【作者】 曲怀敬；

【导师】 彭玉华；

【作者基本信息】 山东大学 ， 信号与信息处理， 2009， 博士

【摘要】 在图像处理领域,图像的稀疏表示有着重要的理论和应用意义。通常,傅立叶变换和小波变换不能最稀疏地表示图像。为了解决此问题,多尺度几何分析(Multiscale Geometric Analysis,MGA)方法被提出,并迅速而广泛地被用于数学分析、图像处理、计算机视觉、模式识别和统计分析等不同的领域。然而,像Ridgelet变换和Curvelet变换等典型的在连续域定义的多尺度几何分析方法都存在着在离散域难以有效实现的问题。为此,一种“真正的”并具有金字塔方向滤波器组结构的图像最优表示方法——Contourlet变换被提出。Contourlet变换是在离散域用滤波器组来定义和实现的。它具有多尺度变换和多方向变换的功能。多尺度变换由拉普拉斯金字塔(LP)来实现,而方向滤波器组(DFB)完成多尺度细节子带的方向变换。Contourlet变换具有很多优良的特性,主要包括:多分辨率分析,局域性,准临界采样,多方向性和基函数的各向异性等。不同于小波变换,Contourlet变换的多方向性和基函数支撑区间具有随尺度长宽比变化的“长条形”结构,使得它能有效地捕捉图像信息中的几何结构特征。更为重要的是,Contouret变换将图像的多尺度和多方向表示灵活而有机地结合起来,因而能准确地、最优地刻画图像。目前,基于Contouret变换的理论和应用是研究的热点。最新研究成果表明,它在图像处理领域具有广阔的应用前景。Contourlet变换,包括改进的Contourlet变换能够最稀疏地刻画图像的特征。而优良的统计特征可以代表图像的内容。因此,在Contourlet变换域进行统计建模有着重要的意义。研究表明,自然图像多重子带的边缘分布能充分地反映其特征,而广义高斯分布(GGD)建模在变换域中被认为是对自然图像最逼近和最成功的边缘分布建模方式。同时,在多尺度变换域,简单的各子带独立同分布的广义高斯分布建模比子带相关的广义高斯分布建模更稳健和有效。因此,对Contourlet变换域各方向子带就可以进行广义高斯分布统计建模。目前,Contourlet变换域的广义高斯建模得到了广泛的应用,但是存在着模型参数估计不准确的问题。本文在这方面进行了深入的研究,提出了一种改进的最大似然参数估计算法。通过将这种新的参数估计方法和现有的相应方法进行性能的比较,证明了它的有效性。同时,利用这种参数估计方法,本文对Contourlet变换域方向子带系数进行了广义高斯分布建模。实验结果表明了这种建模的准确性。随着数字图书馆和多媒体数据库的迅猛发展,纹理图像的检索已成为基于内容的图像检索领域研究的热点。纹理图像检索系统的研究和发展始终是围绕着如何寻找良好的视觉特征以及定义稳健的相似性测度而展开的。由于纹理图像具有层次性和丰富的方向信息,特别适合于使用多尺度方向滤波器组分析。这样,Contourlet变换域的统计建模可以被用来作为提取纹理图像特征的一种有效工具。另一方面,定义与纹理特征相匹配以及能够反映人类视觉感知的相似性测度是一项重要而充满挑战的研究工作。通常,距离度量被用于测量相似性,而支持向量机(SVM)可以有效地反映人类的感知相似性测度。因此,本文将Contourlet变换域方向子带系数的广义高斯分布参数作为纹理图像的特征,以Kullback-Leibler(K-L)距离和SVM作为相似性测度用于纹理图像的检索。除了直接对纹理图像进行检索以外,也可以通过对纹理图像预分类来进行检索。为此,本文在改进的Contourlet变换域,基于结构性和随机性纹理图像,提出了一种混合的检索方案。实验结果表明,这些检索的性能得到了显著的提高。图像去噪的目标是在去除噪声的同时保持边缘和纹理等重要的图像结构信息。目前,研究的热点是将非线性扩散滤波和计算调和领域的多尺度滤波结合起来,分别用于加性噪声和斑点噪声的去除。这两类方法的有机结合可以从一个全新的角度来看待图像的去噪问题。考虑到非线性扩散滤波可以去除多尺度收缩去噪产生的Gibbs伪影,而多尺度、多方向收缩去噪具有快速性,本文提出了一种将Contourlet收缩和空域自适应全变差相结合的图像加性噪声的去除方法。它针对含噪图像与Contourlet收缩去噪图像的差值图像进行空域自适应全变差去噪,从中提取图像的细小边缘和纹理等细节信息。对于斑点噪声,本文提出了一种基于改进Contourlet变换和非线性扩散的斑点去除算法,并被用于处理血管内超声(IVUS)图像。仿真实验结果证明了这些方法的有效性。IVUS图像内、外膜边缘的提取在冠状动脉疾病的诊断和治疗上有着重要的意义。它是医学图像处理领域研究的热点。目前,所提出的IVUS图像边缘提取方法由于严重的斑点噪声影响以及加入了一些不适当的先验假设,边缘提取的效果并不理想。考虑到基于活动轮廓模型的边缘提取是最有前途的方法,本文首先提出了一种基于活动轮廓模型的IVUS仿体序列图像边缘提取的算法。它利用了图像的对比度特征量以及瑞利分布统计特性,通过动态规划和启发式图搜索的方法分别在不同的能量函数下来自动提取内、外膜边缘。而对于含有斑点噪声的实际IVUS图像,本文提出了一种基于Contourlet斑点去噪的IVUS序列图像边缘自动提取的算法。它采用了活动轮廓模型和IVUS图像边缘梯度特征量,通过动态规划最优搜索的方法分别在不同的能量函数下来自动提取冠状动脉血管内、外膜边缘。实验结果反映了这些边缘提取方法的准确性和鲁棒性。目前,Contourlet变换的研究在国内刚刚起步,很多在图像处理领域中的应用需要深入的研究和探讨。本论文主要研究了Contourlet变换在图像统计建模,纹理图像检索,图像去噪和医学图像边缘提取中的应用。本文的主要贡献和创新点包括以下几个方面:(1)针对仿真实现的原始Contourlet变换和改进Contourlet变换,对其方向子带系数进行了准确的广义高斯分布统计建模。对于模型参数的估计,提出了一种改进的迭代算法,并利用了一种新的参数初始值。仿真结果表明,这种参数估计新方法的性能优于目前典型的估计方法。(2)基于纹理图像的Contourlet方向子带系数的能量和广义高斯分布参数特征,提出了一种新的两阶段SVM运行的检索方法。实验结果表明,检索的性能得到显著的改善。(3)基于结构性和随机性纹理图像的有效区分,提出了一种新的混合检索方法。这种检索方法的性能优于目前其他相关方法的最新结果。(4)提出了一种新的基于改进Contourlet变换的硬阈值收缩和空域自适应的非线性扩散相结合的图像去噪方法。它既保持了较强的边缘和有效地去除了加性噪声,又基本不丢失细小的边缘和纹理信息。同时,还有效地减少了去噪后图像中的Gibbs伪影。(5)提出了一种新的基于改进Contourlet变换和非线性扩散的斑点去除算法。这种方法可直接进行IVUS图像斑点噪声的去除,而不需要预先进行同态处理。(6)根据IVUS仿体图像的统计特征,提出了一种对序列图像内、外膜边缘提取的方法。它基于活动轮廓模型、IVUS图像的对比度特征和瑞利统计分布特性,通过采用动态规划和启发式图搜索的方法,对图像边缘进行了最优化的提取。(7)根据实际IVUS图像的几何结构分布特点,提出了一种对序列图像边缘自动提取的算法。它基于经Contourlet变换和各向异性扩散斑点去除后的图像,采用了活动轮廓模型和图像边缘梯度特征量,通过动态规划最优搜索的方法分别在不同的能量函数下来自动提取血管内、外膜边缘。相应地,基于序列图像的时、空域相关信息和形态结构的先验知识以及血液与组织的不同物理特征,提出了一种新的自动确定IVUS图像内膜边缘初始轮廓的方法。实验结果表明,这种边缘自动提取算法简单,准确性较高,对序列图像处理的可重复性和鲁棒性较好。更多还原

