图像颜色量化模型优化方法及其在裂纹图像中的应用
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摘要
目前,对固体材料裂纹扩展过程的研究主要是通过实验数据进行分析。材料的断裂形貌图像是一组记录了材料断裂历程的裂纹图像,对其进行观察分析可以获得裂纹扩展过程的特征信息。利用图像处理的方法从裂纹图像中提取裂纹信息,并分析裂纹扩展过程特征是一种可行的研究途径。然而,许多固体材料的裂纹图像颜色较为杂乱,这会对图像观察分析产生干扰。利用图像处理中的颜色量化技术,可以在确保图像颜色失真度较小的前提下,将含有丰富颜色信息(2563种)的图像用少数的代表色来表示。因而,对颜色较为杂乱的材料裂纹图像进行颜色量化处理,有利于更好地对裂纹信息进行观察分析。聚类算法是较为流行的一类颜色量化方法,然而,聚类算法对初始条件较为敏感,且易于陷入局部最优。随机优化算法能较好地克服聚类算法的这些缺点。近年来,被成功地应用于彩色图像颜色量化问题的随机优化方法主要有：神经网络算法、蚁群算法、遗传算法、粒子群算法等,现有研究表明随机优化算法在求解彩色图像颜色量化问题上具有一定的优越性。然而,一系列新的问题还有待进一步系统研究,如新兴的随机优化算法是否能更好的求解彩色图像颜色量化问题,面向该问题的数学模型有何特征能指导随机优化算法的设计等等。本文围绕彩色图像颜色量化优化模型的建立、模型特征的分析以及面向彩色图像颜色量化问题的随机优化算法设计等进行了研究,为研究固体材料的裂纹扩展规律和预测裂纹增长趋势奠定了基础。具体工作和创新如下：
(1)比较研究了粒子群算法、遗传算法、差分演化算法和K-均值聚类算法在颜色量化问题上的优化效果,实验结果表明差分演化策略具有更好的整体优化效果,进而通过数值实验系统地研究了面向颜色量化问题的差分演化相关参数的设置规律。
(2)研究了彩色图像颜色量化的单目标模型特征,发现彩色图像颜色量化模型对基于种群的随机优化策略的个体元素具有置换等效性,并进一步分析了抑制远距离等效置换的必要性。
(3)针对彩色图像颜色量化问题,结合置换等效性,提出了一种适合彩色图像颜色量化问题的保持种群多样性的演化策略,该策略以差分演化算法的优化策略为基础,通过设置变异策略的阈值和小概率地应用K-均值聚类策略来抑制远距离等效置换；为了避免实际应用中参数的设置问题,进一步提出了一种彩色图像颜色量化自适应混合演化策略,该策略依据面向颜色量化问题的相关参数设置规律来初始化参数,在演化过程中具有自适应的调整算法参数的功能。对常用测试图像进行量化实验,结果表明加入混合策略、变异策略阈值和自适应策略后,演化策略的收敛速度和颜色量化效果均得到了提高。
(4)通过数值实验验证了最小化类内最大距离、最大化类间最小距离和类内均方误差的冲突性,从而,以这三个评估准则为目标函数,建立了彩色图像颜色量化问题的多目标优化模型。
(5)以基于差分演化和K-均值聚类的彩色图像颜色量化自适应混合策略为基础,设计了两个彩色图像颜色量化自适应混合多目标优化算法。常用测试图像的量化实验结果表明了提出的彩色图像颜色量化多目标算法的有效性,且由这两个算法可以得到不同效果的量化图像,从而可以根据实际要求来选择需要的量化图像。
(6)应用提出的彩色图像颜色量化自适应混合多目标优化算法对固体材料裂纹图像进行量化,实验结果表明仅用少数代表色表示的量化图像中保持了完整的裂纹信息。
The characteristics of solid materials crack propagation is commonly analysed according to the experimental data. Fracture pattern images, consisting of a set of crack images, show the development of material crack. For some image processing techniques can be used to extract the information of cracks, it is practicable to research the characteristics of crack propagation according to fracture pattern images. Howere, the rich colors in some crack images may interfer with the observation of cracks. Color image quantization techniquch of image processing can reduce the number of colors in a color image with a smaller image color distortion. So quantizing crack images will benefit the observation of cracks. Cluster algorithms are one popular class of color quntization methods. However, these algorithms are sensitive to initial conditions, and are easy to get into the local optima. Stochastic optimization algorithms are ones, which can overcome the above shortcomings of clustering algorithms. The stochastic optimization methods, having been applied in color image quantization, mainly are neural networks algorithm, ant colony algorithm, genetic algorithm and particle swarm algorithm. Although these stochastic optimization algorithms perform better than some common color qunatization methods, there exist some problems on the application of stochastic optimization methods on color image quantization for further research. For example, do some new stochastic optimization algorihms have better performance for color quantization? And for the color image quantization model, what characteristics can guide us to design the color quantization algorithms based on stochastic optimization? This thesis researches the design and characteristics of color image quantization model, and the design of the color quantization algorithms based on stochastic optimization. These works lay the foundation of the analysis and forecasting on the development of crack propagation. Main works of this thesis are as follows:
