生物医学图像处理中的有界变差函数空间与水平集方法研究
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摘要
为了解决青光眼等致盲性眼病计算机辅助诊断中视乳头医学图像噪声污染大、光照不均匀、对比度非常小、部分视乳头被血管遮挡、不同病人个体间差异大等因素导致的视乳头图像自动分割和度量难题,本文基于特殊有界变差函数空间(SBV: the class of Special functions of Bounded Variation)理论、Mumford-Shah变分方法和水平集方法(level set methods),提出了多层Mumford-Shah(向量值)图像处理模型、形状窄带水平集统计分布先验知识表达模型和集成形状先验知识的统计多层Mumford-Shah(向量值)图像处理模型。通过彩色视乳头、大脑和心脏医学图像处理和InSAR图像相位解缠等实验,展示了这些模型和方法的有效性和应用前景。
本文的创造性成果及其理论与实际意义如下:
1)针对能够同时进行图像分割、去噪与重建的Mumford-Shah图像分割泛涵最小值求解非常困难这一问题,分别提出了多层Mumford-Shah标量和向量值图像分割、去噪与重建模型和求解该多层模型最小值的水平集逐层迭代算法。该多层模型是Mumford-Shah最小分割问题的多层实现模型。大脑、心脏和视乳头医学图像处理实验结果表明,该方法不仅能够同时进行具有T型图像边缘或更复杂拓扑结构图像边缘的图像分割、去噪与重建,而且比Tsai A.等人提出的多层求解轮廓和Chan T.等人提出的多相水平集方法更简单高效。
2)采用窄带水平集方法,提出了目标形状窄带水平集统计分布模型和训练形状图像集配准泛函模型。因为我们注意到目标形状的自然变化通常仅发生在其边界(轮廓)的邻近,采用窄带水平集方法不仅可以描述目标形状的形变模式,而且可大大降低目标形状水平集表达、训练形状配准和水平集曲面分布统计分析的计算复杂度。同时,因为该模型采用符号距离水平集函数描述目标形状边界(轮廓),所以建模时不需要目标形状标志点及其对应关系。青光眼病人视盘形变统计建模实验结果表明,该模型是一种非常有效的目标形状统计建模方法。
3)在最大后验概率(MAP: maximum a posteriori)准则下提出了一个集成形状先验知识的图像分割变分模型,即集成形状窄带水平集分布统计模型的统计多层Mumford-Shah向量值图像分割模型。该模型采用窄带水平集分布模型表达形状先验知识,并在最大目标形状参数后验概率准则下,将目标形状先验知识集成到多层Mumford-Shah向量值图像分割模型中,使该模型具有更坚实的理论基础和更大的灵活性。直接在形状水平集空间内通过目标形状水平集曲面的演化实现分割图像,使水平集曲面演化过程既依赖于当前图像特征向量(如R、G、B值),也依赖于目标形状的局部形变先验知识。早期青光眼病人彩色视乳头图像中视盘的分割实验结果表明该模型可有效地分割被血管部分遮挡的视乳头图像。
4)基于多层Mumford-Shah向量值图像分割、去噪与重建模型和光滑样条曲线拟合技术,提出了一种用于计算机辅助青光眼诊断的视乳头图像视杯和视盘重建、分割与度量的新方法。首先,采用多层模型分割和重建视杯和视盘;然后,基于重建的视乳头图像,结合青光眼视乳头图像杯、盘的先验知识,提取视杯和视盘特征矩形和边缘特征点;最后,采用光滑样条曲线拟合技术,重建被血管遮挡的视杯和视盘部分边缘,并计算杯盘比等病理特征参数值。不同青光眼病人的视乳头图像杯盘重建、分割与度量实验结果表明,该方法能克服噪声污染、血管遮挡、光照不均匀、对比度小、个体间差异大等视网膜图像分割中固有的困难,并能有效重建、分割与度量中、晚期青光眼彩色视乳头图像中的视杯和视盘。
5)提出了一种新的InSAR相位解缠算法,它基于InSAR干涉图的相位导数方差质量图和多层Mumford-Shah图像模型,先采用水平集逐层迭代算法对相位导数方差质量图进行逐层分割以确定具有不同质量特性的InSAR干涉图子连通区域,再在此基础上采用改进的Itoh解缠法从高质量区域向低质量区域对InSAR干涉图像像元进行相位解缠。真实的和模拟的InSAR干涉图实验结果表明该算法比现有的如枝切法等InSAR干涉图相位解缠方法更有效。
To solve the key problems of the segmentation and measurement of optic nerve head medical images , which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals, for the computer aided diagnostics of glaucoma, Diabetic Retinopathy, and Age-related Macular Degeneration diseases, several novel models and methods are proposed based on level set methods and Mumford–Shah functional defined in the class of Special functions of Bounded Variation(SBV), which are the hierarchical Mumford–Shah functional model(HMSM or HMSMv) for the simultaneous segmentation, denoise and reconstruction of the given scalar or vector-valued image, the narrow band level set based statistical shape distribution model (NLDM) for the representation of the prior knowledge of“legal”variation in the shape of a class of object, the statistical shape prior-based hierarchical Mumford–Shah model by incorporating prior knowledge(SHMSMv) for the recognition of the object in an image which is similar to the training shapes. Several experimental results for the segmentation and measurement of the color medical images of the optic nerve head, the segmentation and reconstruction of a pathology image of the human brain and a color Doppler ultrasound image of the heart, and the phase unwrapping of a SAR interferogram are supplied, demonstrating the effectiveness of our proposed solutions and indicating their potential.
