相应的快速递推算法,计算时间由从多于3小时减少到只要几秒。     

一种基于遗传算法的最小交叉熵阈值选择方法

最小交叉熵阈值法(MCET) 在二级阈值中是有效的, 但在多极阈值的穷尽搜索中却要付出昂贵的时间代价. 鉴于此, 提出一种基于遗传算法(GA) 的MCET选择方法: 在执行图像分割(IS) 任务之前, 先将IS 转化为在一定约束 条件下待优化的问题; 在寻找待优化问题最优解的计算过程中引入一种回归设计技巧以存储中间结果; 使用这种回 归设计技巧, 在一组标准测试图像上利用GA搜索待优化问题的最优解. 实验结果表明, 利用所提出的方法获得的多 个阈值非常接近于穷尽搜索获得的结果.

     

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.     

A novel hybrid algorithm of gravitational search algorithm with genetic algorithm for multi-level thresholding

The multi-level thresholding is a popular method for image segmentation. However, the method is computationally expensive and suffers from premature convergence when level increases. To solve the two problems, this paper presents an advanced version of gravitational search algorithm (GSA), namely hybrid algorithm of GSA with genetic algorithm (GA) (GSA-GA) for multi-level thresholding. In GSA-GA, when premature convergence occurred, the roulette selection and discrete mutation operators of GA are introduced to diversify the population and escape from premature convergence. The introduction of these operators therefore promotes GSA-GA to perform faster and more accurate multi-level image thresholding. In this paper, two common criteria (1) entropy and (2) between-class variance were utilized as fitness functions. Experiments have been performed on six test images using various numbers of thresholds. The experimental results were compared with standard GSA and three state-of-art GSA variants. Comparison results showed that the GSA-GA produced superior or comparative segmentation accuracy in both entropy and between-class variance criteria. Moreover, the statistical significance test demonstrated that GSA-GA significantly reduce the computational complexity for all of the tested images.     

基于遗传算法的彩色图像二维熵多阈值自适应分割

提出一种基于遗传算法的二维熵多阈值自适应图像分割方法.在分析研究二维熵阈值分割原理的基础上,将可变码长的遗传算法应用于多阈值分割处理过程,采用基于多阈值的整数编码方式,将图像分割的类别数即染色体的码长融合到适应度函数中,从而实现了在对阈值寻优的同时得以优化分割类别数,最终实现图像的多阈值自适应分割处理.实验分析结果表明,该方法具有实现阈值寻优速度快,最优解对应图像分割效果好的特点.     

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BBO算法的二维交叉熵多阈值图像分割*

针对复杂图像的分割问题,提出一种基于生物地理学优化算法(BBO,Biogeography-Based Optimization)的二维交叉熵多阈值图像分割方法。首先,根据二维直方图斜分法得出交叉熵阈值选取公式,并将此推广到多阈值分割,以求得多个极值提高分割效果,由于二维交叉熵法在多阈值分割时计时长、复杂性高等问题,然后引入BBO算法的思想,实现对多个阈值快速精确地寻优,最后,对标准图像进行分割以验证该算法。结果表明此算法比二维交叉熵穷举法计算效率高。     

图像阈值化的自适应粗糙熵方法

摘 要：目的：图像阈值化将灰度图像转换为二值图像,被广泛应用于多个领域。因实际工程应用中固有的不确定性,自动阈值选择仍然是一个极具挑战的课题。针对图像自动阈值化问题,提出了一种利用粗糙集的自适应方法。方法：该方法分析了基于粗糙集的图像表示框架,建立了图像粗糙粒度与局部灰度标准差的相互关系,通过最小化自适应粗糙粒度准则获得最优的划分粒度。进一步在该粒度下构造了图像目标和背景的上下近似集及其粗糙不确定度,通过搜索灰度级最大化粗糙熵获得图像最优灰度阈值,并将图像目标和背景的边界作为过渡区,利用其灰度均值作为阈值完成图像二值化。结果：对所提出的方法通过多个图像分三组进行了实验比较,包括三种经典阈值化方法和一种利用粗糙集的方法。其中,所提出的方法生成的可视化二值图像结果远远优于传统粗糙集阈值化方法。此外,也采用了误分率、平均结构相似性、假阴率和假阳率等指标进一步量化评估与比较相关实验结果。定性和定量的实验结果表明,所提出方法的图像分割质量较高、性能稳定。结论：所提出的方法适应能力较好,具有合理性和有效性,可以作为现有经典方法的有力补充。     

结合遗传算法的局部最小误差孔穴图像分割法

针对遗传算法和最小误差分割法各自的优缺点,将最小误差分割法与遗传算法进行改进并且相互结合,提出了一种结合遗传算法的局部最小误差孔穴图像分割法。该方法利用局部图像信息确定最佳阈值范围,并根据模拟退火思想对个体适应度进行自适应的调整,从而避免了早熟现象,提高了运算速度。实验结果表明:该方法不但能够准确地分割出孔穴图像,而且运算速度较快,是一种有效的孔穴图像分割方法。     

