基于小波变换和模糊粗糙集技术的图像识别
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摘要
图像识别是近二十年来模式识别和图像处理研究的热点,是用现代信息处理技术与计算机技术完成对图像的认识、理解过程。它研究的主要内容是根据图像的特征进行识别(或分类),已在许多领域得到广泛应用。图像识别过程大致可分为图像预处理、图像特征提取和图像识别(或分类)三个步骤。其中,图像特征提取和图像分类是两个核心环节,本文主要在这两方面开展研究。
在图像特征提取研究中,主要工作包括以下2方面:
1.将小波变换和二维投影子空间技术有机地结合起来,从变换系数中提取图像的代数特征。研究了小波子段图像的选取问题,提出了①基于小波变换和二维主成分分析的图像特征提取方法;②基于小波变换和双向二维主成分分析的图像特征提取方法;③基于小波变换和二维线性判别分析的图像特征提取方法。在ORL、YALE、JAFFE和UMIST四个人脸数据库上的实验结果表明了该方法的有效性。
2.作为一种矩阵分解方法,奇异值分解可用于提取图像的代数特征。图像的奇异值特征具有很多好的性质,如稳定性、几何不变性、对噪声的不敏感性。但是只用一个尺度的图像奇异值特征难以获得高识别率。基于小波变换和奇异值分解,提出了基于小波多尺度奇异值分解的图像特征提取方法,它将多个尺度的小波子图奇异值特征组合起来用于图像识别。在ORL、YALE和JAFFE三个人脸数据库上的识别率分别达到82.11%、100%和95.68%。
在图像分类方法的研究中,基于模糊粗糙集技术,提出了以下三种分类方法:
1.针对二维主成分分析提取的图像特征依然存在冗余这一问题,提出了基于二维主成分分析和模糊粗糙集技术的图像识别方法。该方法利用模糊粗糙集技术的属性约简进行属性选择,将对分类比较重要的属性选择出来,将冗余的属性去掉。实验结果表明该方法优于基于二维主成分分析的图像识别方法。
2.模糊粗糙集是粗糙集的扩展,它将数据的模糊性和粗糙性结合起来。基于模糊粗糙集技术,提出了一种模糊决策树分类方法。该方法利用模糊条件属性相对于模糊决策属性的重要度选择扩展属性,它集成了数据中的两种不确定性,比基于纯模糊熵的模糊决策树分类方法具有更好的分类能力。实例分析和实验结果均表明该方法优于模糊ID3算法。
3.对于给定的模糊信息系统,可以求得多个模糊属性约简,而每个模糊属性约简对分类都有不同程度的贡献。如果只用其中一个模糊属性约简,即便它是最重要的模糊属性约简来产生分类规则,那么隐藏在其他模糊属性约简中的有用信息将不可避免地被丢失。针对这一问题,提出了一种基于模糊粗糙集技术的多模糊决策树归纳方法,该方法融合了多个模糊属性约简对分类的贡献。实例分析及实验结果均表明这一方法优于单个模糊属性约简的模糊决策树方法。
另外,本文还研究了信息系统信息粒度的粗细对决策树产生的影响,得出结论:粗信息粒的信息熵不小于细信息粒的信息熵,细信息粒下选取扩展属性产生的决策树优于粗信息粒下选取扩展属性产生的决策树。
Image recognition is the process of image cognition and image understanding by using modern information processing technology and computer technology, which has attracted lots of attention in pattern recognition and image processing during the last two decades. Image recognition mainly investigates the image classification based on image features and has been widely applied to many fields. It roughly consists of three steps: image preprocessing, image feature extraction, and image classification. The image feature extraction and image classification are two vital steps, which are the major focuses of this thesis. The contributions of this thesis in image feature extraction mainly include the following two aspects:
(1) This thesis integrates the wavelet transforms (WT) and two-dimensional projection subspace techniques effectively. The selection of wavelet sub-band images used for image recognition is studied. Three methods for image feature extraction are proposed,①image features extraction method based on WT and two-dimensional principal component analysis (2DPCA),②image features extraction method based on WT and two-directional two-dimensional principal component analysis ((2D)2PCA), and③image features extraction method based on WT and two-dimensional linear discriminant analysis (2DLDA). The experimental results on four face databases (ORL, YALE, JAFFE, and UMIST) verify the effectiveness of the proposed methods.
