基于Contourlet变换的图像处理关键技术研究
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摘要
多尺度几何分析理论(Multiscale Geometric Analysis, MGA)是近年来在计算理论与调和分析的基础上所发展起来的面向高维信号处理的重要理论,其主要分析工具包括Brushlet、Wedgelet、Beamlet、Ridgelet、Curvelet、Bandelet以及Contourlet和非下采样Contourlet (Nonsubsampled Contourlet Transform,NSCT)等。MGA理论的目的在于通过对图像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变换不能有效提取图像结构中的直线和曲线等高维奇异性且只能获得有限方向性信息的缺陷,具有广阔的应用前景。研究多尺度几何分析理论并结合具体的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际应用价值,已成为当前国内外图像信号处理领域的研究热点。
Contourlet是新兴的MGA工具,除具备良好的多尺度、局部化、各向异性以及多方向特性,还兼具便捷的实现方式和数字处理的友好性；此外非下采样Contourlet在Contourlet的基础上进一步扩展,提供良好的平移不变特性,代表了高维信号处理方法的发展趋势。本文以这两类多尺度几何分析工具为主线,对其理论及在若干图像处理应用中的关键技术进行深入研究。论文主要工作及贡献如下：
1.深入探讨了多尺度几何分析能够获得更优异图像处理性能的深层次原因；研究了Contourlet和非下采样Contourlet的基本原理、实现方案、滤波器组设计等,详细分析了其所拥有的方向性、多尺度、局部化、各向异性,以及数字处理的友好性和稀疏表达方式等优良特性；证明了Contourlet(?)口非下采样Contourlet能够高效捕捉自然图像的高维奇异性,更加适合于各类图像等高维信号表达和处理任务,如图像融合、图像去噪、数字水印、边缘检测等等。
2.针对不同医学影像设备获得的多源图像信息有效融合和综合利用的问题,提出了一种基于Contourlet区域特性的医学图像融合算法(CRSIF算法)。该算法借助于Contourlet变换的优良特性,在Contourlet变换域综合使用加权平均和选择方式实现频域系数的有效融合。为保证融合图像与人类视觉系统(HVS)的感知特性相吻合,使用了基于区域的融合规则：低频子带采用加权局部能量,高频子带基于尺度间内在的树型结构使设计并使用了Contourlet区域方向对比度。通过对CT/MR医学图像的仿真实验证明了该算法的有效性。
3.针对成像系统中焦平面外的目标呈现模糊形态不能真实反映外界场景信息的问题,提出了一种基于光学成像机理的Contourlet域多聚焦图像融合算法(OIPIF算法)。在详细探讨离焦成像系统的低通函数特性的基础上,针对低频/高频系数特点设计两类区域性聚焦度量准则,并制定了相应的模值取大系数选择方案,结合Contourlet变换的独特优势在变换域的不同子带独立实施系数融合。该算法能够得到与标准清晰图像更为接近的融合图像,在综合性能方面有显著提升。
4.将NSCT引入抗几何攻击数字水印技术中,提出了一种基于SIFT特征的NSCT域抗几何攻击水印算法(SND算法)。该算法通过提取宿主图像在空间域的尺度不变特征变换(SIFT)特征,在有效特征点周围的圆形区域实施多尺度NSCT,借助于NSCT的时频不变性和冗余性,在变换域的低频系数中完成水印信息嵌入。为进一步提高算法抗几何攻击的性能,该算法中同时提出了一种基于等面积圆环区域的水印嵌入方案。实验结果表明该算法具有良好的抗几何攻击特性和优秀的不可见性。
5.针对激光水下成像过程中存在不同程度的散斑噪声使图像的质量变差问题,提出了一种基于NSCT变换的激光水下图像散斑抑制算法(CTSNS算法)。系统研究了激光成像中的散斑产生机理与统计特性,在此基础上将原始图像经对数同态变换和NSCT变换进行处理,通过施加约束条件,依据NSCT高频子带的系数分布模型等先验信息,设计了尺度相关的Bayes闽值对高频子带系数实施阈值萎缩,最后通过逆变换和指数运算重构图像。该算法在有效抑制散斑的同时较好地保持了激光图像中目标的边缘结构,较好地改善了图像的主客观效果。
6.针对传统边缘检测算法在定位精度、轮廓平滑性和噪声抑制等方面存在的不足,首次将NSCT技术应用到图像边缘检测中,提出了一种基于NSCT的多尺度边缘检测算法(NIED算法)。该算法将原始图像分解至NSCT变换域,针对低频子带与多个尺度上的高频子带的特性分别提取边缘信息：低频子带使类似于Canny算子的空间域检测算法,高频子带则采用NSCT域的模极大值检测策略,通过归一化融合规则融合多尺度中不同方向的边缘信息,基于高频子带和低频子带信息的联合检测和边缘闭合输出最终的边缘检测结果。该算法能够达到更优的边缘检测性能。
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 for2-D piecewise smooth function, thus obtaining highly efficient representation and processing methods. MGA tools includes Brushlet, Wedgelet, Beamlet, Ridgelet, Curvelet, Bandelet, Contourlet and Nonsubsampled Contourlet Transform (NSCT), etc. 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 and nonsubsampled contourlet are the "true" two dimensional sparse representations, nonsubsampled contourlet also has the "Shift Inviance" property, which provide much better anisotropy, multiresolution, directionality and localization properties for2-D signals than existing image representation methods. The main research work in the dissertation is as follows:
1. 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. The varieties of 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. Therefore, they are more appropriate for various image processing tasks. It can be seen that by using contourlet or nonsubsmapled contourlet with proper scheme, better performance would be expected.
2. A novel medical 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-pass 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 CT and MR medical images, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.
