基于多尺度几何分析的图像处理技术研究
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摘要
多尺度几何分析理论(Multiscale Geometric Analysis, MGA)是近年来在计算调和分析基础上发展起来的一系列分析方法的总称,其目的是通过对图像等高维数据内在的几何结构如轮廓、边缘和纹理等进行高效逼近和描述,从而更有效地检测、表示和处理高维空间数据,从根本上克服了二维小波不能有效捕获信号高维奇异性的缺陷,在图像信号处理领域具有广阔的应用前景。研究多尺度几何分析理论及核心技术并结合图像处理应用给出性能更好的处理算法,具有重要的理论意义和实用价值。本文主要以多尺度几何分析工具Contourlet变换为主线,针对其在若干图像处理应用中的关键技术进行了深入系统的研究。主要研究工作及贡献包括如下内容:
1.研究并给出了多尺度几何分析能够高效表示和处理图像信息的根本原因。从自然图像的统计规律和人类视觉系统的信息整合机理两方面进行深入分析,探讨了小波分析的自身局限性;而多尺度几何分析所拥有的方向性、多尺度、局部化、各向异性等优良特性使之能够高效捕捉自然图像的高维奇异性,其稀疏表达方式也更加符合人类视觉系统视皮层细胞感受野的处理机制。
2.系统研究了多尺度几何分析理论的典型工具,包括Beamlet、Brushlet、Bandelet、Ridgelet和Curvelet等,并重点探讨了Contourlet变换和非采样Contourlet变换的基本原理、实现方案、优良特性以及所存在的不足之处,为该领域的应用研究奠定了理论基础。Contourlet继承了多尺度几何分析的优良特性,基函数固定且兼具快速便捷的实现方式和数字处理的友好性,能获得更为优异的图像处理性能。
3.提出了一种基于Contourlet变换的SAR图像相干斑抑制算法。该算法分析了相干斑的产生机理和统计特性,在此基础上将SAR图像经对数同态变换和Contourlet变换进行处理,设计了尺度自适应阈值在Contourlet变换域进行阈值萎缩;深入研究了平移可变特性的信号处理模型,设计二维循环平移变换去除可能出现的人工效应。仿真结果表明该算法在有效抑制相干斑的同时较好地保持了SAR图像中的边缘结构,其主客观效果均优于传统的空域滤波算法和小波去噪算法。
4.根据Contourlet系数尺度间内在的树型结构,提出了Contourlet区域方向对比度的概念,并设计了一种基于Contourlet区域特性的图像融合算法。该算法借助于Contourlet的优良特性,在Contourlet变换域综合使用加权平均和选择两种方式实现频域系数的有效融合。为保证融合图像与视觉系统感知相一致,构造并使用了基于区域的融合规则:低频采用加权局部能量,高频采用Contourlet区域方向对比度。通过遥感图像和医学图像的实验结果证明了该算法的有效性。
5.提出了一种基于非采样Contourlet变换域样本学习的图像超分辨重构框架。针对拥有一幅或多幅低分辨图像以及相同或类似场景的高分辨图像的超分辨重构问题,通过对其降质模型施加约束条件,构造了实用化的图像降质模型;在此基础上算法使用高分辨图像作为参考,利用非采样Contourlet变换所具有的多尺度及平移不变特性构造训练集合,在Contourlet域通过运动估计技术实现最优高频信息的自适应学习与有效整合,重构高分辨率图像。实验结果显示较传统的超分辨重构算法,该算法在图像细部信息的恢复方面有显著提高。
6.针对图像超分辨重构和视频编码等应用中的关键技术——运动估计进行深入研究,构造了具有方向特性的线性-菱形搜索策略(LDS)和六边形-菱形搜索策略(HDS),在此基础上提出了一种运动矢量场和方向双重自适应搜索算法(MDAS)。算法针对运动矢量场的中心偏置性和时空相关性进行预判,对静止块直接中止搜索,根据运动类型自适应选择搜索起始点和搜索策略。实验结果表明,该算法的搜索速度优于传统快速运动估计算法,且搜索精度非常接近于全搜索法。
Based on computational harmonic analysis, a novel Multiscale Geometric Analysis (MGA) theory was proposed to capture the geometrical structure in visual information efficiently, it can achieve optimal approximation behavior for 2-D piecewise smooth function, thus obtaining highly efficient representation and processing methods. Wavelet is an optimal tool only for 1-D piecewise smooth signals, As a result of a separable extension from 1-D bases, wavelet in 2-D is far from optimal. The disappointing behaviors of wavelets have led to a series of MGA tools. MGA theory and its applications still need further research and development. In this dissertation, the author mainly focuses on the research of Contourlet transform and the key techniques of its applications in image processing. As the latest MGA tool, Contourlet is a“true”two dimensional sparse representation, it provides much better anisotropy, multiresolution, directionality and localization properties for 2-D signals than existing image representation methods. Therefore, Contourlet is more appropriate for various image processing tasks and better performance would be expected. The main research work in the dissertation is as follows:
1. Detailed analysis is provided for the advantages of MGA from the view of statistics of natural image and the functionality of human vision system. Based on detailed comparison, the intrinsic reasons are given. The advantages of multiscale geometric analysis make it able to capture high dimensional singularities in natural image efficiently, and also consistent with the perception and integration principle of receptive field of visual cortex in human vision system.