(2) As a matrix decomposition method, singular value decomposition (SVD) can be used to extract algebraic features from images. The SV features of images have many good properties such as stability, geometric invariance, and insensitiveness to noise. However, it is difficult to achieve high recognition rate by only using one scale SV features in image recognition. Based on the wavelet transforms and SVD, this thesis proposes an image feature extraction method which combines multiple scale SV features of wavelet sub-band images. The recognition rates on three face databases (ORL, YALE, and JAFFE) are 82.11%, 100%, and 95.68% respectively, which are higher than the existing SVD based approaches.
For image classification, this thesis proposes three classification methods based on fuzzy rough sets technique.
(1) To handle the redundant features which are extracted from images by using 2DPCA methods, an image recognition method (image classification method) is presented based on 2DPCA and fuzzy rough sets technique. The proposed method selects the important features for classification by using attribute reduction in fuzzy rough sets theory. The experimental results show the proposed method outperforms the existing image recognition methods based on 2DPCA.
(2) Fuzzy rough sets are generalizations of rough sets to deal with both fuzziness and vagueness in data, which integrate fuzzy sets and rough sets together. Based on fuzzy rough sets technique, this thesis proposes a new criterion, in which expanded attributes are selected by using significance of fuzzy conditional attributes with respect to fuzzy decision attributes. Because that two uncertainty (fuzziness and roughness) are integrated together in the proposed method whose power of classification is higher than the one of fuzzy decision tree algorithms based on pure fuzzy entropy. An illustrative example as well as the experimental results statistically confirms that the proposed method is superior to the fuzzy ID3 algorithm.
(3) Given a fuzzy information system, we may find many fuzzy attribute reducts and each of them can have different contributions to decision-making. If only one of the fuzzy attribute reducts, even though the most important one is selected to induce decision rules, some useful information hidden in the other reducts for the decision-making will be losing unavoidably. To make good use of the information provided by every individual fuzzy attribute reduct in the fuzzy information system, this thesis presents a novel induction of multiple fuzzy decision trees based on fuzzy rough sets technique. An illustrative example as well as the experimental results validate that the proposed multiple tree induction has better performance than the single tree induction based on the individual reducts.
In addition, this thesis investigates the influences of the coarse granularity and the fine granularity on the decision tree induction. The investigation leads us to the conclusion that the information entropy under coarse granularity is not less than the one under fine granularity. Furthermore, we draw the conclusion that the decision tree generated by selecting the expanded attribute under fine granularity outperforms the one under coarse granularity.
在图像特征提取研究中,主要工作包括以下2方面:
1.将小波变换和二维投影子空间技术有机地结合起来,从变换系数中提取图像的代数特征。研究了小波子段图像的选取问题,提出了①基于小波变换和二维主成分分析的图像特征提取方法;②基于小波变换和双向二维主成分分析的图像特征提取方法;③基于小波变换和二维线性判别分析的图像特征提取方法。在ORL、YALE、JAFFE和UMIST四个人脸数据库上的实验结果表明了该方法的有效性。
2.作为一种矩阵分解方法,奇异值分解可用于提取图像的代数特征。图像的奇异值特征具有很多好的性质,如稳定性、几何不变性、对噪声的不敏感性。但是只用一个尺度的图像奇异值特征难以获得高识别率。基于小波变换和奇异值分解,提出了基于小波多尺度奇异值分解的图像特征提取方法,它将多个尺度的小波子图奇异值特征组合起来用于图像识别。在ORL、YALE和JAFFE三个人脸数据库上的识别率分别达到82.11%、100%和95.68%。
在图像分类方法的研究中,基于模糊粗糙集技术,提出了以下三种分类方法:
1.针对二维主成分分析提取的图像特征依然存在冗余这一问题,提出了基于二维主成分分析和模糊粗糙集技术的图像识别方法。该方法利用模糊粗糙集技术的属性约简进行属性选择,将对分类比较重要的属性选择出来,将冗余的属性去掉。实验结果表明该方法优于基于二维主成分分析的图像识别方法。
2.模糊粗糙集是粗糙集的扩展,它将数据的模糊性和粗糙性结合起来。基于模糊粗糙集技术,提出了一种模糊决策树分类方法。该方法利用模糊条件属性相对于模糊决策属性的重要度选择扩展属性,它集成了数据中的两种不确定性,比基于纯模糊熵的模糊决策树分类方法具有更好的分类能力。实例分析和实验结果均表明该方法优于模糊ID3算法。
3.对于给定的模糊信息系统,可以求得多个模糊属性约简,而每个模糊属性约简对分类都有不同程度的贡献。如果只用其中一个模糊属性约简,即便它是最重要的模糊属性约简来产生分类规则,那么隐藏在其他模糊属性约简中的有用信息将不可避免地被丢失。针对这一问题,提出了一种基于模糊粗糙集技术的多模糊决策树归纳方法,该方法融合了多个模糊属性约简对分类的贡献。实例分析及实验结果均表明这一方法优于单个模糊属性约简的模糊决策树方法。
另外,本文还研究了信息系统信息粒度的粗细对决策树产生的影响,得出结论:粗信息粒的信息熵不小于细信息粒的信息熵,细信息粒下选取扩展属性产生的决策树优于粗信息粒下选取扩展属性产生的决策树。
