无准则多维图像阈值分割算法——最优进化算法
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摘要
图像阈值分割是图像分割中的重要技术之一,是一个古老而经典的图像处理问题,目前仍然是数字图像处理中的一个焦点问题。图像阈值分割的准确性将直接影响后续任务的有效性,是对图像进一步分析、识别的前提。作为一种传统的图像分割方法,图像阈值分割方法实现简单、计算量小、性能稳定,因而成为图像分割中最基本和应用最广泛的分割技术。本文分析了现有的图像阈值分割算法,与现有方法的研究思路不同,提出了无准则图像阈值分割算法——最优进化算法(Optimal Evolution Algorithm, OEA),并将算法推广到高维空间得到无准则高维图像阈值分割算法。本文的主要工作及创新点如下:
(1)与现有图像阈值分割算法的研究思路不同,提出无准则图像阈值分割的概念。根据生物进化论和遗传算法理论,提出了最优进化方向存在的假设,并提出了最优进化方向必须具有进化的一致性和稳定性。
(2)根据生物进化论和遗传算法,建立了种群进化模型和阈值更新模型,定义了编码规则、采样方法、种群的初始化方法、初始进化方向的设定方法、适值的计算和选择机制,实现了无准则图像阈值分割算法――最优进化算法。设计了大量实验验证了最优进化方向的存在,通过大量实验验证了种群受到最优进化方向的吸引最强烈,无需任何准则函数的指引即可找到最优进化方向,验证了最优进化方向是使得种群的进化最稳定的方向。各类图像的测试结果说明,OEA是有效的图像阈值分割算法。
(3)针对OEA存在的问题,改进了算法的性能。在进一步细化种群进化模型的基础上,发现了种群进化中初始阈值和最优阈值的关系,改进了阈值更新模型,建立了阈值修正模型,得到了收敛迅速,收敛速度和计算结果稳定的OEA。改进后的OEA解决了当初始阈值随机选取时,OEA存在计算结果和迭代次数不稳定的问题;解决了当目标像素点与背景像素点的个数相差较大时,OEA得到的最优阈值易偏向于数量较多的一方,从而使分割结果中产生噪声的问题。用细化后的种群进化模型更清晰地表达了种群的进化过程,通过细化后的种群进化模型及大量的实验更进一步验证了假设的合理性。各类图像的测试结果表明,改进后的OEA的算法性能和分割效果有了显著提高,改进后的OEA是高效的无准则图像阈值分割算法。
(4)在OEA的理论基础上,给合二维图像阈值分割思想,将OEA推广到二维,提出了一种通用的,无准则函数的二维图像阈值分割算法框架――二维最优进化算法(Two-dimensional Optimal Evolution Algorithm,2D-OEA)。实验结果表明2D-OEA是快速、稳定和有效的图像二维阈值分割算法,2D-OEA的算法性能和分割效果比1D-OEA有了显著提高。
(5)针对目前的图像阈值分割方法仅限于一维或二维的现状,和高维空间中图像阈值分割算法面临的计算复杂度高和区域划分等问题,建立了法向量定向模型,提出了超体划分和超平面划分两种区域划分方法,实现了无准则高维图像阈值分割算法(N-dimensional Optimal Evolution Algorithm,ND-OEA)。提出的ND-OEA收敛迅速,收敛速度和计算结果稳定,算法复杂度远远小于高维图像阈值分割的理论算法复杂度( )
O L2 N。用各类图像对ND-OEA的两种划分方式进行了测试,超体分划分随着空间维数的增高,目标丢失越来越严重;超平面划分方式的分割效果稳定。ND-OEA实现了无准则高维图像阈值分割算法,实现了高维空间中的快速图像阈值分割算法。随着空间维数的增高,ND-OEA越来越趋于反应图像中目标和背景的整体特性,细节越来越少,目标与背景的对比越来越强烈,符合人类视觉系统的信息选择机制,是一种智能化的算法。
(6)将最优进化算法推广到了彩色图像阈值分割和灰度图像的边缘检测问题中,对3幅现有图像阈值分割方法难以得到理想分割效果的彩色图像进行了测试。实验结果表明,ND-OEA不需要进行颜色空间建模,也能自适应地在RGB空间找到最优分割面;基于ND-OEA的边缘检测方法提取出的边缘清晰、细节丰富、连通性好,是有效的边缘检测方法。
Image thresholding is one of the most classical and important techniques of image segmentation. It is an old but hot topic in digital image processing. Image thresholding is the pre-processing of most of image processing techniques. It will deeply affect the following image understanding or image analysis. As a traditional image segmentation method, image thresholding is one of the most basic and popular techniques of image segmentation, because of its simple process, low time complexity but efficient results. After analyzing most of image thresholding methods, this paper proposed an image thresholding algorithm without a criterion——the optimal evolution algorithm (OEA) which is different from other image thresholding methods. Furthermore, the optimal evolution algorithm has been extended to high dimensional space. The principal work and remarks of this paper are as follow:
(1) Unlike other image thresholding algorithms, we try to find an image thresholding algorithm without a criterion. According to the theories of biological evolution and genetic algorithm, we assume that there exists an optimal evolution direction. The direction is consistent and stable in the evolution process.