【Abstract】 In the image processing domain, sparse representation of images has important significance in both theory and the applications. Usually, the Fourier transform and the wavelet transform can not most sparsely represent an image. In order to resolve this problem, the multi-scale geometric analysis (MGA) methods are proposed. They are rapidly and widely used in the different fields, such as mathematical analysis, image processing, computer vision, pattern recognition and statistical analysis etc. However, the MGA methods, like the ridgelet transform and the curvelet transform which are defined in the continuous domain, have difficulties in discrete implementation. Therefore, a "ture" and optimal image representation method which has pyramid directional filter bank structure is proposed, called contourlet transform.The contourlet transform is defined and implemented by the filter banks in the discrete domain. It has the function of the multi-scale transform and the multi-directional transform. The multi-scale transform is achieved by Laplacian pyramid (LP), and the directional transform of the multi-scale detail subbands is implemented by the directional filter bank (DFB). The contourlet transform has a lot of good properties, which include multi-resolution analysis, localization, nearly critical sampling, multi-directionality and anisotropy of the basis functions. Different from the wavelet transform, the multi-directionality and the property that the support of basis functions has a variety of elongated shaped with different aspect ratios make it effectively capture the geometric structure features of the image information. More importantly, the contourlet transform can flexibly and effectively combine the multi-scale with the multi-directionality for image representation, therefore it can accurately and optimally describe an image. Currently, the theory and applications based on the contourlet transform are the research focus. The recent studies show that it has wide application prospects in the image processing domain.The contourlet transform, including the improved contourlet transform, can most sparsely characterize the features of an image. The good statistical features can represent the contents of an image. Therefore, the statistical modeling has important significance in the contourlet transform domain. The research shows that the margin distribution of the multi-subbands of natural images can sufficiently represent their features, and the modeling of generalized Gaussian distribution (GGD) is considered as the most approximate and successful modeling form of the margin distribution for natural images in the transform domain. At the same time, the simple independent and identically distributed GGD models can be more robust and efficient than subband-dependent GGD models. Consequently, the directional subbands of the contourlet transform can be modeled statistically as the GGD. At present, the GGD modeling in the contourlet transform domain finds wide applications. However, it has the problem that the model parameters can not be accurately estimated. In this thesis, we do further research on this problem, and propose an algorithm about the improved maximum likelihood parameter estimation. Performance comparisons between the new method and the other corresponding one verify its efficiency. At the same time, using this parameter estimation method, we have modeled the directional subband coefficients in the contourlet transform domain as GGD. The experimental results show the accuracy of this modeling method.With the explosive growth in the volume of digital library and multi-media databases, the texture image retrieval has become the research hotspot in content-based image retrieval domain. The research and development of the texture image retrieval revolve around finding good visual features or defining robust similarity measurements. Because of having the hierarchy and rich directional information, the texture