3. A novel multifocus image fusion algorithm based on region statistics in contourlet domain was developed. According to the optical imaging principle, the defocused imaging system can be characterized as a lowpass filtering. For contourlet can handle intrinsic features in natural image much more effectively than wavelet. Original images was first decomposed by contourlet transform, fusion operation was implemented for all directional subbands in each scale, different region based fusion rules were used for lowpass and highpass subband, they are local energy and regional variance. Experimental results show that compared with traditional algorithms, the proposed multifocus image fusion algorithm can obtain a more satisfactory outcome.
4. A geometrically robust image watermarking algorithm based on nonsubsmpaled contourlet transform (NSCT) and scale invariant feature transform (SIFT) is proposed in this paper. The SIFT features points are first computed from the host image, in which the suitable SIFT points for watermark embedding are selected and tested according to their magnitude changes after being modified. NSCT was adopted by virtual of its advantages over traditional wavelet transform and other multiresolution geometric analysis tools. NSCT decomposition is implemented on the SIFT feature circle region. The lowpass coefficients within the circle region are modified to embed the watermarking bits. To enhance watermarking detection performance, we proposed an equal area based circle pattern and improved odd-even quantization algorithm. Experimental results demonstrate that the proposed scheme is robust against the geometric attacks like rotation, scaling, cropping and moving, as well as the general processing operations.
5. Based on the speckle noise modeling for underwater laser image, an adaptive speckle reduction algorithm using nonsubsampled contourlet transform (NSCT) is proposed. The statistical model for speckle noise is first analyzed to obtain a simple and tractable solution in a closed analytical form. Gaussian distribution for speckle noise and a general Gaussian distribution are adopted to model the statistics of contourlet coefficients in logarithmically transformed laser images. Then based on the maximizing the a posteriori estimation with the assumption that speckle noise is spatially correlated within a small window, we utilize a locally adaptive Bayesian processor whose parameters are obtained from the neighboring coefficients in highpass subbands. Experimental results show that comparing with classical wavelet method, the proposed algorithm shows a superior performance in suppressing the speckle noise and retaining geometrical structures of the image.
6. Available image edge detection schemes based on the spacial domain or wavelet transform domain cancapture only limited directional edges in images. A novel multiscale edge detection algorithm based on nonsubsampled contourlet transform (NSCT) was proposed in chapter7. The input image is first decomposed into NSCT domain, different edge detection techniques are applied in lowpass subband and highpass subbands:a spatial domain algorithm like Canny operator is used in lowpass subband, every coefficient in t he subbands is thresholded by comparing against the adaptive thresholds. Based on the directions of each directional subband and its gradient, modulus maxima of the transform coefficients are obtained by comparing the modulus amplitudes of the samples and the neighborhood coefficients on the direction of the gradient. The scheme requires lower complexity without complicated link operation, while edge detecting performance is improved. The results show the proposed algorithm is superior to the image edge detection method based on wavelet modulus maxima by approximating better the edges of images and has lower computational complexity.