2. A systematical research of the development and common analysis tools are given firstly, including Ridgelet, Curvelet, Beamlet, Bandelet, etc. For Contourlet transform and its novel extension—Nonsubsampled Contourlet Transform, we provide a detailed analysis to its basic principles, implementation schemes, advantages and disadvantages, which can be seen as the foundation of following image processing applications.
3. Based on the speckle noise modeling for SAR image, a new speckle reduction algorithm using Contourlet transform is proposed. Logarithmic transform is first performed to convert the original multiplicative speckle noise into additive noise. For noise can be effectively separated from real image signal in Contourlet transform domain, a Contourlet based hard thresholding algorithm is then applied. Monte-Carlo method is adopted to estimate the statistics of Contourlet coefficients for speckle noise, thus determining the optimal threshold set. The cycle-spinning technique is utilized to suppress the Gibbs effect. Experimental results show that the proposed Contourlet based algorithm outperforms conventional algorithms in terms of both speckle reduction and edge preservation.
4. A novel image fusion algorithm based on local statistics in Contourlet domain is proposed. All fusion operations are performed in Contourlet domain. Based on the tree structure among parent and children coefficients in Contourlet domain, the Contourlet contrast measurement is developed. It is proved to be more suitable for human vision system. Other fusion rules like local energy, weighted average and selection are combined with“region”idea for coefficient selection in the low- and high-pass subbands. The final fusion image is obtained by directly applying inverse Contourlet transform to the fused subbands. Extensive fusion experiments have been made on remote sensing images and medical multimodality images, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.
5. An example based super-resolution algorithm for digital image using nonsubsampled Contourlet transform (NSCT) is proposed. The input is one or more low resolution images together with a high resolution still image of similar content. For the good properties of shift-invariance, the nonsubsampled Contourlet is utilized to create the training set of transform coefficient patches from the high resolution still image. Low resolution images are first interpolated to the same spatial resolution as the reference still image. Block based motion estimation is then applied inside the complete training set to find the best matching between interpolated frame and reference still image. According to the correspondence between low frequency and high frequency pairs, the missing high frequency information of the input image can be easily learned from the training set. Finally, an inverse Contourlet transform is applied to recover the super-resolved image. Preliminary experimental results show that the proposed super-resolution algorithm outperforms conventional algorithm both in visual quality and the PSNR value.
