基于模糊逻辑的图像处理算法研究
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摘要
本文首先概要地介绍了数字图像处理的基本概念、基本理论、基本方法以及它们在实际中的应用；然后介绍了模糊数学理论的基本概念与基本理论；在此基础上提出了一些基于模糊逻辑的图像处理新方法和新思想,并取得了良好的效果。
主要包括以下六个方面内容：
第一,为克服单一使用中值滤波方法去除脉冲噪声会造成图像细节信息丢失,使图像变模糊的缺陷,本文第三章提出一种基于模糊逻辑的图像去噪算法。该算法通过分析像素不同方向邻域像素灰度值分布情况来检测脉冲噪声点,为更好地保持图像边缘等细节特征,使用改进MMEM(maximum-minimum exclusive median)算法对噪声像素点的灰度值进行估计。最后,新算法通过引入模糊逻辑规则,更加合理地进行噪声污染像素点的灰度值复原。仿真实验表明,与其它改进中值滤波算法相比该算法在去除脉冲噪声时能取得更好的效果。
第二,在研究图像噪声过滤时,为了既有效地去除噪声,又能够较好地保持图像边缘和重要的细节信息,本文第四章将模糊逻辑思想与Perona-Malik方法相结合,提出了一种对噪声图像更有效更有适应性的基于模糊逻辑的偏微分方程去噪算法。该算法把PM方法中扩散方程的扩散系数看作像素梯度对于图像平滑区域的模糊隶属度函数,并通过定义合理的模糊隶属度函数,使得对不同的像素梯度大小采用不同的扩散系数。实验结果表明,该算法在去除噪声的同时,能更好地保持图像的边缘细节,具有较好的处理效果。
第三,本文第五章将粒子群优化算法与模糊C—均值聚类算法相结合,应用于图像边缘检测,以期解决标准FCM算法在图像边缘检测中对初始值敏感及容易陷入局部极小的两大缺陷。首先,基于数学测度概念构造一个描述边缘点信息的特征向量,将灰度图像中的每一个像素点看成是一个数据样本,将该点灰度值处理后构成其边缘点信息特征向量,形成具有三维特征的数据集,然后对这个数据集应用粒子群模糊聚类算法进行分类,自适应地检测出图像的边缘点,达到提取边缘的目的。仿真实验表明,此算法具有良好的抗噪性能,能够得到较好的边缘效果,提高了边缘定位的精度。
第四,本文第六章在分析Pal模糊边缘提取算法的基础上,为克服Pal算法图像增强区域单一、图像增强后造成低灰度信息损失且没有做抑噪处理的缺陷,提出一种新的基于模糊增强的图像边缘提取算法。新算法通过引入模糊熵,进行有目的选取不同灰度层次的阈值,同时增强图像中不同灰度层次的边缘信息,通过定义新的隶属函数和一种新的模糊增强算子,结合图像平滑滤波处理进行图像边缘提取,有效地克服了Pal算法速度慢且损失图像部分灰度信息的缺陷,取得了优于基于传统Pal算法进行图像边缘提取的效果。
第五,在第七章为确定图像分割的最佳阈值,本文提出了一种新的有效的图像阈值分割方法。该方法首先给出一个新模糊熵的定义,这个模糊熵定义不仅考虑到图像在模糊域中划分区域时随隶属函数变化而变化的情况,同时也考虑到图像在空域中划分区域时随隶属函数变化而变化的情况,这样就使得图像依照最大熵准则变换到模糊域更能够有效地反映图像的固有信息。然后,采用自适应粒子群优化算法寻求隶属函数的最优参数,得到分割的最佳阈值,并用该阈值对图像进行分割。将新算法应用于图像分割中,取得了优于现有大多数阈值分割算法的效果。
第六,本文第八章提出了一种新的图像阈值分割方法,该方法首先给出模糊连通度定义。然后,采用图像划分测度作为区分目标和背景的阈值分割准则,计算图像划分测度时采用基于灰度级的权值矩阵来代替通常所用的基于像素的权值矩阵来描述图像中各像素之间的关系,从而减少算法实现的复杂性,提高算法运算速度。仿真实验结果表明：与现有大多数模糊阈值分割方法相比,本章提出的方法更具优越性。
The basic concepts, basic theorys and basic methods of digital image processing are summarily introduced firstly. Then the basic concepts and basic theorys of fuzzy logic are introduced. At last, new ideas and methods based on fuzzy logic processing technique are proposed. The research results mainly include the following six aspects:
(1) A new adaptive image de-noising algorithm based on fuzzy logic is proposed by analyzing the deficiencies of median filter when it is used to eliminate impulsive noise. The new algorithm based on grayscale distribution of neighboring pixels in different directions detections noise points, and it uses the improved algorithm of maximum-minimum exclusive median method to estimate the gray level of current noisy pixels. Finaly, introducing the fuzzy logic rules into the new algorithm, the gray level of noisy pixels will be restored more reasonably. Simulation results show that the new algorithm may bring better effect in eliminating impulsive noise in comparison with the improved medium filter methods.