image can be analyzed especially well by using multiscale directional filter bank. Thus, the statistical modeling in the contourlet transform domain can be used as an efficient tool of detecting the features of the texture image. On the other hand, defining the similarity measurements which can match the texture features and reflect human perception is an important and challenging task. Usually, the similarity measurements adopt the distance metrics, but the support vector machine (SVM) can effectively reflect the similarity measurements of the human perception. Therefore, in this thesis the GGD parameters of the directional subband coefficients in the contourlet transform domain are used as the features of texture images, and the Kullback-Leibler (K-L) distance and SVM are adopted as the similarity measurements for the texture image retrieval. Except retrieving the texture image directly, the pre-classification of texture images can also be used to retrieve. Therefore, in this thesis, a mixture retrieval scheme based on the structural and random texture image is also proposed in the improved contourlet transform domain. The experimental results show that the retrieval performance has been remarkably improved.The goal of image denoising is to reduce noise sufficiently with image structures, such as edges and textures well preserved. Currently, the research focus lies in combining non-linear diffusion filtering with the multiscale filtering in the computation harmony domain, which is used for reducing the additive noise and speckle noise. The effective combination of thses two methods can interpret the image denoising problems in bran-new angle of view. Considering that the non-linear diffusion filtering can reduce the Gibbs artifacts which are produced by the multiscale shrinkage denoising, and the multiscale and multi-directional shrinkage denoising methods are fast, an additive noise reduction method which combines the contourlet shrinkage with the spatially adaptive total variation is proposed in this thesis. The difference image of the noisy image and the denoised image by the contourlet shrinkage is filtered using the spatially adaptive total variation method, and the detail information of small edges and textures is detected. For the speckle noise, a speckle denoising algorithm based on the improved contourlet transform and non-linear diffusion is proposed in this thesis, and it is used for processing the intravascular ultrasound (IVUS) image. The results of the simulation experiments show their effectiveness.The intima and adventitia edge detection of IVUS images has great significance in the diagnosis and treatment of the coronary artery disease. It is the research hotspot in medical image processing domain. Currently, the effectiveness based on the methods of the IVUS image edge detection is not ideal because of the severe speckle noise and some unadvisable priori hypotheses. Consider that the edge detection method based on active contour model is the most promising techniques. In this thesis, an edge detection algorithm of the simulated IVUS sequential images based on active contour model is firstly proposed. It uses the contrast and Raylaigh distribution characteristics of the IVUS image, and automatically detects the intima and adventitia edge under different energy functions through the dynamic programming and heuristic graph searching. For the real IVUS image containing speckle noise, an automatic edge detection algorithm of IVUS sequential images is proposed based on the contourlet speckle denoising in this thesis. It uses the active contour model and the edge