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.      

基于广义调和均值距离的图像分割新算法

提出了基于广义调和均值距离的最小偏差图像阈值化分割新算法。Otsu阈值法是图像分割中最典型阈值法之一,因其计算简单、速度快和性能稳定等优点而在图像分割中得到广泛应用;但是,传统Otsu阈值法是基于欧式距离的最小偏差阈值法,由于欧式距离没有可调节参数而导致Otsu阈值法分割图像缺乏鲁棒性。首先将Otsu图像分割法中的欧式距离用广义调和均值距离代替并得到一种具有鲁棒性的图像分割新算法,其次给出该算法中参数选取办法。大量实验结果表明,新的图像分割算法相比Otsu法更有效。     

融合非局部空间灰度信息的三维Otsu法

为了提高最大类间方差阈值分割法(Otsu)对于图像噪声的鲁棒性,提出融合非局部空间灰度信息的三维Otsu法。该方法利用图像像素的灰度信息、邻域中值灰度信息和非局部空间灰度信息进行直方图统计,构建新颖的三维直方图,采用最大类间方差作为阈值选取准则。实验结果表明新方法对于噪声的鲁棒性要优于原始三维Otsu法,能够获得更加令人满意的分割结果。     

A hybrid differential evolution for optimal multilevel image thresholding

Image thresholding is a process for separating interesting objects within an image from their background. An optimal threshold’s selection can be regarded as a single objective optimization problem, where obtaining a solution can be computationally expensive and time-consuming, especially when the number of thresholds increases greatly. This paper proposes a novel hybrid differential evolution algorithm for selecting the optimal threshold values for a given gray-level input image, using the criterion defined by Otsu. The hybridization is done by adding a reset strategy, adopted from the Cuckoo Search, within the evolutionary loop of differential evolution. Additionally a study of different evolutionary or swarm-based intelligence algorithms for the purpose of thresholding, with a higher number of thresholds was performed, since many real-world applications require more than just a few thresholds for further processing. Experiments were performed on eleven real world images. The efficiency of the hybrid was compared to the cuckoo search and self-adaptive differential evolution, the original differential evolution, particle swarm optimization, and artificial bee colony where the results showed the superiority of the hybrid in terms of better segmentation results with the increased number of thresholds. Since the proposed method needs only two parameters adjusted, it is by far a better choice for real-life applications.     

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.

     

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.     

二维Otsu阈值法的快速算法

最大类间方差法(Otsu)是图像分割的经典算法,在其基础之上发展起来的二维Otsu阈值分割法由于计算复杂而制约了其应用。针对这一缺点,提出一种改进的二维Otsu阈值法的快速算法。首先将原始二维直方图划分成M×M个区域,将每个区域视为1个点,构造新的二维直方图,在其上利用二维Otsu以及快速递推算法,得到分割阈值所处的区域编号;既而对所确定的区域再次使用二维Otsu算法得到原始图像的分割阈值。实验结果证明,改进算法有效地提高了计算速度,降低了算法的空间复杂度,且分割效果与原始算法基本一致。     

利用混沌布谷鸟优化的二维Renyi灰度熵图像阈值选取

为了进一步降低现有的Renyi熵阈值法的计算复杂度,提出了基于混沌布谷鸟算法和二维Renyi灰度熵的阈值选取。首先,引入一维Renyi灰度熵阈值选取公式,建立基于像素灰度和邻域梯度的二维直方图,推导出基于该直方图的二维Renyi灰度熵阈值选取公式,通过快速递推公式来减少阈值准则函数的计算量;最后,采用混沌布谷鸟算法搜索最优阈值来完成图像分割。结果表明,与二维Arimoto熵法、基于粒子群的二维Renyi熵法、基于混沌粒子群的二维Tsallis灰度熵法、基于布谷鸟算法的二维Renyi灰度熵法相比,所提出的方法能够准确实现图像分割,且运算速度有所提升。     

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。     

A new social and momentum component adaptive PSO algorithm for image segmentation