(2) According to the theories of biological evolution and genetic algorithm, we established the population evolution model and the threshold updating model. After defining the chromosomes’coding rule, the sampling method, the initialization method of the evolution direction, the fitness function and the selection mechanism, we proposed an image thresholding algorithm without a criterion—the optimal evolution algorithm. Experimental results show that the optimal evolution direction does exist; the population is strongly attracted by the direction; the direction is the most stable direction during the population’s evolution. The optimal evolution algorithm performs well in image thresholding experiments.
(3) To solve the problems found in the experiments, we improve the optimal evolution algorithm. We discover the relationship between the initial threshold and the optimal threshold in biological evolution by detailed in the population evolution model. Based on the relationship, we improve the threshold updating model; establish a threshold modification model to obtain a fast and stable OEA. The improved OEA solved the problems that the optimal threshold obtained by OEA and the iterative times are unstable while randomly initialize the threshold; thresholding results contain some noise because the optimal threshold obtained by OEA is too close to the class which has more samples than the other. Detailed population evolution model supports the existence of the optimal evolution direction. Experimental results show that the improved OEA is much more efficient.
(4) Based on theories of OEA and the idea of two-dimensional image thresholding methods, we extended OEA to two-dimensional space, and proposed an algorithm framework for two-dimensional image thresholding without a criterion—2D-OEA. Results show that 2D-OEA is a fast, stable and efficient image thresholding algorithm. Compared with 1D-OEA, the properties and the results of 2D-OEA are much better.
(5) Image thresholding algorithm is one-dimensional or two-dimensional, because the computational complexity is too high and there is no corresponding region division method in high-dimensional space for image thresholding. To decrease computational complexity and find a region division method in high-dimensional space, we establish an orientation model of normal vector, and propose hypercubic division method and hyperplane division method in high-dimensional space for image thresholding. Based on these two region division methods in high-dimensional space, we proposed a high-dimensional image thresholding algorithm without a criterion—N-dimensional optimal evolution algorithm, ND-OEA. The ND-OEA has a rapid and stable convergence. The computational complexity of ND-OEA is much lower than ( )O L2 N which is the computational complexity of high-dimensional image thresholding algorithm in theory. Experimental results show that ND-OEA is a fast and efficient image thresholding algorithm. With the increasing of the space’s dimension, hypercubic division method is losing more and more pixels belonging to the object, but hyperplane division method’s thresholding results are stable. ND-OEA presents a multi-dimensional image thresholding algorithm without a criterion. It solves the problem of computational complexity in high-dimensional space. With the increasing of space’s dimension, the global relationship between the object and the background is getting more and more clear, details of the object are losing more and more seriously, but the contrast between object and background is getting more and more strong. ND-OEA’s thresholding results, which is strong contrast between the object and the background in high-dimensional space, are consistent with the selection mechanism of human visual system. So ND-OEA is an intelligent algorithm.
