方向性多分辨率图像分析研究：理论和应用
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摘要
本论文研究方向性多分辨率分析和神经网络PCNN在图像分析中的应用。
有关方向性多分辨率分析的研究一直是信号处理的重点内容。有许多在多分辨率分析框架下提取信号方向性信息的方法，这些方法都试图提供高维信号的方向性表达，附加地还必须满足理想重构，低冗余度，高计算效率等性质。DTCWT、Contourlets、NSCT、PDTDFB等变换是目前流行的方向性多分辨率分析方法，但它们都有各自结构性的缺陷。
神经网络PCNN是优异的图像分析工具，是一种具有旋转不变、尺度不变、平移不变等特点的图像变换方法。PCNN可以提供对原图像在不同尺度下的逼近序列，因而具有多分辨率分析的性质。与小波和多尺度分析不同，PCNN直接检测边缘信息，这些边缘信息可用于特征提取、图像分割、目标识别、除噪和增强等应用。
本论文的主要内容和贡献如下：
1、基于解析信号复小波变换的思想，提出了基于解析信号的P-Contourlet变换，通过在原始信号的解析信号上实施Contourlet变换，实现了一种平移不变的方向性多分辨率方法，变换具有相信息。根据方向性分辨率的不同，我们将该方法分为单通道方法P-Contourlet-Ⅰ和双通道方法P-Contourlet-Ⅱ。P-Contourlet实现结构简单，冗余度较低。纹理分类实验结果表明，P-Contourlet是一种非常有效的图像分析工具。
2、基于对偶树复小波的思想，提出对偶树Contourlet变换DTCT。我们研究PDTDFB的结构和实现方法，认知到它在滤波器设计和系统实现上存在一些问题，所以我们提出一种易于实现的结构DTCT。两个级联的DFBs树形结构对拉普拉斯金字塔的高通子带进行方向性分解，单独的每个树形结构构造为正交系统，实树和虚树对应的滤波器之间满足一定的相约束条件，整个变换为紧框架。我们分析了DTCT的系统结构和滤波器特性，并提出了系统所需要的滤波器设计方法。DTCT实现了近似的平移不变性，方向性分辨率和PDTDFB相同，由于是双树结构，变换具有相信息。与PDTDFB相比，具有结构上的简单性和实现的有效性。
3、提出了一种基于二值傅里叶谱的纹理预分类算法，将纹理库中的图像分为结构纹理和随机纹理。实验表明，对结构纹理，利用方向性分解来分析，可实质性地提高检索率。
4、基于滤波器组的图像分析方法(小波、Contourlets及基于DFBs的方法等)对图像的旋转和尺度的变换非常敏感，我们提出了一种基于PCNN的图像检索方法，图像特征具有旋转不变、尺度不变和抗噪声的特点。实验表明该方法是有效的。
This thesis is concerned primarily with the research of image analysis based on thedirectional multiresolution transforms and PCNN.
The research of directional multiresolution transforms has been one of the hottesttopics of signal processing.There are many methods that retrieve the directionalinformation with the multiresolution analysis.These methods are trying to provide thedirectional representation of high dimension signals and satisfy some properties such asperfect reconstruction,low redundancy and high computing performance.DTCWT,Contourlets,NSCT,PDTDFB are the widely used tools for directional multiresolutiontransforms,but they all suffer from problems for their own structures.
PCNN is an outstanding tool for image analysis,which is rotation-invariant,scale-invariant and shift-invariant.PCNN provides different approximate sequences atdifferent scales; therefore it is a multiresolution transform.PCNN checks the edgeinformation directly,which is different from wavelet and other multiscale methods,andsuch edge information can be used in features extraction,image segmentation,targetsrecognition,denoising,enhancement and other applications.
The main contents and contributions of the thesis are as follows:
Firstly,we present P-Contourlet transform which performs the Contourlettransform on the analytic signals of the original signals and is like the idea of complexwavelet on analytic signal.P-Contourlet is a kind of shift-invariant,high directionalselectivity transform with phase information.Based on the directional selectivity,weclassify P-Contourlet into two categories:P-Contourlet-Ⅰwhich has one channel andperforms Contourlet transform only once and P-Contourlet-Ⅱwhich has two channelsand performs Contourlet transform on each channel once.P-Contourlet has simpleimplementation structure and lower redundancy.The experiments on textureclassification show that P-Contourlet transform is an efficient tool for image analysis.
Secondly,we propose a dual tree Contourlet transform which is motivated by theDTCWT.We study the structure and implementation of PDTDFB and realize that it hassome problems both on filter design and whole system implementation,so we propose a structure named as DTCT which is easy to implementation.The high pass subbandsof Laplacian pyramid are filtered by two parallel trees which are both cascade DFBs toobtain high directional selectivity.Each tree is constructed to be an orthogonal systemand filters of the prime tree and the corresponding filters of dual tree satisfy certainphase constraint conditions,and the whole system is a tight frame.We analyze thespecial structure of DTCT and the properties of the filters and propose a solution fordesigning filters that the system required.DTCT is near shift-invariant and has thesame high directional selectivity as PDTDFB,and has phase information from the dualtree scheme.DTCT has a simple structure and effective implementation compared toPDTDFB.
Thirdly,we present an algorithm to pre-classify the texture images based onbinary Fourier spectrum.This algorithm classifies the whole texture images intostructure texture and random texture.The experiments show that the retrieval rate canbe substantially improved in analyzing of structure texture images by using directionalmultiresolution analysis.
Lastly,the image analysis methods based on filter banks (such as wavelet,Contourlet,DFBs,etc.) are sensitive to the changes caused by rotation,scale and shift,so we propose an image retrieval algorithm based on PCNN.The features extractedfrom the output of PCNN are invariant to rotation,scale and noise interfering.Theexperiments show the efficiency of our algorithm.