In this paper, we present a new variant of Particle Swarm Optimization (PSO) for image segmentation using optimal multi-level thresholding. Some objective functions which are very efficient for bi-level thresholding purpose are not suitable for multi-level thresholding due to the exponential growth of computational complexity. The present paper also proposes an iterative scheme that is practically more suitable for obtaining initial values of candidate multilevel thresholds. This self iterative scheme is proposed to find the suitable number of thresholds that should be used to segment an image. This iterative scheme is based on the well known Otsu’s method, which shows a linear growth of computational complexity. The thresholds resulting from the iterative scheme are taken as initial thresholds and the particles are created randomly around these thresholds, for the proposed PSO variant. The proposed PSO algorithm makes a new contribution in adapting ‘social’ and ‘momentum’ components of the velocity equation for particle move updates. The proposed segmentation method is employed for four benchmark images and the performances obtained outperform results obtained with well known methods, like Gaussian-smoothing method (Lim, Y. K., & Lee, S. U. (1990). On the color image segmentation algorithm based on the thresholding and the fuzzy c-means techniques. Pattern Recognition, 23, 935–952; Tsai, D. M. (1995). A fast thresholding selection procedure for multimodal and unimodal histograms. Pattern Recognition Letters, 16, 653–666), Symmetry-duality method (Yin, P. Y., & Chen, L. H. (1993). New method for multilevel thresholding using the symmetry and duality of the histogram. Journal of Electronics and Imaging, 2, 337–344), GA-based algorithm (Yin, P. -Y. (1999). A fast scheme for optimal thresholding using genetic algorithms. Signal Processing, 72, 85–95) and the basic PSO variant employing linearly decreasing inertia weight factor.     

一种对光照具有鲁棒性的图像分割方法

研究了灰度图像的OTSU(最大类间方差)自动阈值分割法。OTSU方法作为一种单一阈值的分割方法,当图像受光照和反射光等的影响明显时,将会出现严重的误分割现象。考虑到OTSU方法的最大类间方差化的思想,根据灰度图像的像素点灰度的直方图分布、空间分布,提出了一个新的分割阈值方法。先根据OTSU方法的特点自设计一个函数,对图像进行变换,以便后面的处理,再对其图像以改进的OTSU方法进行分割。通过对化学实验中两种液体的拍摄图片及数字图像处理中标准图片进行试验,理论分析与实验结果表明：该方法能够对受光照及反射光影响大的图像实现正确的分割,将目标图像清晰地从背景中分割出来。     

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。     

An image segmentation method using automatic threshold based on improved genetic selecting algorithm

In this paper, an image segmentation method using automatic threshold based on improved genetic selecting algorithm is presented. Optimal threshold for image segmentation is converted into an optimization problem in this new method. In order to achieve good effects for image segmentation, the optimal threshold is solved by using optimizing efficiency of improved genetic selecting algorithm that can achieve a global optimum. The genetic selecting algorithm is optimized by using simulated annealing temperature parameters to achieve appropriate selective pressures. Encoding, crossover, mutation operator and other parameters of genetic selecting algorithm are improved moderately in this method. It can overcome the shortcomings of the existing image segmentation methods, which only consider pixel gray value without considering spatial features and large computational complexity of these algorithms. Experiment results show that the new algorithm greatly reduces the optimization time, enhances the anti-noise performance of image segmentation, and improves the efficiency of image segmentation. Experimental results also show that the new algorithm can get better segmentation effect than that of Otsu’s method when the gray-level distribution of the background follows normal distribution approximately, and the target region is less than the background region. Therefore, the new method can facilitate subsequent processing for computer vision, and can be applied to realtime image segmentation.     

基于图像边缘信息的2维阈值分割方法

为了改善2维阈值分割性能,提高图像分割的效率,在传统2维Otsu阈值分割算法的基础上,提出了一种基于图像边缘信息的2维阈值分割方法。这种改进的方法保留了2维Otsu阈值分割算法分割结果准确的优点,并在此基础上充分利用图像的边缘信息,通过分析图像的边缘直方图和阈值的关系来得到最优分割阈值。仿真实验结果表明,该方法与传统2维分割算法相比,不仅计算简单,而且实时性好。     

