A comparison of stochastic optimization techniques for image segmentation

Image segmentation denotes a process by which a raw input image is partitioned into nonoverlapping regions such that each region is homogeneous and the union of any two adjacent regions is heterogenous. A segmented image is considered to be the highest domain‐independent abstraction of an input image. In this paper, the image segmentation problem is treated as one of combinatorial optimization. A cost function which incorporates both, edge information and region gray‐scale variances is defined. The cost function is shown to be multivariate with several local minima. Three stochastic optimization techniques, namely, simulated annealing (SA), microcanonical annealing (MCA), and the random cost algorithm (RCA) are investigated and compared in the context of minimization of the aforementioned cost function for image segmentation. Experimental results on gray‐scale images are presented. © 2000 John Wiley & Sons, Inc.     

Evolutionary Approaches to Figure-Ground Separation

The problem of figure-ground separation is tackled from the perspective of combinatorial optimization. Previous attempts have used deterministic optimization techniques based on relaxation and gradient descent-based search, and stochastic optimization techniques based on simulated annealing and microcanonical annealing. A mathematical model encapsulating the figure-ground separation problem that makes explicit the definition of shape in terms of attributes such as cocircularity, smoothness, proximity and contrast is described. The model is based on the formulation of an energy function that incorporates pairwise interactions between local image features in the form of edgels and is shown to be isomorphic to the interacting spin (Ising) system from quantum physics. This paper explores a class of stochastic optimization techniques based on evolutionary algorithms for the problem of figure-ground separation. A class of hybrid evolutionary stochastic optimization algorithms based on a combination of evolutionary algorithms, simulated annealing and microcanonical annealing are shown to exhibit superior performance when compared to their purely evolutionary counterparts and to classical simulated annealing and microcanonical annealing algorithms. Experimental results on synthetic edgel maps and edgel maps derived from gray scale images are presented.     

一种利用灰度信息和二值信息的手写字符分割

在字符识别系统中,字符的有效分割是识别的关键。该文描述了一种两阶段的手写字符分割方法。根据字符倾斜角度将原字符串图像划分出若干个形状不规则的区域,每个区域含有一条分割线;针对现有分割方法的某些局限性,提出采用字符图像灰度信息和二值信息相结合的方式来求取分割区域中的分割路径。实验结果表明了该方法对于手写字符分割的有效性。     

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.     

Evolutionary segmentation of texture image using genetic algorithms towards automatic decision of optimum number of segmentation areas

Segmentation of an image composed of different kinds of texture fields has difficulty in an exact discrimination of the texture fields and a decision of the optimum number of segmentation areas in an image when the image contains similar and/or unstationary texture fields. In this paper we formulate the segmentation problem upon such images as an optimization problem and adopt evolutionary strategy of genetic algorithms for the clustering of small regions in a feature space. The purpose of this paper is to demonstrate the efficiency of genetic algorithms to the texture segmentation and to develop the automatic texture segmentation method.     

基于模拟退火并行遗传算法的Otsu双阈值

模拟退火和并行遗传算法是两种较好的改进进化算法性能的方法。将这两种思想有机地结合起来,利用遗传算法能全局寻优的优势和模拟退火算法的爬山性能,提出了一种基于模拟退火并行遗传算法的Otsu双阈值医学图像分割算法。在该算法中,进化在多个不同的子群中并行进行,利用模拟退火算法的爬山性能,避免单种群进化过程中出现的过早收敛现象,提高整个算法的收敛速度。实验证明,这种新的图像分割算法与并行遗传算法相比,不仅能够对图像进行准确的分割,而且具有更强的精确性和稳定性。其收敛速度明显比并行遗传算法的Otsu双阈值医学图像分割快。     

Color image segmentation—an innovative approach

In this paper we describe a color image segmentation system that performs color clustering in a color space and then color region segmentation in the image domain. For color segmentation, we developed a fuzzy clustering algorithm that iteratively generates color clusters using a uniquely defined fuzzy membership function and an objective function for clustering optimization. The fuzzy membership function represents belief value of a color belonging to a color cluster and the mutual interference of neighboring clusters. The region segmentation algorithm merges clusters in the image domain based on color similarity and spatial adjacency. We developed three different methods for merging regions in the image domain. Unlike many existing clustering algorithms, the image segmentation system does not require the knowledge about the number of the color clusters to be generated at each stage and the resolution of the color regions can be controlled by one single parameter, the radius of a cluster. The color image segmentation system has been implemented and tested on a variety of color images including satellite images, car and face images. The experiment results are presented and the performance of each algorithm in the segmentation system is analyzed. The system has shown to be both effective and efficient.     