(2) In research of image denoising, in order to remove noise effectively and preserve edges and key details, an effective image denoising algorithm based on fuzzy logic PDEs is proposed. This algorithm combines the fuzzy logical with the Perona-Malik method. This algorithm builds a new diffusion coefficient in partial derivative equation with the fuzzy membership between the image gradient and the corresponding smooth regions.By defining reasonable fuzzy membership function, the algorithm bases on a selective and improved diffusion coefficient and performes adaptively towards different gradients. Simulated experiments show the algorithm can effectively reduce the noises of the image, and its results needn't to be adjusted, which can enhancement the precision of edge orientation.
(3) An effective PSO fuzzy clustering edge detection algorithm is proposed. PSO (particle swarm optimization) algorithm and Fuzzy C-Mean (FCM) algorithm are combined to overcome two shortcomings, namely the initialization sensitivity and the local minimum of standard FCM algorithm in image edge detection. At first, a vector is constructed to describe edge point informations, which includes neighborhood homogeneity information measure, orientation information measure, and gradient strength. Then we regard a pixel point in a gray image as a data sample, and its gray values which are worked by our defined vector's operator as the feature vectors of this data sample, in this way we can obtain a data set with three-dimensional features. Then we use the PSO fuzzy clustering algorithm on this data set, it can detect out the edge points adaptively. Simulated experiments show the algorithm can effectively reduce the noises of the image, and its results needn't to be adjusted, which can enhance the precision of edge orientation.
(4) A novel image edge extraction algorithm based on fuzzy enhancement is proposed by analyzing the deficiencies of Pal fuzzy edge extraction algorithm (Pal algorithm). This algorithm introduces fuzzy entropy and selects the threshold value in different gray levels. Defining a new membership function and a new fuzzy enhancement function, the new algorithm can enhance image edges of different gray levels. In addition, the new algorithm simplifies the complex transformation calculation. We can get a better result than that of the traditional Pal image edge extraction algorithm.
(5) To determine the optimal thresholds in image segmentation, an effective image threshold segmentation method is presented that base on Fuzzy logic. A new fuzzy entropy is defined, that is not only related to the membership (fuzzy domain) but also related to the probability distribution (space domain), it can respond to the variety of image input information. In addition, by introducing a novel particle swarm optimization (PSO) algorithm, the optimal threshold can be gotten to find the optimization parameters of the membership, so that one image can be segmented by using the threshold. Using our novel algorithm to segment images, we can get a better result than that of most threshold segmentation algorithm.
(6) A novel thresholding algorithm is presented. At first, a definition of fuzzy connectedness is proposed. Then the algorithm uses image cut measure as the thresholding principle to distinguish an object from background, the weight matrices are used in evaluating the image cuts measure based on the gray levels of an image, rather than image pixels, for most images, the complexity of the algorithm can be reduced and the speed of the calculation can be improved. Simulation results show that the new algorithm may bring better segmentation effect in comparison with lots of other image thresholding method.