To summarize, the original contributions and applications of our work are the following:
1)A novel hierarchical Mumford–Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given scalar or vector-valued image(HMSM or HMSMv), and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford–Shah minimal partition problem. At the same time, a new iterative tier-by-tier algorithm based on techniques of level set is proposed to minimize the functional, which is more effective and more simply than existing algorithms such as the hierarchical approach proposed by Tsai A et al. and the multiphase level set methods proposed by Chan T et al.
2)A novel narrow band level set based statistical shape distribution model is proposed, namely NLDM, which is to modeling the pattern of“legal”variation in the shape of an object from a given class of training images which are of complex and variable structures and provide noisy and possibly incomplete evidence, such as medical images. At the same time, a new alignment model based on narrow band level set is proposed also, which is a modified version of the gradient-based approach from a variational perspective proposed by A. Tsai et al. and align more efficiently all the training shapes to eliminate variations in pose. Modeling the shape of the optic nerve head in color fundus medical images demonstrates its efficacy.
3)A novel NLDM-based statistical hierarchical Mumford–Shah model(SHMSMv) by incorporating prior knowledge is proposed to segment medical images. First, a statistical shape model based on NLDM is established to represent the prior knowledge of the expected shapes of structures from a given class of training images. Then, the statistical shape model is integrated with a level set-based hierarchical Mumford–Shah modelm by maximum a posteriori(MAP). This novel model can segment vector-valued images whose boundaries are not necessarily defined by gradient, and specially recognise the object in an image which is similar to the training shapes. We demonstrate this technique by applying it to the segmentation of the optic disk in color optic nerve head images of early glaucoma patients.
4)A HMSMv-based method was proposed to reconstruct, segment and measure the optic cup and disk in a color image of optic nerve heads for the computer aided diagnostics of glaucoma diseases. First, a hierarchical Mumford–Shah model was employed to reconstruct the optic cup and disk. Then, the optic cup and disk characteristic rectangles and edge points were extracted based on the color reconstruct image of an optic nerve head by incorporating the prior knowledge of the optic cup and disk shapes. Finally, smoothing spline curve fitting was resorted to reconstruct the edges of the optic cup and disk obscured by blood vessels, and the measurements of the optic cup and disk were estimated. The tests with the color optic nerve head images of different glaucoma patients showed that this method is able to handle this kind of images, which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals and to effectively segment, reconstruct and measure the optic cup and disk in a color of optic nerve head images of glaucoma patients.
5)A novel HMSM-based algorithm was proposed in this paper for InSAR phase unwrapping. To determine the connected components in an InSAR whose quality are distinct, the quality image defined by the variance of the derivative of the phase of an InSAR was first segmented based on the hierarchical Mumford--Shah functional model by an iterative tier-by-tier level set algorithm. Then, SAR interferogram was unwrapped independently in these components by improved Itoh unwrapping algorithm ,first in the best quality component, then the better quality one, and finally the worst quality one, and so on. The phase unwrapping results on real and simulated SAR interferograms show that the algorithm is more effective than some existing algorithms such as the branch-cut algorithm.
本文的创造性成果及其理论与实际意义如下:
1)针对能够同时进行图像分割、去噪与重建的Mumford-Shah图像分割泛涵最小值求解非常困难这一问题,分别提出了多层Mumford-Shah标量和向量值图像分割、去噪与重建模型和求解该多层模型最小值的水平集逐层迭代算法。该多层模型是Mumford-Shah最小分割问题的多层实现模型。大脑、心脏和视乳头医学图像处理实验结果表明,该方法不仅能够同时进行具有T型图像边缘或更复杂拓扑结构图像边缘的图像分割、去噪与重建,而且比Tsai A.等人提出的多层求解轮廓和Chan T.等人提出的多相水平集方法更简单高效。
2)采用窄带水平集方法,提出了目标形状窄带水平集统计分布模型和训练形状图像集配准泛函模型。因为我们注意到目标形状的自然变化通常仅发生在其边界(轮廓)的邻近,采用窄带水平集方法不仅可以描述目标形状的形变模式,而且可大大降低目标形状水平集表达、训练形状配准和水平集曲面分布统计分析的计算复杂度。同时,因为该模型采用符号距离水平集函数描述目标形状边界(轮廓),所以建模时不需要目标形状标志点及其对应关系。青光眼病人视盘形变统计建模实验结果表明,该模型是一种非常有效的目标形状统计建模方法。