Image recognition is the process of image cognition and image understanding by using modern information processing technology and computer technology, which has attracted lots of attention in pattern recognition and image processing during the last two decades. Image recognition mainly investigates the image classification based on image features and has been widely applied to many fields. It roughly consists of three steps: image preprocessing, image feature extraction, and image classification. The image feature extraction and image classification are two vital steps, which are the major focuses of this thesis. The contributions of this thesis in image feature extraction mainly include the following two aspects:
(1) This thesis integrates the wavelet transforms (WT) and two-dimensional projection subspace techniques effectively. The selection of wavelet sub-band images used for image recognition is studied. Three methods for image feature extraction are proposed,①image features extraction method based on WT and two-dimensional principal component analysis (2DPCA),②image features extraction method based on WT and two-directional two-dimensional principal component analysis ((2D)2PCA), and③image features extraction method based on WT and two-dimensional linear discriminant analysis (2DLDA). The experimental results on four face databases (ORL, YALE, JAFFE, and UMIST) verify the effectiveness of the proposed methods.
(2) As a matrix decomposition method, singular value decomposition (SVD) can be used to extract algebraic features from images. The SV features of images have many good properties such as stability, geometric invariance, and insensitiveness to noise. However, it is difficult to achieve high recognition rate by only using one scale SV features in image recognition. Based on the wavelet transforms and SVD, this thesis proposes an image feature extraction method which combines multiple scale SV features of wavelet sub-band images. The recognition rates on three face databases (ORL, YALE, and JAFFE) are 82.11%, 100%, and 95.68% respectively, which are higher than the existing SVD based approaches.
For image classification, this thesis proposes three classification methods based on fuzzy rough sets technique.
(1) To handle the redundant features which are extracted from images by using 2DPCA methods, an image recognition method (image classification method) is presented based on 2DPCA and fuzzy rough sets technique. The proposed method selects the important features for classification by using attribute reduction in fuzzy rough sets theory. The experimental results show the proposed method outperforms the existing image recognition methods based on 2DPCA.
(2) Fuzzy rough sets are generalizations of rough sets to deal with both fuzziness and vagueness in data, which integrate fuzzy sets and rough sets together. Based on fuzzy rough sets technique, this thesis proposes a new criterion, in which expanded attributes are selected by using significance of fuzzy conditional attributes with respect to fuzzy decision attributes. Because that two uncertainty (fuzziness and roughness) are integrated together in the proposed method whose power of classification is higher than the one of fuzzy decision tree algorithms based on pure fuzzy entropy. An illustrative example as well as the experimental results statistically confirms that the proposed method is superior to the fuzzy ID3 algorithm.
(3) Given a fuzzy information system, we may find many fuzzy attribute reducts and each of them can have different contributions to decision-making. If only one of the fuzzy attribute reducts, even though the most important one is selected to induce decision rules, some useful information hidden in the other reducts for the decision-making will be losing unavoidably. To make good use of the information provided by every individual fuzzy attribute reduct in the fuzzy information system, this thesis presents a novel induction of multiple fuzzy decision trees based on fuzzy rough sets technique. An illustrative example as well as the experimental results validate that the proposed multiple tree induction has better performance than the single tree induction based on the individual reducts.
In addition, this thesis investigates the influences of the coarse granularity and the fine granularity on the decision tree induction. The investigation leads us to the conclusion that the information entropy under coarse granularity is not less than the one under fine granularity. Furthermore, we draw the conclusion that the decision tree generated by selecting the expanded attribute under fine granularity outperforms the one under coarse granularity.
引文
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