主要包括以下六个方面内容：
第一,为克服单一使用中值滤波方法去除脉冲噪声会造成图像细节信息丢失,使图像变模糊的缺陷,本文第三章提出一种基于模糊逻辑的图像去噪算法。该算法通过分析像素不同方向邻域像素灰度值分布情况来检测脉冲噪声点,为更好地保持图像边缘等细节特征,使用改进MMEM(maximum-minimum exclusive median)算法对噪声像素点的灰度值进行估计。最后,新算法通过引入模糊逻辑规则,更加合理地进行噪声污染像素点的灰度值复原。仿真实验表明,与其它改进中值滤波算法相比该算法在去除脉冲噪声时能取得更好的效果。
第二,在研究图像噪声过滤时,为了既有效地去除噪声,又能够较好地保持图像边缘和重要的细节信息,本文第四章将模糊逻辑思想与Perona-Malik方法相结合,提出了一种对噪声图像更有效更有适应性的基于模糊逻辑的偏微分方程去噪算法。该算法把PM方法中扩散方程的扩散系数看作像素梯度对于图像平滑区域的模糊隶属度函数,并通过定义合理的模糊隶属度函数,使得对不同的像素梯度大小采用不同的扩散系数。实验结果表明,该算法在去除噪声的同时,能更好地保持图像的边缘细节,具有较好的处理效果。
第三,本文第五章将粒子群优化算法与模糊C—均值聚类算法相结合,应用于图像边缘检测,以期解决标准FCM算法在图像边缘检测中对初始值敏感及容易陷入局部极小的两大缺陷。首先,基于数学测度概念构造一个描述边缘点信息的特征向量,将灰度图像中的每一个像素点看成是一个数据样本,将该点灰度值处理后构成其边缘点信息特征向量,形成具有三维特征的数据集,然后对这个数据集应用粒子群模糊聚类算法进行分类,自适应地检测出图像的边缘点,达到提取边缘的目的。仿真实验表明,此算法具有良好的抗噪性能,能够得到较好的边缘效果,提高了边缘定位的精度。
第四,本文第六章在分析Pal模糊边缘提取算法的基础上,为克服Pal算法图像增强区域单一、图像增强后造成低灰度信息损失且没有做抑噪处理的缺陷,提出一种新的基于模糊增强的图像边缘提取算法。新算法通过引入模糊熵,进行有目的选取不同灰度层次的阈值,同时增强图像中不同灰度层次的边缘信息,通过定义新的隶属函数和一种新的模糊增强算子,结合图像平滑滤波处理进行图像边缘提取,有效地克服了Pal算法速度慢且损失图像部分灰度信息的缺陷,取得了优于基于传统Pal算法进行图像边缘提取的效果。
第五,在第七章为确定图像分割的最佳阈值,本文提出了一种新的有效的图像阈值分割方法。该方法首先给出一个新模糊熵的定义,这个模糊熵定义不仅考虑到图像在模糊域中划分区域时随隶属函数变化而变化的情况,同时也考虑到图像在空域中划分区域时随隶属函数变化而变化的情况,这样就使得图像依照最大熵准则变换到模糊域更能够有效地反映图像的固有信息。然后,采用自适应粒子群优化算法寻求隶属函数的最优参数,得到分割的最佳阈值,并用该阈值对图像进行分割。将新算法应用于图像分割中,取得了优于现有大多数阈值分割算法的效果。
第六,本文第八章提出了一种新的图像阈值分割方法,该方法首先给出模糊连通度定义。然后,采用图像划分测度作为区分目标和背景的阈值分割准则,计算图像划分测度时采用基于灰度级的权值矩阵来代替通常所用的基于像素的权值矩阵来描述图像中各像素之间的关系,从而减少算法实现的复杂性,提高算法运算速度。仿真实验结果表明：与现有大多数模糊阈值分割方法相比,本章提出的方法更具优越性。
The basic concepts, basic theorys and basic methods of digital image processing are summarily introduced firstly. Then the basic concepts and basic theorys of fuzzy logic are introduced. At last, new ideas and methods based on fuzzy logic processing technique are proposed. The research results mainly include the following six aspects:
(1) A new adaptive image de-noising algorithm based on fuzzy logic is proposed by analyzing the deficiencies of median filter when it is used to eliminate impulsive noise. The new algorithm based on grayscale distribution of neighboring pixels in different directions detections noise points, and it uses the improved algorithm of maximum-minimum exclusive median method to estimate the gray level of current noisy pixels. Finaly, introducing the fuzzy logic rules into the new algorithm, the gray level of noisy pixels will be restored more reasonably. Simulation results show that the new algorithm may bring better effect in eliminating impulsive noise in comparison with the improved medium filter methods.