(1) Some experiments for color images quantization are run to compare the performance of genetic algorithm, particle swarm algorithm, differential evolution algorithm and K-means algorithm. And the experimental results show that differential evolution performs better. Furthermore, the paremeters set of differential evolution suitable for the color image quantization is suggested by some experiments.
(2) The characteristics of color image quantization model are analysed. And it is found that the stochastic optimization algorithms based on population have the permutation equivalence of the elements of each individual. This characteristic can guide us to improve the stochastic optimization algorithms for color quantization.
(3) For restraining the permutation equivalence of the color image quantization model, a new evolution algorithm with diversity maintaining mechanism is presented. In this hybrid algorithm, the optimization strategy of differential evolution is applied, a threshold of the mutation difference vecter is set according to the permutation equivalence, and K-means is used with a little probability. Furthermore, a selfadaptive strategy to control the parameters is applied in the hybrid algorithm. Then a selfadaptive hybrid color image quantization algorithm is proposed. In this algorithm, its parameters are adjusted during evolution process. By some comparing experiments on some common test color images, the selfadaptive hybrid stragtegy with a threshold of the mutation difference vecter improves the convergence speed of quantization algorithms and the quality of quantized images.
(4) A color image quantization multi-objective model is constructed with three objectives, that is, intra-cluster distance, inter-cluster separation and mean square error, which are verified to be conflicting by some experiments.
(5) Two selfadaptive hybrid multi-objective optimization algorithms for color image quantization are presented. The experimental results on some common test color images show that the two proposed multi-objective optimization algorithms perform better on the color image quantization. Sbving the color image quantization multi-objective model with the two proposed multi-objective optimization algorithms can generate some different quantized images, which can satisfy the practical requirement.
(6) The presented selfadaptive hybrid multi-objective optimization algorithms for color image quantization are applied to some crack images. The experimental results show that all the cracks are retained in the quantized images only with few colors.