6. Motion estimation (ME) is one of the key techniques in exampled based super resolution and video coding. A novel fast motion estimation algorithm, or the Motion vector field and Direction Adaptive Search technique (MDAS) is proposed. In MDAS, the type of local motion activity and initial search center is first determined according to the motion vector field, different search algorithms are adaptively used according to the motion activity of current block. Two novel search algorithms: Line-Diamond Search (LDS) and Hexagon -Diamond Search (HDS) are proposed, which all have strong directional property, and can obtain faster searching speed. Stop criteria is also set to detect the stationary block, thus terminating current search. Experimental results show that the proposed algorithm provides faster searching speed than other existing fast block-matching algorithm, while the distortion is almost the same as the FS algorithm.
1.研究并给出了多尺度几何分析能够高效表示和处理图像信息的根本原因。从自然图像的统计规律和人类视觉系统的信息整合机理两方面进行深入分析,探讨了小波分析的自身局限性;而多尺度几何分析所拥有的方向性、多尺度、局部化、各向异性等优良特性使之能够高效捕捉自然图像的高维奇异性,其稀疏表达方式也更加符合人类视觉系统视皮层细胞感受野的处理机制。
2.系统研究了多尺度几何分析理论的典型工具,包括Beamlet、Brushlet、Bandelet、Ridgelet和Curvelet等,并重点探讨了Contourlet变换和非采样Contourlet变换的基本原理、实现方案、优良特性以及所存在的不足之处,为该领域的应用研究奠定了理论基础。Contourlet继承了多尺度几何分析的优良特性,基函数固定且兼具快速便捷的实现方式和数字处理的友好性,能获得更为优异的图像处理性能。
3.提出了一种基于Contourlet变换的SAR图像相干斑抑制算法。该算法分析了相干斑的产生机理和统计特性,在此基础上将SAR图像经对数同态变换和Contourlet变换进行处理,设计了尺度自适应阈值在Contourlet变换域进行阈值萎缩;深入研究了平移可变特性的信号处理模型,设计二维循环平移变换去除可能出现的人工效应。仿真结果表明该算法在有效抑制相干斑的同时较好地保持了SAR图像中的边缘结构,其主客观效果均优于传统的空域滤波算法和小波去噪算法。
4.根据Contourlet系数尺度间内在的树型结构,提出了Contourlet区域方向对比度的概念,并设计了一种基于Contourlet区域特性的图像融合算法。该算法借助于Contourlet的优良特性,在Contourlet变换域综合使用加权平均和选择两种方式实现频域系数的有效融合。为保证融合图像与视觉系统感知相一致,构造并使用了基于区域的融合规则:低频采用加权局部能量,高频采用Contourlet区域方向对比度。通过遥感图像和医学图像的实验结果证明了该算法的有效性。
5.提出了一种基于非采样Contourlet变换域样本学习的图像超分辨重构框架。针对拥有一幅或多幅低分辨图像以及相同或类似场景的高分辨图像的超分辨重构问题,通过对其降质模型施加约束条件,构造了实用化的图像降质模型;在此基础上算法使用高分辨图像作为参考,利用非采样Contourlet变换所具有的多尺度及平移不变特性构造训练集合,在Contourlet域通过运动估计技术实现最优高频信息的自适应学习与有效整合,重构高分辨率图像。实验结果显示较传统的超分辨重构算法,该算法在图像细部信息的恢复方面有显著提高。
6.针对图像超分辨重构和视频编码等应用中的关键技术——运动估计进行深入研究,构造了具有方向特性的线性-菱形搜索策略(LDS)和六边形-菱形搜索策略(HDS),在此基础上提出了一种运动矢量场和方向双重自适应搜索算法(MDAS)。算法针对运动矢量场的中心偏置性和时空相关性进行预判,对静止块直接中止搜索,根据运动类型自适应选择搜索起始点和搜索策略。实验结果表明,该算法的搜索速度优于传统快速运动估计算法,且搜索精度非常接近于全搜索法。
Based on computational harmonic analysis, a novel Multiscale Geometric Analysis (MGA) theory was proposed to capture the geometrical structure in visual information efficiently, it can achieve optimal approximation behavior for 2-D piecewise smooth function, thus obtaining highly efficient representation and processing methods. Wavelet is an optimal tool only for 1-D piecewise smooth signals, As a result of a separable extension from 1-D bases, wavelet in 2-D is far from optimal. The disappointing behaviors of wavelets have led to a series of MGA tools. MGA theory and its applications still need further research and development. In this dissertation, the author mainly focuses on the research of Contourlet transform and the key techniques of its applications in image processing. As the latest MGA tool, Contourlet is a“true”two dimensional sparse representation, it provides much better anisotropy, multiresolution, directionality and localization properties for 2-D signals than existing image representation methods. Therefore, Contourlet is more appropriate for various image processing tasks and better performance would be expected. The main research work in the dissertation is as follows:
1. Detailed analysis is provided for the advantages of MGA from the view of statistics of natural image and the functionality of human vision system. Based on detailed comparison, the intrinsic reasons are given. The advantages of multiscale geometric analysis make it able to capture high dimensional singularities in natural image efficiently, and also consistent with the perception and integration principle of receptive field of visual cortex in human vision system.
