基于分形与迭代的图象特征表示
摘要
图象特征表示是研究从图象中提取与组织特征，它是图象研究领域最基本最重要的工作，可以被用于图象数据库索引与查找、图象识别、图象压缩等各个方面。图象特征表示也属于人工智能的研究范畴，是人工智能中知识表示的一个复杂而有代表性的特例。因为图象是数学意义上的函数或矩阵，所以图象特征表示与各种数学运算方法有关，诸多的数学工具都被用于图象特征的提取与组织。迭代与分形是一种新的数学理论方法，基于迭代分形的图象特征表示的研究近年已经开始。
本文使用迭代与分形理论方法研究图象特征表示。主要工作，一是对函数迭代方面的内容进行研究，归纳并且发现了迭代分形覆盖特性与相关的混沌变化规律等；二是对图象的分形表示方法进行研究，给出了一个原图象索引查找方法，在理论研究方面，发现了图象集合的分形维数方面的规律；三是基于迭代方法，提出了两种图象特征表示方法。
本文的创新工作是：
1、对相关的函数迭代特性进行研究，提出了IFS(Iterated Function System，迭代函数系统)迭代分形覆盖的相交交点数目变化曲线(CIPN，The Curve of the Intersection Points Number)的概念，给出了CIPN的生成算法，研究了CIPN的变化特性。这些结果可以作为图象分形特征表示新方法的理论基础；另外，研究小波函数迭代的混沌分岔特性，给出了当其参数变化时出现的分岔图的一些规律性结论。这些结论对构造图象特征的迭代表示方法有很重要的参考价值。
2、基于分形方法，利用分形的二叉树结构，分别把图象的逐次分块重量与分块重心作为二叉树的节点，然后定义两种距离，构造类似R-树的最小包围盒，实现原图象的查找。这种方法对污染破损、变形等图象具有较好的查找效果；Korn等(2001)指出，使用R树结构对高维空间点集进行索引时，搜索时间复杂性取决于该点集的分形维数。基于分形维数理论，本文对图象构成的点集与其特征点集的分形维数进行分析，证明了奇异值特征点集与小波分解系数构成的点集的分形维数小于图象点集的分形维数，得到了序列图象作为高维点集时的分形维数远小于它所在空间的维数等结论。该结论说明，在使用图象特征对图象集合进行索引时，查找效率是比较高的。
3、基于IFS迭代覆盖，提出了一种图象特征表示方法。首先对图象的各种特征进行提取，再将提取得到的特征向量作为二元二次迭代式的系数组成迭代式，然后进行随机迭代，根据迭代出来点的分布特性对图象进行分类。由于二元二次迭代式收敛性不好，本文用乘以小波函数的方法来控制迭代的发散。与2003年著名学者Han等使用的方法
This paper is concern that image representation methods and theory on the fractal structure and iterate procedure. Meanwhile it shows some new experimental plans and theoretical results. The main assignments are as follows:
Study the Iterated Function System (IFS), study the covering properties when we draw the fractal graphs by the computers using the same iterated codes, give some meaningful experimental results and analyze some theoretical questions; When all the formula in the IFS are multiplied by a constant α, the behaviors of the system will be changed. The bifurcation diagram of a wavelet function is discussed. Its diagram shows specially that not only from period to chaotic state but also from the chaotic state to period. Above property of the IFS is used in the next parts of the paper.
Study the fractal representation method, give the exchange method of Hilbert alignment and the structure of binary tree. Use the structure of binary tree and the weight center to index the image, define two kinds of distances, index and search the image database. This index methods have a good search effect to the images which are polluted, damaged and deformed. Analyze the fractal dimensions of the image set and the feature set, prove that the fractal dimensions of some image feature sets are less than that of the image set at the high dimension space, give the conclusion that the fractal dimension of the image sequence is far less than the space dimension.
A new representation algorithm based on the iterated functions is applied to classify the football match images, the neighborhood and the learning factor of the SOF NN is used to enhance the robustness of the algorithm. In addition, a new scheme that employs the image as weight matrix is introduced to build a chaos neural network which has improved from the Hopfield neural network. In the network, each artificial neuron accumulates the stimulus effect which bases on the image weight matrix. So it is possible for the neural network to recall the embedded memories and associate the temporal image.