Contourlet是新兴的MGA工具,除具备良好的多尺度、局部化、各向异性以及多方向特性,还兼具便捷的实现方式和数字处理的友好性；此外非下采样Contourlet在Contourlet的基础上进一步扩展,提供良好的平移不变特性,代表了高维信号处理方法的发展趋势。本文以这两类多尺度几何分析工具为主线,对其理论及在若干图像处理应用中的关键技术进行深入研究。论文主要工作及贡献如下：
1.深入探讨了多尺度几何分析能够获得更优异图像处理性能的深层次原因；研究了Contourlet和非下采样Contourlet的基本原理、实现方案、滤波器组设计等,详细分析了其所拥有的方向性、多尺度、局部化、各向异性,以及数字处理的友好性和稀疏表达方式等优良特性；证明了Contourlet(?)口非下采样Contourlet能够高效捕捉自然图像的高维奇异性,更加适合于各类图像等高维信号表达和处理任务,如图像融合、图像去噪、数字水印、边缘检测等等。
2.针对不同医学影像设备获得的多源图像信息有效融合和综合利用的问题,提出了一种基于Contourlet区域特性的医学图像融合算法(CRSIF算法)。该算法借助于Contourlet变换的优良特性,在Contourlet变换域综合使用加权平均和选择方式实现频域系数的有效融合。为保证融合图像与人类视觉系统(HVS)的感知特性相吻合,使用了基于区域的融合规则：低频子带采用加权局部能量,高频子带基于尺度间内在的树型结构使设计并使用了Contourlet区域方向对比度。通过对CT/MR医学图像的仿真实验证明了该算法的有效性。
3.针对成像系统中焦平面外的目标呈现模糊形态不能真实反映外界场景信息的问题,提出了一种基于光学成像机理的Contourlet域多聚焦图像融合算法(OIPIF算法)。在详细探讨离焦成像系统的低通函数特性的基础上,针对低频/高频系数特点设计两类区域性聚焦度量准则,并制定了相应的模值取大系数选择方案,结合Contourlet变换的独特优势在变换域的不同子带独立实施系数融合。该算法能够得到与标准清晰图像更为接近的融合图像,在综合性能方面有显著提升。
4.将NSCT引入抗几何攻击数字水印技术中,提出了一种基于SIFT特征的NSCT域抗几何攻击水印算法(SND算法)。该算法通过提取宿主图像在空间域的尺度不变特征变换(SIFT)特征,在有效特征点周围的圆形区域实施多尺度NSCT,借助于NSCT的时频不变性和冗余性,在变换域的低频系数中完成水印信息嵌入。为进一步提高算法抗几何攻击的性能,该算法中同时提出了一种基于等面积圆环区域的水印嵌入方案。实验结果表明该算法具有良好的抗几何攻击特性和优秀的不可见性。
5.针对激光水下成像过程中存在不同程度的散斑噪声使图像的质量变差问题,提出了一种基于NSCT变换的激光水下图像散斑抑制算法(CTSNS算法)。系统研究了激光成像中的散斑产生机理与统计特性,在此基础上将原始图像经对数同态变换和NSCT变换进行处理,通过施加约束条件,依据NSCT高频子带的系数分布模型等先验信息,设计了尺度相关的Bayes闽值对高频子带系数实施阈值萎缩,最后通过逆变换和指数运算重构图像。该算法在有效抑制散斑的同时较好地保持了激光图像中目标的边缘结构,较好地改善了图像的主客观效果。
6.针对传统边缘检测算法在定位精度、轮廓平滑性和噪声抑制等方面存在的不足,首次将NSCT技术应用到图像边缘检测中,提出了一种基于NSCT的多尺度边缘检测算法(NIED算法)。该算法将原始图像分解至NSCT变换域,针对低频子带与多个尺度上的高频子带的特性分别提取边缘信息：低频子带使类似于Canny算子的空间域检测算法,高频子带则采用NSCT域的模极大值检测策略,通过归一化融合规则融合多尺度中不同方向的边缘信息,基于高频子带和低频子带信息的联合检测和边缘闭合输出最终的边缘检测结果。该算法能够达到更优的边缘检测性能。
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 for2-D piecewise smooth function, thus obtaining highly efficient representation and processing methods. MGA tools includes Brushlet, Wedgelet, Beamlet, Ridgelet, Curvelet, Bandelet, Contourlet and Nonsubsampled Contourlet Transform (NSCT), etc. 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 and nonsubsampled contourlet are the "true" two dimensional sparse representations, nonsubsampled contourlet also has the "Shift Inviance" property, which provide much better anisotropy, multiresolution, directionality and localization properties for2-D signals than existing image representation methods. The main research work in the dissertation is as follows:
1. 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. The varieties of 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. Therefore, they are more appropriate for various image processing tasks. It can be seen that by using contourlet or nonsubsmapled contourlet with proper scheme, better performance would be expected.