(2) In research of image denoising, in order to remove noise effectively and preserve edges and key details, an effective image denoising algorithm based on fuzzy logic PDEs is proposed. This algorithm combines the fuzzy logical with the Perona-Malik method. This algorithm builds a new diffusion coefficient in partial derivative equation with the fuzzy membership between the image gradient and the corresponding smooth regions.By defining reasonable fuzzy membership function, the algorithm bases on a selective and improved diffusion coefficient and performes adaptively towards different gradients. Simulated experiments show the algorithm can effectively reduce the noises of the image, and its results needn't to be adjusted, which can enhancement the precision of edge orientation.
(3) An effective PSO fuzzy clustering edge detection algorithm is proposed. PSO (particle swarm optimization) algorithm and Fuzzy C-Mean (FCM) algorithm are combined to overcome two shortcomings, namely the initialization sensitivity and the local minimum of standard FCM algorithm in image edge detection. At first, a vector is constructed to describe edge point informations, which includes neighborhood homogeneity information measure, orientation information measure, and gradient strength. Then we regard a pixel point in a gray image as a data sample, and its gray values which are worked by our defined vector's operator as the feature vectors of this data sample, in this way we can obtain a data set with three-dimensional features. Then we use the PSO fuzzy clustering algorithm on this data set, it can detect out the edge points adaptively. Simulated experiments show the algorithm can effectively reduce the noises of the image, and its results needn't to be adjusted, which can enhance the precision of edge orientation.
(4) A novel image edge extraction algorithm based on fuzzy enhancement is proposed by analyzing the deficiencies of Pal fuzzy edge extraction algorithm (Pal algorithm). This algorithm introduces fuzzy entropy and selects the threshold value in different gray levels. Defining a new membership function and a new fuzzy enhancement function, the new algorithm can enhance image edges of different gray levels. In addition, the new algorithm simplifies the complex transformation calculation. We can get a better result than that of the traditional Pal image edge extraction algorithm.
(5) To determine the optimal thresholds in image segmentation, an effective image threshold segmentation method is presented that base on Fuzzy logic. A new fuzzy entropy is defined, that is not only related to the membership (fuzzy domain) but also related to the probability distribution (space domain), it can respond to the variety of image input information. In addition, by introducing a novel particle swarm optimization (PSO) algorithm, the optimal threshold can be gotten to find the optimization parameters of the membership, so that one image can be segmented by using the threshold. Using our novel algorithm to segment images, we can get a better result than that of most threshold segmentation algorithm.
(6) A novel thresholding algorithm is presented. At first, a definition of fuzzy connectedness is proposed. Then the algorithm uses image cut measure as the thresholding principle to distinguish an object from background, the weight matrices are used in evaluating the image cuts measure based on the gray levels of an image, rather than image pixels, for most images, the complexity of the algorithm can be reduced and the speed of the calculation can be improved. Simulation results show that the new algorithm may bring better segmentation effect in comparison with lots of other image thresholding method.
引文
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