(1)比较研究了粒子群算法、遗传算法、差分演化算法和K-均值聚类算法在颜色量化问题上的优化效果,实验结果表明差分演化策略具有更好的整体优化效果,进而通过数值实验系统地研究了面向颜色量化问题的差分演化相关参数的设置规律。
(2)研究了彩色图像颜色量化的单目标模型特征,发现彩色图像颜色量化模型对基于种群的随机优化策略的个体元素具有置换等效性,并进一步分析了抑制远距离等效置换的必要性。
(3)针对彩色图像颜色量化问题,结合置换等效性,提出了一种适合彩色图像颜色量化问题的保持种群多样性的演化策略,该策略以差分演化算法的优化策略为基础,通过设置变异策略的阈值和小概率地应用K-均值聚类策略来抑制远距离等效置换；为了避免实际应用中参数的设置问题,进一步提出了一种彩色图像颜色量化自适应混合演化策略,该策略依据面向颜色量化问题的相关参数设置规律来初始化参数,在演化过程中具有自适应的调整算法参数的功能。对常用测试图像进行量化实验,结果表明加入混合策略、变异策略阈值和自适应策略后,演化策略的收敛速度和颜色量化效果均得到了提高。
(4)通过数值实验验证了最小化类内最大距离、最大化类间最小距离和类内均方误差的冲突性,从而,以这三个评估准则为目标函数,建立了彩色图像颜色量化问题的多目标优化模型。
(5)以基于差分演化和K-均值聚类的彩色图像颜色量化自适应混合策略为基础,设计了两个彩色图像颜色量化自适应混合多目标优化算法。常用测试图像的量化实验结果表明了提出的彩色图像颜色量化多目标算法的有效性,且由这两个算法可以得到不同效果的量化图像,从而可以根据实际要求来选择需要的量化图像。
(6)应用提出的彩色图像颜色量化自适应混合多目标优化算法对固体材料裂纹图像进行量化,实验结果表明仅用少数代表色表示的量化图像中保持了完整的裂纹信息。
The characteristics of solid materials crack propagation is commonly analysed according to the experimental data. Fracture pattern images, consisting of a set of crack images, show the development of material crack. For some image processing techniques can be used to extract the information of cracks, it is practicable to research the characteristics of crack propagation according to fracture pattern images. Howere, the rich colors in some crack images may interfer with the observation of cracks. Color image quantization techniquch of image processing can reduce the number of colors in a color image with a smaller image color distortion. So quantizing crack images will benefit the observation of cracks. Cluster algorithms are one popular class of color quntization methods. However, these algorithms are sensitive to initial conditions, and are easy to get into the local optima. Stochastic optimization algorithms are ones, which can overcome the above shortcomings of clustering algorithms. The stochastic optimization methods, having been applied in color image quantization, mainly are neural networks algorithm, ant colony algorithm, genetic algorithm and particle swarm algorithm. Although these stochastic optimization algorithms perform better than some common color qunatization methods, there exist some problems on the application of stochastic optimization methods on color image quantization for further research. For example, do some new stochastic optimization algorihms have better performance for color quantization? And for the color image quantization model, what characteristics can guide us to design the color quantization algorithms based on stochastic optimization? This thesis researches the design and characteristics of color image quantization model, and the design of the color quantization algorithms based on stochastic optimization. These works lay the foundation of the analysis and forecasting on the development of crack propagation. Main works of this thesis are as follows:
(1) Some experiments for color images quantization are run to compare the performance of genetic algorithm, particle swarm algorithm, differential evolution algorithm and K-means algorithm. And the experimental results show that differential evolution performs better. Furthermore, the paremeters set of differential evolution suitable for the color image quantization is suggested by some experiments.
(2) The characteristics of color image quantization model are analysed. And it is found that the stochastic optimization algorithms based on population have the permutation equivalence of the elements of each individual. This characteristic can guide us to improve the stochastic optimization algorithms for color quantization.
(3) For restraining the permutation equivalence of the color image quantization model, a new evolution algorithm with diversity maintaining mechanism is presented. In this hybrid algorithm, the optimization strategy of differential evolution is applied, a threshold of the mutation difference vecter is set according to the permutation equivalence, and K-means is used with a little probability. Furthermore, a selfadaptive strategy to control the parameters is applied in the hybrid algorithm. Then a selfadaptive hybrid color image quantization algorithm is proposed. In this algorithm, its parameters are adjusted during evolution process. By some comparing experiments on some common test color images, the selfadaptive hybrid stragtegy with a threshold of the mutation difference vecter improves the convergence speed of quantization algorithms and the quality of quantized images.
(4) A color image quantization multi-objective model is constructed with three objectives, that is, intra-cluster distance, inter-cluster separation and mean square error, which are verified to be conflicting by some experiments.
(5) Two selfadaptive hybrid multi-objective optimization algorithms for color image quantization are presented. The experimental results on some common test color images show that the two proposed multi-objective optimization algorithms perform better on the color image quantization. Sbving the color image quantization multi-objective model with the two proposed multi-objective optimization algorithms can generate some different quantized images, which can satisfy the practical requirement.
(6) The presented selfadaptive hybrid multi-objective optimization algorithms for color image quantization are applied to some crack images. The experimental results show that all the cracks are retained in the quantized images only with few colors.
引文
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