gradient of IVUS image, and automatically detects the intima and adventitia of coronary artery vessel under the different energy functions through the dynamic programming. The experimental results show that these edge detection methods are accurate and robust.Currently, the studies on the contourlet transform have just started in domestic, therefore many applications need to be further researched and explored in image processing fields. In this thesis, the applications of the contourlet transform in statistical image modeling, texture image retrieval, image denoising and the edge detections of medical images are mainly studied. The main contributions and innovations of this thesis are as follows:(1) For the original contourlet transform and the improved contourlet transform which are achieved by simulation, their directional subband coefficients are accurately modeled using generalized Gaussian statistical distribution. For the parameter estimation of the model, an improved iterative algorithm is proposed, and a new initial value of the parameter is used. The simulated results show that the performance of the new parameter estimation method is superior to the currently typical estimation method.(2) Based on the energy and GGD parameter features of the contourlet directional subband coefficients of the texture image, a new retrieval method of two-run SVM is proposed. The experimental results show that the performance of the retrieval is greatly improved.(3) Based on the effective discrimination of the structural and random texture images, a new mixture retrieval method is proposed. The performance of this retrieval method is superior to the recent results of the other methods.(4) A new image denoising method based on combining the hard threshold shrinkage of the improved contourlet transform with the spatially adaptive non-linear diffusion is proposed. It can reduce the additive noise effectively with stronger edges well prserved, and will nearly not lose the weak edges and texture information. At the same time, the Gibbs artifacts are effectively reduced in the denoised image.(5) A new speckle reduction algorithm is proposed based on the improved contourlet transform and non-linear diffusion. It can directly reduce the speckle noise of IVUS image, and do not need the homomorphic pre-processing.(6) A detection method of the inima and adventitia edges of sequential IVUS simulated images is proposed by means of their statistical features. It is based on active contour model, contrast and Raylaigh distribution characteristics of the IVUS image, and optimally detects the image edge by using dynamic programming and heuristic graph searching method.(7) An automatic edge detection algorithm of sequential images is proposed according to the geometric structures of the real IVUS images. It works on the images in which speckle noise is reduced by the contourlet transform and the anisotropic diffusion, uses active contour model and the edge gradient of the image, and automatically detects the intima and adventitia edges of the vessel by using the optimal searching method of dynamic programming under the different energy functions respectively. Accordingly, a new method which can automatically estimate the initial contour of the intima edge of IVUS image is proposed based on different physical properties of the blood and tissue, a priori information of the vessel geometry, and the temporal and spatial information of sequential images. The experimental results show that this method is algorithmically simple, statistically accurate, reproducible and robust for sequential IVUS images.更多还原