A fast technique for image segmentation based on two Meta-heuristic algorithms

Image segmentation is a primary task in image processing which is widely used in object detection and recognition. Multilevel thresholding is one of the prominent technique in the field of image segmentation. However, the computational cost of multilevel thresholding increases exponentially as the number of threshold value increases, which leads to use of meta-heuristic optimization to find the optimal number of threshold. To overcome this problem, this paper investigates the ability of two nature-inspired algorithms namely: antlion optimisation (ALO) and multiverse optimization (MVO). ALO is a population-based method and mimics the hunting behaviour of antlions in nature. Whereas, MVO is based on the multiverse theory which depicts that there is over one universe exist. These two metaheuristic algorithms are used to find the optimal threshold values using Kapur’s entropy and Otsu’s between class variance function. They examine the outcomes of the proposed algorithm with other evolutionary algorithms based on cost value, stability analysis, feature similarity index (FSIM), structural similarity index (SSIM), peak signal to noise ratio (PSNR), computational time. We also provide Wilcoxon test which justify the response of these parameters. The experimental results showed that the proposed algorithm gives better results than other existing methods. It is noticed that MVO is faster than other algorithms. The proposed method is also tested on medical images to detect the tumor from MRI T1-weighted contrast-enhanced brain images.

     

改进的二维最小卡方散度图像分割方法

传统的交叉熵阈值法具有抗噪性能差,计算时间长等问题。为了改进算法的性能,提出了一种二维最小卡方散度图像阈值化分割新准则,构建了基于改进中值滤波的新型二维直方图。利用对称卡方散度描述分割前后图像之间的差异程度。使用关键阈值对滤波图像进行分割,达到最佳的分割效果。实验结果表明,与二维Otsu和二维最小交叉熵法相比,提出的方法不仅大大缩短了分割时间,而且分割性能与抗噪性能更强。     

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.     

一种改进粒子群优化算法的Otsu图像阈值分割方法

阈值法分割图像时只利用图像的灰度信息,具有直观、实现简单的特点。针对传统的粒子群优化算法(Particle Swarm Optimization,PSO)分割图像易陷入局部最优的缺点,提出一种基于改进粒子群优化算法的Otsu图像阈值分割方法。以Otsu算法的类间方差作为适应度函数,在每次迭代中选取适应度较好的粒子同时加入新的粒子,以提高粒子多样性。实验表明,与Otsu算法和PSO算法相比,改进的粒子群优化算法不仅加快了收敛速度和运算速度,而且提高了图像分割的准确率。     

Multi-objective and multi-level image thresholding based on dominance and diversity criteria

The Kapur and Otsu methods are widely used image thresholding approaches and they are very efficient in bi-level thresholding applications. Evolutionary algorithms have been developed to extend the Kapur and Otsu methods to the multi-level thresholding case. However, there remains an unsolved argument that neither Kapur nor Otsu objective can optimally fit diverse content contained in different kinds of images. This paper proposes a multi-objective model which seeks to find the Pareto-optimal set with respect to Kapur and Otsu objectives. Based on dominance and diversity criteria, we developed a hybrid multi-objective particle swarm optimization (MOPSO) method by incorporating several intelligent search strategies. The ensemble strategy is also applied to automatically select the best search strategy to perform at various algorithm stages according to its historic performances. The experimental result shows that the solutions to our multi-objective model consistently produce equal or better segmentation results than those by the optimal solutions to the original Kapur and Otsu models, and that the proposed hybrid algorithm with and without the ensemble strategy produces a better approximation to the ideal Pareto front than those obtained by two other MOPSO variants and the MOEA/D. In comparison with the most recent multilevel thresholding methods, our approach also consistently obtains better performance in the segmentation result for several benchmark images.     

Image segmentation using Atanassov’s intuitionistic fuzzy sets

The problem of segmentation in spite of all the work over the last decades, is still an important research field and also a critical preprocessing step for image processing, mostly due to the fact that finding a global optimal threshold that works well for all kind of images is indeed a very difficult task that, probably, will never be accomplished.During the past years, fuzzy logic theory has been successfully applied to image thresholding. In this paper we describe a thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs). This approach uses Atanassov’s intuitionistic index values for representing the hesitance of the expert in determining whether the pixel belongs to the background or that it belongs to the object. First, we describe the general framework of this approach to bi-level thresholding. Then we present its natural extension to multilevel thresholding. This multilevel threshold methodology segments the image into several distinct regions which correspond to a background and several objects.Segmentation experimental results and comparison with Otsu’s multilevel thresholding algorithm for the calculation of two and three thresholds are presented.