Figure-ground discrimination: a combinatorial optimization approach

The figure-ground discrimination problem is considered from a combinatorial optimization perspective. A mathematical model encoding the figure-ground discrimination problem that makes explicit a definition of shape based on cocircularity, smoothness, proximity, and contrast is presented. This model consists of building a cost function on the basis of image element interactions. This cost function fits the constraints of an interacting spin system that, in turn, is a well suited physical model that solves hard combinatorial optimization problems. Two combinatorial optimization methods for solving the figure-ground problem, namely mean field annealing, which combines mean field approximation theory and annealing, and microcanonical annealing, are discussed. Mean field annealing may be viewed as a deterministic approximation of stochastic methods such as simulated annealing. The theoretical bases of these methods are described, and the computational models are derived. The efficiencies of mean field annealing, simulated annealing, and microcanonical annealing algorithms are compared. Within the framework of such a comparison, the figure-ground problem may be viewed as a benchmark     

一种改进遗传退火算法的图像分割方法

图像分割是图像处理和分析的基础,本文通过分析遗传算法（Genetic Algorithm, GA）在图像分割中的应用优劣,提出利用模拟退火思想的改进遗传退火（Genetic Simulated Annealing Algorithm, GASA）的图像阈值分割算法,算法整个运行过程由冷却温度进度表控制,使用改进的最大类间方差公式作为遗传算法的适应度函数,从而求得灰度图像的一个最佳阈值用于图像分割。实验结果表明,基于改进遗传退火算法的最大类间方差图像分割方法能较好提高算法的全局搜索能力,避免遗传算法陷入局部最优,并且能更快速、更稳定收敛到最佳的分割阈值,得到更好的图像分割效果。     

Image Thresholding Improved by Global Optimization Methods

Image thresholding is a common segmentation technique with applications in various fields, such as computer vision, pattern recognition, microscopy, remote sensing, and biology. The selection of threshold values for segmenting pixels into foreground and background regions is usually based on subjective assumptions or user judgments under empirical rules or manually determined. This work describes and evaluates six effective threshold selection strategies for image segmentation based on global optimization methods: genetic algorithms, particle swarm, simulated annealing, and pattern search. Experiments are conducted on several images to demonstrate the effectiveness of the proposed methodology.     

基于区域间协同优化的立体匹配算法

提出了一种基于分割区域间协同优化的立体匹配算法. 该算法以图像区域为匹配基元, 利用区域的彩色特征以及相邻区域间应满足的平滑和遮挡关系定义了区域的匹配能量函数, 并引入区域之间的合作竞争机制, 通过协同优化使所定义的匹配能量极小化, 从而得到比较理想的视差结果. 算法首先对参考图像进行分割, 利用相关法得到各分割区域的初始匹配; 然后用平面模型对各区域的视差进行拟合, 得到各区域的视差平面参数; 最后, 基于协同优化的思想, 采用局部优化的方法对各区域的视差平面参数进行迭代优化, 直至得到比较合理的视差图为止. 采用Middlebury test set进行的实验结果表明, 该方法在性能上可以和目前最好的立体匹配算法相媲美, 得到的视差结果接近于真实视差.     

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。     

A robust stochastic genetic algorithm (StGA) for global numerical optimization

Many real-life problems can be formulated as numerical optimization of certain objective functions. However, often an objective function possesses numerous local optima, which could trap an algorithm from moving toward the desired global solution. Evolutionary algorithms (EAs) have emerged to enable global optimization; however, at the present stage, EAs are basically limited to solving small-scale problems due to the constraint of computational efficiency. To improve the search efficiency, this paper presents a stochastic genetic algorithm (StGA). A novel stochastic coding strategy is employed so that the search space is dynamically divided into regions using a stochastic method and explored region-by-region. In each region, a number of children are produced through random sampling, and the best child is chosen to represent the region. The variance values are decreased if at least one of five generated children results in improved fitness, otherwise, the variance values are increased. Experiments on 20 test functions of diverse complexities show that the StGA is able to find the near-optimal solution in all cases. Compared with several other algorithms, StGA achieves not only an improved accuracy, but also a considerable reduction of the computational effort. On average, the computational cost required by StGA is about one order less than the other algorithms. The StGA is also shown to be able to solve large-scale problems.     

基于感兴趣区域函数优化的静脉图像分割算法

提出一种基于局部感兴趣区域中熵与梯度函数优化的近红外手背静脉图像分割算法。该算法首先基于压缩感知理论对图像进行去噪。其次,通过条带波变换提取存在静脉信息的感兴趣区域,在这些区域中对建立的关于熵和梯度的函数进行约束与优化,实现静脉与背景分离。最后,融合所有区域的分割结果,完成静脉图像的分割。实验表明在处理近红外静脉图像分割问题时,该算法相对其它算法能保留更完整的静脉特征。此外,该算法对于具有纹理特征的指静脉、掌静脉图像的分割具有较好的借鉴价值。     

