图像宏微观特征偏序结构一体化表示与相似性度量研究
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摘要
在模式识别过程中，特征表示是否得当是后续分类效果高低的前提条件，也是整个模式识别系统性能优劣的重要条件。目前，结构模式识别与统计模式识别是模式识别领域的两大分支，如何将统计模式识别和结构模式识别相结合，取长补短，联合进行模式识别任务，是解决模式识别问题的新方向。
本文针对模式识别中的图像特征表示与分类问题，以宏观结构特征和微观统计特征相结合为基本思想，以偏序结构作为表示方法，以距离度量作为分类手段，构造图像宏微观特征偏序结构一体化表示的理论框架与相似性度量方法。
首先针对结构模式识别中基元提取与基元关系构造问题，提出了序化的图像结构特征表达模型。通过构造图像基元的形式背景，应用几何代数中的多向量标记图像基元位置，再按照图像基元的属性偏序关系构造关系图，从而得到基于几何代数表示的图像结构特征表达方式。
其次针对图像空间特征描述的表示与相似性度量问题，提出图像宏观结构特征与微观统计特征相集成的图像特征提取与分类方法。一方面以四叉树分解对图像进行空间结构特征表示，并提出基于几何代数表示的标签四叉树距离计算方法；另一方面在图像四叉树分解的基础上，利用区域协方差描述子提出一种图像的多尺度局部特征提取与相似性度量方法；最后将图像宏观结构距离与微观统计特征距离加权融合用于图像整体的相似性度量。论文在四组人脸图像数据库上进行实验，并与现有文献中方法进行比较。实验结果表明，将微观统计特征和宏观结构特征相结合进行图像特征表示与分类的方法，能够获得较高的分类精度，是一种有效的模式识别方法。
最后研究了图像多尺度特征描述的表示与相似性度量问题。一方面应用四元数小波变换对图像进行多尺度分解，将不同尺度上的图像视作图像基元，并利用形式概念分析挖掘图像基元的序结构，建立图像基元的属性树结构；另一方面针对属性树结点特征提取问题，以协方差矩阵和奇异值分解为工具构造不同尺度图像基元的微结构表达，并建立了属性树父子结点间的加权关系，最终构成图像宏微观一体化的多尺度加权属性树表示模型，将图像分类问题转化成对应属性树相似性度量问题，并在此基础上设计了一种属性树距离计算方法。最后在国际标准纹理图片库UIUC以及一组医学显微CT数据集上进行测试，并与传统方法相比较，实验结果表明，提出的方法可以显著提高分类精度。
研究结果表明，本文提出的图像宏观微观特征偏序结构一体化表示与相似性度量方法，具有特征表示统一化，识别方法简单化，有利于知识利用和生成等特点。该方法有望进一步发展和完善，并应用于其他领域的模式识别问题。
In the process of pattern recognition, whether the feature representation is proper ornot, is the precondition to decide whether the subsequent classification results are high orlow; and also the important condition for the performance of the entire pattern recognitionsystem to be good or not. At present, the field of pattern recognition has twobranches---structural pattern recognition and statistical pattern recognition. How tocombine the statistical pattern recognition with the structural pattern recognition, learnfrom the other' strong points to offset its weaknesses, and jointly fulfill the tasks of patternrecognition, are the new directions to solve the problems of pattern recognition.
Towards the image feature representation and classification problem in the patternrecognition, and taking the combination of macro-structural features and micro-statisticalfeatures as the basic idea, partially ordered structure as the way of representation, anddistance measure as the method of classification, the paper builds the theoreticalframework and provides the similarity measure method for the unification representationof the partially ordered structure of the macroscopic features and microscopic features ofimages.
Firstly, towards the primitive extraction and primitive relationship construction instructural pattern recognition, the ordered image structural feature expression models areput forward. Through the formal context where the image primitives are built, themulti-vectors in geometric algebra are applied to mark the positions of the imageprimitives, and then the relational graph is formulated according to the partial order of theattributes of the image primitives, thus obtaining the image structural feature expressionmeans based on the geometric algebra representation.