A two-dimensional multilevel thresholding method for image segmentation

In this work, we develop a two-dimensional multilevel thresholding technique based on Rényi and Tsallis entropies. The formulation of the proposed method gives rise to an NP-hard combinatorial optimization problem. In order to solve efficiently this problem, two leading evolutionary algorithms, namely the quantum genetic algorithm (QGA) and the differential evolution (DE) have been employed and compared. The effectiveness of both the proposed method and the optimizers was demonstrated on a sample of real-world and synthetic images showing different types of gray-level distributions. Moreover, the contribution of the two-dimensional histogram to the segmentation quality has been highlighted on some images corrupted by noise and containing shadow or reflection effects. Experimental results demonstrated, first, that DE is less time consuming than QGA which is slightly more efficient on complex problems. Second, the Rényi and Tsallis entropies leads to similar image segmentation quality. Finally, we have shown that the proposed method is more appropriate than bilevel thresholding for multimodal and noisy images segmentation.     

Fuzzy entropy based optimal thresholding using bat algorithm

Image segmentation is a very significant process in image analysis. Much effort based on thresholding has been made on this field as it is simple and intuitive, commonly used thresholding approaches are to optimize a criterion such as between-class variance or entropy for seeking appropriate threshold values. However, a mass of computational cost is needed and efficiency is broken down as an exhaustive search is utilized for finding the optimal thresholds, which results in application of evolutionary algorithm and swarm intelligence to obtain the optimal thresholds. This paper considers image thresholding as a constrained optimization problem and optimal thresholds for 1-level or multi-level thresholding in an image are acquired by maximizing the fuzzy entropy via a newly proposed bat algorithm. The optimal thresholding is achieved through the convergence of bat algorithm. The proposed method has been tested on some natural and infrared images. The results are compared with the fuzzy entropy based methods that are optimized by artificial bee colony algorithm (ABC), genetic algorithm (GA), particle swarm optimization (PSO) and ant colony optimization (ACO); moreover, they are also compared with thresholding methods based on criteria of between-class variance and Kapur's entropy optimized by bat algorithm. It is demonstrated that the proposed method is robust, adaptive, encouraging on the score of CPU time and exhibits the better performance than other methods involved in the paper in terms of objective function values.     

两种二维交叉熵阈值法等价性证明及快速实现

二维直方图斜分最大类间交叉熵阈值(TOSMICE)法和二维交叉熵直线型阈值(TMCELT)法是两种有效的分割方法,且都是二维交叉熵阈值法,为了考查二者分割结果是否相同,提出对两种二维交叉熵阈值法的等价性探讨。首先分析两种二维交叉熵阈值法：虽然名称不同但经过证明其分割原理相同,然后对两种选取公式进行推导得到一种最简阈值选取公式,从而证明了二者的等价性,随之提出基于最简公式的一般递推算法,最后将二维直方图分布特性与这种算法有机结合得到新型快速的递推算法。实验结果表明,两种方法获取的阈值相等,分割结果相同;并且与当前二维直方图斜分递推算法相比,所提出的新型递推算法速度更快。     

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.     

基于加权香农熵的图像阈值法

熵阈值法是图像分割的一种重要方法,在图像处理与识别中广为应用。针对最大熵阈值法是基于图像灰度分布的均匀性假设,导致它对有些图像分割无效的问题,首先提出了加权信息熵的图像分割新方法,其次对加权信息熵的灰度级权因子选取方式进行了探讨,最后给出了基于类内熵和类间熵相结合的图像分割效果评价新方法。实验结果表明,提出的方法是可行的。     

粒子群优化在图像最小误差阈值化中的应用

提出了一种基于粒子群优化（PSO）的图像最小误差阈值化方法。将粒子群优化算法应用于图像最小误差阈值化中,克服了常规最小误差阈值化计算量大的缺点。实验证明该算法能有效降低常规图像最小误差阈值化的计算量,与遗传算法相比,该方法有更好的收敛性和稳定性。     

基于量子粒子群优化算法的最小交叉熵多阈值图像分割*

首先提出了一种减少最小交叉熵适应度函数计算量的快速递推编程技术;然后采用量子粒子群优化法搜索获得图像最优多阈值,并用该阈值实现图像分割。实验分析结果表明,该方法具有实现阈值寻优速度快,最优解对应图像分割效果好的特点。     

基于分解的二维Renyi灰度熵的图像阈值分割

针对传统二维Renyi熵阈值法的高计算复杂性,提出一种新的基于分解的二维Renyi灰度熵阈值分割方法。该方法通过求解两个一维Renyi灰度熵阈值替代二维Renyi灰度熵的最佳阈值,理论上证明当满足一定条件时,两者等价;同时将计算复杂度由O(L4)降到O(L),所耗时间约为传统二维Renyi熵算法的1/10 000。