A stochastic gravitational approach to feature based color image segmentation

In this paper, a novel image segmentation algorithm based on the theory of gravity is presented, which is called as “stochastic feature based gravitational image segmentation algorithm (SGISA)”. The proposed SGISA uses color, texture, and spatial information to partition the image into homogenous and semi-compact segments. The proposed method benefits from the advantages of both clustering and region growing image segmentation techniques. The SGISA is equipped with a new operator called “escape” that is inspired by the concept of escape velocity in physics. Moreover, motivated by heuristic search algorithms, we incorporate a stochastic characteristic with the SGISA, which gives algorithm the ability to search the image for finding the fittest regions (pixels) that are suitable for merging. Several experiments on various standard images as well as Berkley standard image database are reported. Results are compared with a well-known clustering based segmentation method, C-means, a gravitational based clustering method (SGC), and the well-known mean-shift method. The results are reported using unsupervised criteria and pre-ground-truthed measures. The obtained results confirm the effectiveness of the proposed method in color image segmentation.     

一种基于主动轮廓模型的医学图像序列分割算法

介绍了一种结合live wire算法和活动轮廓模型的医学图像序列的分割方法.通过把live wire算法和图像分割中一般的区域增长方法结合,对传统live wire算法进行了改进,并用改进后的算法对医学图像序列中的单张或多张切片进行交互式地准确分割.然后计算机利用活动轮廓模型自动分割相邻的未分割切片.还通过在活动轮廓模型的边缘点中引入记录已分割物体边缘附近局部区域特征的灰度模型,把已分割切片中的物体与背景的局部区域特征带入相邻的未分割切片中,并用由灰度模型定义的区域相似性代替活动轮廓模型中的外能来引导边缘轮廓收敛到物体的实际边缘.最后介绍了一种基于live wire算法思想的简单的分割结果交互式修复方法.实验结果表明该算法仅需少量用户交互就能快速准确地从医学图像序列中分割出感兴趣的物体,在医学图像分析中具有实用价值.     

Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm

A modified differential evolution (DE) algorithm is presented for clustering the pixels of an image in the gray-scale intensity space. The algorithm requires no prior information about the number of naturally occurring clusters in the image. It uses a kernel induced similarity measure instead of the conventional sum-of-squares distance. Use of the kernel function makes it possible to partition data that is linearly non-separable and non hyper-spherical in the original input space, into homogeneous groups in a transformed high-dimensional feature space. A novel search-variable representation scheme is adopted for selecting the optimal number of clusters from several possible choices. Extensive performance comparison over a test-suite of 10 gray-scale images and objective comparison with manually segmented ground truth indicates that the proposed algorithm has an edge over a few state-of-the-art algorithms for automatic multi-class image segmentation.     

C-PSA: Constrained Pareto simulated annealing for constrained multi-objective optimization

In recent years, evolutionary algorithms (EAs) have been extensively developed and utilized to solve multi-objective optimization problems. However, some previous studies have shown that for certain problems, an approach which allows for non-greedy or uphill moves (unlike EAs), can be more beneficial. One such approach is simulated annealing (SA). SA is a proven heuristic for solving numerical optimization problems. But owing to its point-to-point nature of search, limited efforts has been made to explore its potential for solving multi-objective problems. The focus of the presented work is to develop a simulated annealing algorithm for constrained multi-objective problems. The performance of the proposed algorithm is reported on a number of difficult constrained benchmark problems. A comparison with other established multi-objective optimization algorithms, such as infeasibility driven evolutionary algorithm (IDEA), Non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective Scatter search II (MOSS-II) has been included to highlight the benefits of the proposed approach.     

自适应梯度重建分水岭分割算法

目的 针对灰度分水岭算法存在过分割且难以直接应用到彩色图像分割的问题,提出一种自适应梯度重建分水岭分割算法。方法 该方法首先利用PCA技术对彩色图像降维,然后计算降维后的梯度图像,并采用自适应重建算法修正梯度图像,最后对优化后的梯度图像应用分水岭变换实现对彩色图像的正确分割。结果 采用融合了颜色距离、均方差和区域信息的性能指标和分割区域数对分割效果进行评估,对不同类型的彩色图像进行分割实验,本文算法在正确分割图像的同时获得了较高的性能指标。与现有的分水岭分割算法相比,提出的方法能有效剔除图像中的伪极小值,减少图像中的极小值数目,从而解决了过分割问题,有效提升了分割效果。结论 本文算法具有较好的适用性和较高的鲁棒性。     

改进的谱聚类图像分割方法

图像分割作为图像识别的一个重要处理步骤,但存在效果不理想或者计算复杂度过高的问题。提出一种新的灰度图像二值化的方法。该方法将Ncut作为谱聚类的量度,在计算该值时使用基于图像灰度级的权重矩阵,而非普通基于图像像素的权重矩阵。这样,计算复杂度和空间复杂度都明显降低。通过对实际场景中文本图像的实验,数据表明此方法在时间和系统开销方面比传统基于阈值的分割方法具有更优的性能。