有关方向性多分辨率分析的研究一直是信号处理的重点内容。有许多在多分辨率分析框架下提取信号方向性信息的方法，这些方法都试图提供高维信号的方向性表达，附加地还必须满足理想重构，低冗余度，高计算效率等性质。DTCWT、Contourlets、NSCT、PDTDFB等变换是目前流行的方向性多分辨率分析方法，但它们都有各自结构性的缺陷。
神经网络PCNN是优异的图像分析工具，是一种具有旋转不变、尺度不变、平移不变等特点的图像变换方法。PCNN可以提供对原图像在不同尺度下的逼近序列，因而具有多分辨率分析的性质。与小波和多尺度分析不同，PCNN直接检测边缘信息，这些边缘信息可用于特征提取、图像分割、目标识别、除噪和增强等应用。
本论文的主要内容和贡献如下：
1、基于解析信号复小波变换的思想，提出了基于解析信号的P-Contourlet变换，通过在原始信号的解析信号上实施Contourlet变换，实现了一种平移不变的方向性多分辨率方法，变换具有相信息。根据方向性分辨率的不同，我们将该方法分为单通道方法P-Contourlet-Ⅰ和双通道方法P-Contourlet-Ⅱ。P-Contourlet实现结构简单，冗余度较低。纹理分类实验结果表明，P-Contourlet是一种非常有效的图像分析工具。
2、基于对偶树复小波的思想，提出对偶树Contourlet变换DTCT。我们研究PDTDFB的结构和实现方法，认知到它在滤波器设计和系统实现上存在一些问题，所以我们提出一种易于实现的结构DTCT。两个级联的DFBs树形结构对拉普拉斯金字塔的高通子带进行方向性分解，单独的每个树形结构构造为正交系统，实树和虚树对应的滤波器之间满足一定的相约束条件，整个变换为紧框架。我们分析了DTCT的系统结构和滤波器特性，并提出了系统所需要的滤波器设计方法。DTCT实现了近似的平移不变性，方向性分辨率和PDTDFB相同，由于是双树结构，变换具有相信息。与PDTDFB相比，具有结构上的简单性和实现的有效性。
3、提出了一种基于二值傅里叶谱的纹理预分类算法，将纹理库中的图像分为结构纹理和随机纹理。实验表明，对结构纹理，利用方向性分解来分析，可实质性地提高检索率。
4、基于滤波器组的图像分析方法(小波、Contourlets及基于DFBs的方法等)对图像的旋转和尺度的变换非常敏感，我们提出了一种基于PCNN的图像检索方法，图像特征具有旋转不变、尺度不变和抗噪声的特点。实验表明该方法是有效的。
This thesis is concerned primarily with the research of image analysis based on thedirectional multiresolution transforms and PCNN.
The research of directional multiresolution transforms has been one of the hottesttopics of signal processing.There are many methods that retrieve the directionalinformation with the multiresolution analysis.These methods are trying to provide thedirectional representation of high dimension signals and satisfy some properties such asperfect reconstruction,low redundancy and high computing performance.DTCWT,Contourlets,NSCT,PDTDFB are the widely used tools for directional multiresolutiontransforms,but they all suffer from problems for their own structures.
PCNN is an outstanding tool for image analysis,which is rotation-invariant,scale-invariant and shift-invariant.PCNN provides different approximate sequences atdifferent scales; therefore it is a multiresolution transform.PCNN checks the edgeinformation directly,which is different from wavelet and other multiscale methods,andsuch edge information can be used in features extraction,image segmentation,targetsrecognition,denoising,enhancement and other applications.
The main contents and contributions of the thesis are as follows:
Firstly,we present P-Contourlet transform which performs the Contourlettransform on the analytic signals of the original signals and is like the idea of complexwavelet on analytic signal.P-Contourlet is a kind of shift-invariant,high directionalselectivity transform with phase information.Based on the directional selectivity,weclassify P-Contourlet into two categories:P-Contourlet-Ⅰwhich has one channel andperforms Contourlet transform only once and P-Contourlet-Ⅱwhich has two channelsand performs Contourlet transform on each channel once.P-Contourlet has simpleimplementation structure and lower redundancy.The experiments on textureclassification show that P-Contourlet transform is an efficient tool for image analysis.
Secondly,we propose a dual tree Contourlet transform which is motivated by theDTCWT.We study the structure and implementation of PDTDFB and realize that it hassome problems both on filter design and whole system implementation,so we propose a structure named as DTCT which is easy to implementation.The high pass subbandsof Laplacian pyramid are filtered by two parallel trees which are both cascade DFBs toobtain high directional selectivity.Each tree is constructed to be an orthogonal systemand filters of the prime tree and the corresponding filters of dual tree satisfy certainphase constraint conditions,and the whole system is a tight frame.We analyze thespecial structure of DTCT and the properties of the filters and propose a solution fordesigning filters that the system required.DTCT is near shift-invariant and has thesame high directional selectivity as PDTDFB,and has phase information from the dualtree scheme.DTCT has a simple structure and effective implementation compared toPDTDFB.
Thirdly,we present an algorithm to pre-classify the texture images based onbinary Fourier spectrum.This algorithm classifies the whole texture images intostructure texture and random texture.The experiments show that the retrieval rate canbe substantially improved in analyzing of structure texture images by using directionalmultiresolution analysis.
Lastly,the image analysis methods based on filter banks (such as wavelet,Contourlet,DFBs,etc.) are sensitive to the changes caused by rotation,scale and shift,so we propose an image retrieval algorithm based on PCNN.The features extractedfrom the output of PCNN are invariant to rotation,scale and noise interfering.Theexperiments show the efficiency of our algorithm.
引文
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