2. A systematical research of the development and common analysis tools are given firstly, including Ridgelet, Curvelet, Beamlet, Bandelet, etc. For Contourlet transform and its novel extension—Nonsubsampled Contourlet Transform, we provide a detailed analysis to its basic principles, implementation schemes, advantages and disadvantages, which can be seen as the foundation of following image processing applications.
3. Based on the speckle noise modeling for SAR image, a new speckle reduction algorithm using Contourlet transform is proposed. Logarithmic transform is first performed to convert the original multiplicative speckle noise into additive noise. For noise can be effectively separated from real image signal in Contourlet transform domain, a Contourlet based hard thresholding algorithm is then applied. Monte-Carlo method is adopted to estimate the statistics of Contourlet coefficients for speckle noise, thus determining the optimal threshold set. The cycle-spinning technique is utilized to suppress the Gibbs effect. Experimental results show that the proposed Contourlet based algorithm outperforms conventional algorithms in terms of both speckle reduction and edge preservation.
4. A novel image fusion algorithm based on local statistics in Contourlet domain is proposed. All fusion operations are performed in Contourlet domain. Based on the tree structure among parent and children coefficients in Contourlet domain, the Contourlet contrast measurement is developed. It is proved to be more suitable for human vision system. Other fusion rules like local energy, weighted average and selection are combined with“region”idea for coefficient selection in the low- and high-pass subbands. The final fusion image is obtained by directly applying inverse Contourlet transform to the fused subbands. Extensive fusion experiments have been made on remote sensing images and medical multimodality images, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.
5. An example based super-resolution algorithm for digital image using nonsubsampled Contourlet transform (NSCT) is proposed. The input is one or more low resolution images together with a high resolution still image of similar content. For the good properties of shift-invariance, the nonsubsampled Contourlet is utilized to create the training set of transform coefficient patches from the high resolution still image. Low resolution images are first interpolated to the same spatial resolution as the reference still image. Block based motion estimation is then applied inside the complete training set to find the best matching between interpolated frame and reference still image. According to the correspondence between low frequency and high frequency pairs, the missing high frequency information of the input image can be easily learned from the training set. Finally, an inverse Contourlet transform is applied to recover the super-resolved image. Preliminary experimental results show that the proposed super-resolution algorithm outperforms conventional algorithm both in visual quality and the PSNR value.
6. Motion estimation (ME) is one of the key techniques in exampled based super resolution and video coding. A novel fast motion estimation algorithm, or the Motion vector field and Direction Adaptive Search technique (MDAS) is proposed. In MDAS, the type of local motion activity and initial search center is first determined according to the motion vector field, different search algorithms are adaptively used according to the motion activity of current block. Two novel search algorithms: Line-Diamond Search (LDS) and Hexagon -Diamond Search (HDS) are proposed, which all have strong directional property, and can obtain faster searching speed. Stop criteria is also set to detect the stationary block, thus terminating current search. Experimental results show that the proposed algorithm provides faster searching speed than other existing fast block-matching algorithm, while the distortion is almost the same as the FS algorithm.
引文
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