(6) We apply ND-OEA to color image thresholding, and propose an edge detection algorithm based on ND-OEA. Three color images, whose objects are hardly segmented from the background by most image thresholding algorithm, are selected to test ND-OEA. Results show that ND-OEA can find the optimal hyperplane in color space without building a color space model; edge detection algorithm based on ND-OEA is an efficient edge detection algorithm, and edges detected by it have clear contours, rich details, nice connectivity.
(1)与现有图像阈值分割算法的研究思路不同,提出无准则图像阈值分割的概念。根据生物进化论和遗传算法理论,提出了最优进化方向存在的假设,并提出了最优进化方向必须具有进化的一致性和稳定性。
(2)根据生物进化论和遗传算法,建立了种群进化模型和阈值更新模型,定义了编码规则、采样方法、种群的初始化方法、初始进化方向的设定方法、适值的计算和选择机制,实现了无准则图像阈值分割算法――最优进化算法。设计了大量实验验证了最优进化方向的存在,通过大量实验验证了种群受到最优进化方向的吸引最强烈,无需任何准则函数的指引即可找到最优进化方向,验证了最优进化方向是使得种群的进化最稳定的方向。各类图像的测试结果说明,OEA是有效的图像阈值分割算法。
(3)针对OEA存在的问题,改进了算法的性能。在进一步细化种群进化模型的基础上,发现了种群进化中初始阈值和最优阈值的关系,改进了阈值更新模型,建立了阈值修正模型,得到了收敛迅速,收敛速度和计算结果稳定的OEA。改进后的OEA解决了当初始阈值随机选取时,OEA存在计算结果和迭代次数不稳定的问题;解决了当目标像素点与背景像素点的个数相差较大时,OEA得到的最优阈值易偏向于数量较多的一方,从而使分割结果中产生噪声的问题。用细化后的种群进化模型更清晰地表达了种群的进化过程,通过细化后的种群进化模型及大量的实验更进一步验证了假设的合理性。各类图像的测试结果表明,改进后的OEA的算法性能和分割效果有了显著提高,改进后的OEA是高效的无准则图像阈值分割算法。
(4)在OEA的理论基础上,给合二维图像阈值分割思想,将OEA推广到二维,提出了一种通用的,无准则函数的二维图像阈值分割算法框架――二维最优进化算法(Two-dimensional Optimal Evolution Algorithm,2D-OEA)。实验结果表明2D-OEA是快速、稳定和有效的图像二维阈值分割算法,2D-OEA的算法性能和分割效果比1D-OEA有了显著提高。
(5)针对目前的图像阈值分割方法仅限于一维或二维的现状,和高维空间中图像阈值分割算法面临的计算复杂度高和区域划分等问题,建立了法向量定向模型,提出了超体划分和超平面划分两种区域划分方法,实现了无准则高维图像阈值分割算法(N-dimensional Optimal Evolution Algorithm,ND-OEA)。提出的ND-OEA收敛迅速,收敛速度和计算结果稳定,算法复杂度远远小于高维图像阈值分割的理论算法复杂度( )
O L2 N。用各类图像对ND-OEA的两种划分方式进行了测试,超体分划分随着空间维数的增高,目标丢失越来越严重;超平面划分方式的分割效果稳定。ND-OEA实现了无准则高维图像阈值分割算法,实现了高维空间中的快速图像阈值分割算法。随着空间维数的增高,ND-OEA越来越趋于反应图像中目标和背景的整体特性,细节越来越少,目标与背景的对比越来越强烈,符合人类视觉系统的信息选择机制,是一种智能化的算法。
(6)将最优进化算法推广到了彩色图像阈值分割和灰度图像的边缘检测问题中,对3幅现有图像阈值分割方法难以得到理想分割效果的彩色图像进行了测试。实验结果表明,ND-OEA不需要进行颜色空间建模,也能自适应地在RGB空间找到最优分割面;基于ND-OEA的边缘检测方法提取出的边缘清晰、细节丰富、连通性好,是有效的边缘检测方法。
Image thresholding is one of the most classical and important techniques of image segmentation. It is an old but hot topic in digital image processing. Image thresholding is the pre-processing of most of image processing techniques. It will deeply affect the following image understanding or image analysis. As a traditional image segmentation method, image thresholding is one of the most basic and popular techniques of image segmentation, because of its simple process, low time complexity but efficient results. After analyzing most of image thresholding methods, this paper proposed an image thresholding algorithm without a criterion——the optimal evolution algorithm (OEA) which is different from other image thresholding methods. Furthermore, the optimal evolution algorithm has been extended to high dimensional space. The principal work and remarks of this paper are as follow:
(1) Unlike other image thresholding algorithms, we try to find an image thresholding algorithm without a criterion. According to the theories of biological evolution and genetic algorithm, we assume that there exists an optimal evolution direction. The direction is consistent and stable in the evolution process.