2. A novel medical 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-pass 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 CT and MR medical images, both visual and quantitative analysis show that comparing with conventional image fusion algorithms, the proposed approach can provide a more satisfactory fusion outcome.
3. A novel multifocus image fusion algorithm based on region statistics in contourlet domain was developed. According to the optical imaging principle, the defocused imaging system can be characterized as a lowpass filtering. For contourlet can handle intrinsic features in natural image much more effectively than wavelet. Original images was first decomposed by contourlet transform, fusion operation was implemented for all directional subbands in each scale, different region based fusion rules were used for lowpass and highpass subband, they are local energy and regional variance. Experimental results show that compared with traditional algorithms, the proposed multifocus image fusion algorithm can obtain a more satisfactory outcome.
4. A geometrically robust image watermarking algorithm based on nonsubsmpaled contourlet transform (NSCT) and scale invariant feature transform (SIFT) is proposed in this paper. The SIFT features points are first computed from the host image, in which the suitable SIFT points for watermark embedding are selected and tested according to their magnitude changes after being modified. NSCT was adopted by virtual of its advantages over traditional wavelet transform and other multiresolution geometric analysis tools. NSCT decomposition is implemented on the SIFT feature circle region. The lowpass coefficients within the circle region are modified to embed the watermarking bits. To enhance watermarking detection performance, we proposed an equal area based circle pattern and improved odd-even quantization algorithm. Experimental results demonstrate that the proposed scheme is robust against the geometric attacks like rotation, scaling, cropping and moving, as well as the general processing operations.
5. Based on the speckle noise modeling for underwater laser image, an adaptive speckle reduction algorithm using nonsubsampled contourlet transform (NSCT) is proposed. The statistical model for speckle noise is first analyzed to obtain a simple and tractable solution in a closed analytical form. Gaussian distribution for speckle noise and a general Gaussian distribution are adopted to model the statistics of contourlet coefficients in logarithmically transformed laser images. Then based on the maximizing the a posteriori estimation with the assumption that speckle noise is spatially correlated within a small window, we utilize a locally adaptive Bayesian processor whose parameters are obtained from the neighboring coefficients in highpass subbands. Experimental results show that comparing with classical wavelet method, the proposed algorithm shows a superior performance in suppressing the speckle noise and retaining geometrical structures of the image.
6. Available image edge detection schemes based on the spacial domain or wavelet transform domain cancapture only limited directional edges in images. A novel multiscale edge detection algorithm based on nonsubsampled contourlet transform (NSCT) was proposed in chapter7. The input image is first decomposed into NSCT domain, different edge detection techniques are applied in lowpass subband and highpass subbands:a spatial domain algorithm like Canny operator is used in lowpass subband, every coefficient in t he subbands is thresholded by comparing against the adaptive thresholds. Based on the directions of each directional subband and its gradient, modulus maxima of the transform coefficients are obtained by comparing the modulus amplitudes of the samples and the neighborhood coefficients on the direction of the gradient. The scheme requires lower complexity without complicated link operation, while edge detecting performance is improved. The results show the proposed algorithm is superior to the image edge detection method based on wavelet modulus maxima by approximating better the edges of images and has lower computational complexity.
引文
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