Secondly, towards the representation of the image spatial feature description andsimilarity measure, the image feature extraction and classification methods by integratingthe image macro-structural features and micro-statistical features have been put forward.On one hand, the spatial structural features of the images are represented by the quadtreedecomposition, and then the labeled quadtree distance calculation method based on the geometric algebraic representation is proposed; on the other hand, on the basis of theimage quadtree decomposition, the regional covariance descriptor is applied to present akind of image multi-scale local feature extraction method, and then the covariance matrixdistance is used to measure the similarities of the microscopic features of images. Finally,the weighting fusion of the image macro-structural distance and micro-statistical featuresdistance is applied in the overall similarity measure of images. The paper conductsexperiments on the four groups of face image databases, and then the comparisons aremade with the methods in the current literature. The results of the experiments suggest thatthe method of integrating the micro-statistical characteristics and the macro-structuralcharacteristic for the representation and classification of the image features, can obtainhigher precision of classification. It is an effective pattern recognition method.
Finally, the image multi-scale feature description representation and the similaritymeasure are researched. On one hand, the methods to obtain primitives in the structuralpattern recognition are extended to multi-scale field. The method is to apply theQuaternion Wavelet Transformation to decompose the images in a multi-scale manner, andthen regard the images in different scales as the image primitives; besides, the formalconcept analysis is applied to analyze and explore the ordered structures of the imageprimitives, and establish the attribute tree structures of the image primitives. On the otherhand, towards the node feature extraction issue of the attribute tree, the covariance matrixand singular value decomposition are taken as the tools to build the microstructurerepresentation of the image primitives in different scales, and the weighted relationshipbetween the parent-child nodes of the attribute tree is established, and finally constitutingthe image macroscopic and microscopic integrated multi-scale weighted attribute treerecognition pattern, and transform the image classification problem into the correspondingsimilarity measure issue of the attribute tree. On this basis, a kind of attribute tree distancecalculation method is designed. At last, some tests are conducted on the internationalstandard texture image gallery UIUC and a group of medical micro-CT dataset, and thenthe comparison is made with the traditional methods. The results of the experiment showthat the methods put forward can significantly improve the precision of classification.
The results of the research show that the unification representation and similarity by the partially ordered structures of the macroscopic and microscopic features of image datamethod put forward by this paper，which has merits of unification of feature representation,making classification simple and facilitating the utilizing and generating of expertknowledge. This method is expected to obtain further development and improvement, andbe applied to other domains’ pattern recognition problems.
本文针对模式识别中的图像特征表示与分类问题，以宏观结构特征和微观统计特征相结合为基本思想，以偏序结构作为表示方法，以距离度量作为分类手段，构造图像宏微观特征偏序结构一体化表示的理论框架与相似性度量方法。
首先针对结构模式识别中基元提取与基元关系构造问题，提出了序化的图像结构特征表达模型。通过构造图像基元的形式背景，应用几何代数中的多向量标记图像基元位置，再按照图像基元的属性偏序关系构造关系图，从而得到基于几何代数表示的图像结构特征表达方式。
其次针对图像空间特征描述的表示与相似性度量问题，提出图像宏观结构特征与微观统计特征相集成的图像特征提取与分类方法。一方面以四叉树分解对图像进行空间结构特征表示，并提出基于几何代数表示的标签四叉树距离计算方法；另一方面在图像四叉树分解的基础上，利用区域协方差描述子提出一种图像的多尺度局部特征提取与相似性度量方法；最后将图像宏观结构距离与微观统计特征距离加权融合用于图像整体的相似性度量。论文在四组人脸图像数据库上进行实验，并与现有文献中方法进行比较。实验结果表明，将微观统计特征和宏观结构特征相结合进行图像特征表示与分类的方法，能够获得较高的分类精度，是一种有效的模式识别方法。
最后研究了图像多尺度特征描述的表示与相似性度量问题。一方面应用四元数小波变换对图像进行多尺度分解，将不同尺度上的图像视作图像基元，并利用形式概念分析挖掘图像基元的序结构，建立图像基元的属性树结构；另一方面针对属性树结点特征提取问题，以协方差矩阵和奇异值分解为工具构造不同尺度图像基元的微结构表达，并建立了属性树父子结点间的加权关系，最终构成图像宏微观一体化的多尺度加权属性树表示模型，将图像分类问题转化成对应属性树相似性度量问题，并在此基础上设计了一种属性树距离计算方法。最后在国际标准纹理图片库UIUC以及一组医学显微CT数据集上进行测试，并与传统方法相比较，实验结果表明，提出的方法可以显著提高分类精度。
研究结果表明，本文提出的图像宏观微观特征偏序结构一体化表示与相似性度量方法，具有特征表示统一化，识别方法简单化，有利于知识利用和生成等特点。该方法有望进一步发展和完善，并应用于其他领域的模式识别问题。
In the process of pattern recognition, whether the feature representation is proper ornot, is the precondition to decide whether the subsequent classification results are high orlow; and also the important condition for the performance of the entire pattern recognitionsystem to be good or not. At present, the field of pattern recognition has twobranches---structural pattern recognition and statistical pattern recognition. How tocombine the statistical pattern recognition with the structural pattern recognition, learnfrom the other' strong points to offset its weaknesses, and jointly fulfill the tasks of patternrecognition, are the new directions to solve the problems of pattern recognition.