(2) According to the theories of biological evolution and genetic algorithm, we established the population evolution model and the threshold updating model. After defining the chromosomes’coding rule, the sampling method, the initialization method of the evolution direction, the fitness function and the selection mechanism, we proposed an image thresholding algorithm without a criterion—the optimal evolution algorithm. Experimental results show that the optimal evolution direction does exist; the population is strongly attracted by the direction; the direction is the most stable direction during the population’s evolution. The optimal evolution algorithm performs well in image thresholding experiments.
(3) To solve the problems found in the experiments, we improve the optimal evolution algorithm. We discover the relationship between the initial threshold and the optimal threshold in biological evolution by detailed in the population evolution model. Based on the relationship, we improve the threshold updating model; establish a threshold modification model to obtain a fast and stable OEA. The improved OEA solved the problems that the optimal threshold obtained by OEA and the iterative times are unstable while randomly initialize the threshold; thresholding results contain some noise because the optimal threshold obtained by OEA is too close to the class which has more samples than the other. Detailed population evolution model supports the existence of the optimal evolution direction. Experimental results show that the improved OEA is much more efficient.
(4) Based on theories of OEA and the idea of two-dimensional image thresholding methods, we extended OEA to two-dimensional space, and proposed an algorithm framework for two-dimensional image thresholding without a criterion—2D-OEA. Results show that 2D-OEA is a fast, stable and efficient image thresholding algorithm. Compared with 1D-OEA, the properties and the results of 2D-OEA are much better.
(5) Image thresholding algorithm is one-dimensional or two-dimensional, because the computational complexity is too high and there is no corresponding region division method in high-dimensional space for image thresholding. To decrease computational complexity and find a region division method in high-dimensional space, we establish an orientation model of normal vector, and propose hypercubic division method and hyperplane division method in high-dimensional space for image thresholding. Based on these two region division methods in high-dimensional space, we proposed a high-dimensional image thresholding algorithm without a criterion—N-dimensional optimal evolution algorithm, ND-OEA. The ND-OEA has a rapid and stable convergence. The computational complexity of ND-OEA is much lower than ( )O L2 N which is the computational complexity of high-dimensional image thresholding algorithm in theory. Experimental results show that ND-OEA is a fast and efficient image thresholding algorithm. With the increasing of the space’s dimension, hypercubic division method is losing more and more pixels belonging to the object, but hyperplane division method’s thresholding results are stable. ND-OEA presents a multi-dimensional image thresholding algorithm without a criterion. It solves the problem of computational complexity in high-dimensional space. With the increasing of space’s dimension, the global relationship between the object and the background is getting more and more clear, details of the object are losing more and more seriously, but the contrast between object and background is getting more and more strong. ND-OEA’s thresholding results, which is strong contrast between the object and the background in high-dimensional space, are consistent with the selection mechanism of human visual system. So ND-OEA is an intelligent algorithm.
(6) We apply ND-OEA to color image thresholding, and propose an edge detection algorithm based on ND-OEA. Three color images, whose objects are hardly segmented from the background by most image thresholding algorithm, are selected to test ND-OEA. Results show that ND-OEA can find the optimal hyperplane in color space without building a color space model; edge detection algorithm based on ND-OEA is an efficient edge detection algorithm, and edges detected by it have clear contours, rich details, nice connectivity.
引文
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