Although the fractal and iterated representation methods are all in the elementary period, they has already shown the potential. At the end of the paper, some existed questions of the fractal and iterated representation and the work in the next step are discussed.
本文使用迭代与分形理论方法研究图象特征表示。主要工作，一是对函数迭代方面的内容进行研究，归纳并且发现了迭代分形覆盖特性与相关的混沌变化规律等；二是对图象的分形表示方法进行研究，给出了一个原图象索引查找方法，在理论研究方面，发现了图象集合的分形维数方面的规律；三是基于迭代方法，提出了两种图象特征表示方法。
本文的创新工作是：
1、对相关的函数迭代特性进行研究，提出了IFS(Iterated Function System，迭代函数系统)迭代分形覆盖的相交交点数目变化曲线(CIPN，The Curve of the Intersection Points Number)的概念，给出了CIPN的生成算法，研究了CIPN的变化特性。这些结果可以作为图象分形特征表示新方法的理论基础；另外，研究小波函数迭代的混沌分岔特性，给出了当其参数变化时出现的分岔图的一些规律性结论。这些结论对构造图象特征的迭代表示方法有很重要的参考价值。
2、基于分形方法，利用分形的二叉树结构，分别把图象的逐次分块重量与分块重心作为二叉树的节点，然后定义两种距离，构造类似R-树的最小包围盒，实现原图象的查找。这种方法对污染破损、变形等图象具有较好的查找效果；Korn等(2001)指出，使用R树结构对高维空间点集进行索引时，搜索时间复杂性取决于该点集的分形维数。基于分形维数理论，本文对图象构成的点集与其特征点集的分形维数进行分析，证明了奇异值特征点集与小波分解系数构成的点集的分形维数小于图象点集的分形维数，得到了序列图象作为高维点集时的分形维数远小于它所在空间的维数等结论。该结论说明，在使用图象特征对图象集合进行索引时，查找效率是比较高的。
3、基于IFS迭代覆盖，提出了一种图象特征表示方法。首先对图象的各种特征进行提取，再将提取得到的特征向量作为二元二次迭代式的系数组成迭代式，然后进行随机迭代，根据迭代出来点的分布特性对图象进行分类。由于二元二次迭代式收敛性不好，本文用乘以小波函数的方法来控制迭代的发散。与2003年著名学者Han等使用的方法
This paper is concern that image representation methods and theory on the fractal structure and iterate procedure. Meanwhile it shows some new experimental plans and theoretical results. The main assignments are as follows:
Study the Iterated Function System (IFS), study the covering properties when we draw the fractal graphs by the computers using the same iterated codes, give some meaningful experimental results and analyze some theoretical questions; When all the formula in the IFS are multiplied by a constant α, the behaviors of the system will be changed. The bifurcation diagram of a wavelet function is discussed. Its diagram shows specially that not only from period to chaotic state but also from the chaotic state to period. Above property of the IFS is used in the next parts of the paper.
Study the fractal representation method, give the exchange method of Hilbert alignment and the structure of binary tree. Use the structure of binary tree and the weight center to index the image, define two kinds of distances, index and search the image database. This index methods have a good search effect to the images which are polluted, damaged and deformed. Analyze the fractal dimensions of the image set and the feature set, prove that the fractal dimensions of some image feature sets are less than that of the image set at the high dimension space, give the conclusion that the fractal dimension of the image sequence is far less than the space dimension.
A new representation algorithm based on the iterated functions is applied to classify the football match images, the neighborhood and the learning factor of the SOF NN is used to enhance the robustness of the algorithm. In addition, a new scheme that employs the image as weight matrix is introduced to build a chaos neural network which has improved from the Hopfield neural network. In the network, each artificial neuron accumulates the stimulus effect which bases on the image weight matrix. So it is possible for the neural network to recall the embedded memories and associate the temporal image.
Although the fractal and iterated representation methods are all in the elementary period, they has already shown the potential. At the end of the paper, some existed questions of the fractal and iterated representation and the work in the next step are discussed.
引文
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