Towards the image feature representation and classification problem in the patternrecognition, and taking the combination of macro-structural features and micro-statisticalfeatures as the basic idea, partially ordered structure as the way of representation, anddistance measure as the method of classification, the paper builds the theoreticalframework and provides the similarity measure method for the unification representationof the partially ordered structure of the macroscopic features and microscopic features ofimages.
Firstly, towards the primitive extraction and primitive relationship construction instructural pattern recognition, the ordered image structural feature expression models areput forward. Through the formal context where the image primitives are built, themulti-vectors in geometric algebra are applied to mark the positions of the imageprimitives, and then the relational graph is formulated according to the partial order of theattributes of the image primitives, thus obtaining the image structural feature expressionmeans based on the geometric algebra representation.
Secondly, towards the representation of the image spatial feature description andsimilarity measure, the image feature extraction and classification methods by integratingthe image macro-structural features and micro-statistical features have been put forward.On one hand, the spatial structural features of the images are represented by the quadtreedecomposition, and then the labeled quadtree distance calculation method based on the geometric algebraic representation is proposed; on the other hand, on the basis of theimage quadtree decomposition, the regional covariance descriptor is applied to present akind of image multi-scale local feature extraction method, and then the covariance matrixdistance is used to measure the similarities of the microscopic features of images. Finally,the weighting fusion of the image macro-structural distance and micro-statistical featuresdistance is applied in the overall similarity measure of images. The paper conductsexperiments on the four groups of face image databases, and then the comparisons aremade with the methods in the current literature. The results of the experiments suggest thatthe method of integrating the micro-statistical characteristics and the macro-structuralcharacteristic for the representation and classification of the image features, can obtainhigher precision of classification. It is an effective pattern recognition method.
Finally, the image multi-scale feature description representation and the similaritymeasure are researched. On one hand, the methods to obtain primitives in the structuralpattern recognition are extended to multi-scale field. The method is to apply theQuaternion Wavelet Transformation to decompose the images in a multi-scale manner, andthen regard the images in different scales as the image primitives; besides, the formalconcept analysis is applied to analyze and explore the ordered structures of the imageprimitives, and establish the attribute tree structures of the image primitives. On the otherhand, towards the node feature extraction issue of the attribute tree, the covariance matrixand singular value decomposition are taken as the tools to build the microstructurerepresentation of the image primitives in different scales, and the weighted relationshipbetween the parent-child nodes of the attribute tree is established, and finally constitutingthe image macroscopic and microscopic integrated multi-scale weighted attribute treerecognition pattern, and transform the image classification problem into the correspondingsimilarity measure issue of the attribute tree. On this basis, a kind of attribute tree distancecalculation method is designed. At last, some tests are conducted on the internationalstandard texture image gallery UIUC and a group of medical micro-CT dataset, and thenthe comparison is made with the traditional methods. The results of the experiment showthat the methods put forward can significantly improve the precision of classification.
The results of the research show that the unification representation and similarity by the partially ordered structures of the macroscopic and microscopic features of image datamethod put forward by this paper，which has merits of unification of feature representation,making classification simple and facilitating the utilizing and generating of expertknowledge. This method is expected to obtain further development and improvement, andbe applied to other domains’ pattern recognition problems.
引文
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