3)在最大后验概率(MAP: maximum a posteriori)准则下提出了一个集成形状先验知识的图像分割变分模型,即集成形状窄带水平集分布统计模型的统计多层Mumford-Shah向量值图像分割模型。该模型采用窄带水平集分布模型表达形状先验知识,并在最大目标形状参数后验概率准则下,将目标形状先验知识集成到多层Mumford-Shah向量值图像分割模型中,使该模型具有更坚实的理论基础和更大的灵活性。直接在形状水平集空间内通过目标形状水平集曲面的演化实现分割图像,使水平集曲面演化过程既依赖于当前图像特征向量(如R、G、B值),也依赖于目标形状的局部形变先验知识。早期青光眼病人彩色视乳头图像中视盘的分割实验结果表明该模型可有效地分割被血管部分遮挡的视乳头图像。
4)基于多层Mumford-Shah向量值图像分割、去噪与重建模型和光滑样条曲线拟合技术,提出了一种用于计算机辅助青光眼诊断的视乳头图像视杯和视盘重建、分割与度量的新方法。首先,采用多层模型分割和重建视杯和视盘;然后,基于重建的视乳头图像,结合青光眼视乳头图像杯、盘的先验知识,提取视杯和视盘特征矩形和边缘特征点;最后,采用光滑样条曲线拟合技术,重建被血管遮挡的视杯和视盘部分边缘,并计算杯盘比等病理特征参数值。不同青光眼病人的视乳头图像杯盘重建、分割与度量实验结果表明,该方法能克服噪声污染、血管遮挡、光照不均匀、对比度小、个体间差异大等视网膜图像分割中固有的困难,并能有效重建、分割与度量中、晚期青光眼彩色视乳头图像中的视杯和视盘。
5)提出了一种新的InSAR相位解缠算法,它基于InSAR干涉图的相位导数方差质量图和多层Mumford-Shah图像模型,先采用水平集逐层迭代算法对相位导数方差质量图进行逐层分割以确定具有不同质量特性的InSAR干涉图子连通区域,再在此基础上采用改进的Itoh解缠法从高质量区域向低质量区域对InSAR干涉图像像元进行相位解缠。真实的和模拟的InSAR干涉图实验结果表明该算法比现有的如枝切法等InSAR干涉图相位解缠方法更有效。
To solve the key problems of the segmentation and measurement of optic nerve head medical images , which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals, for the computer aided diagnostics of glaucoma, Diabetic Retinopathy, and Age-related Macular Degeneration diseases, several novel models and methods are proposed based on level set methods and Mumford–Shah functional defined in the class of Special functions of Bounded Variation(SBV), which are the hierarchical Mumford–Shah functional model(HMSM or HMSMv) for the simultaneous segmentation, denoise and reconstruction of the given scalar or vector-valued image, the narrow band level set based statistical shape distribution model (NLDM) for the representation of the prior knowledge of“legal”variation in the shape of a class of object, the statistical shape prior-based hierarchical Mumford–Shah model by incorporating prior knowledge(SHMSMv) for the recognition of the object in an image which is similar to the training shapes. Several experimental results for the segmentation and measurement of the color medical images of the optic nerve head, the segmentation and reconstruction of a pathology image of the human brain and a color Doppler ultrasound image of the heart, and the phase unwrapping of a SAR interferogram are supplied, demonstrating the effectiveness of our proposed solutions and indicating their potential.
To summarize, the original contributions and applications of our work are the following:
1)A novel hierarchical Mumford–Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given scalar or vector-valued image(HMSM or HMSMv), and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford–Shah minimal partition problem. At the same time, a new iterative tier-by-tier algorithm based on techniques of level set is proposed to minimize the functional, which is more effective and more simply than existing algorithms such as the hierarchical approach proposed by Tsai A et al. and the multiphase level set methods proposed by Chan T et al.
2)A novel narrow band level set based statistical shape distribution model is proposed, namely NLDM, which is to modeling the pattern of“legal”variation in the shape of an object from a given class of training images which are of complex and variable structures and provide noisy and possibly incomplete evidence, such as medical images. At the same time, a new alignment model based on narrow band level set is proposed also, which is a modified version of the gradient-based approach from a variational perspective proposed by A. Tsai et al. and align more efficiently all the training shapes to eliminate variations in pose. Modeling the shape of the optic nerve head in color fundus medical images demonstrates its efficacy.
3)A novel NLDM-based statistical hierarchical Mumford–Shah model(SHMSMv) by incorporating prior knowledge is proposed to segment medical images. First, a statistical shape model based on NLDM is established to represent the prior knowledge of the expected shapes of structures from a given class of training images. Then, the statistical shape model is integrated with a level set-based hierarchical Mumford–Shah modelm by maximum a posteriori(MAP). This novel model can segment vector-valued images whose boundaries are not necessarily defined by gradient, and specially recognise the object in an image which is similar to the training shapes. We demonstrate this technique by applying it to the segmentation of the optic disk in color optic nerve head images of early glaucoma patients.
4)A HMSMv-based method was proposed to reconstruct, segment and measure the optic cup and disk in a color image of optic nerve heads for the computer aided diagnostics of glaucoma diseases. First, a hierarchical Mumford–Shah model was employed to reconstruct the optic cup and disk. Then, the optic cup and disk characteristic rectangles and edge points were extracted based on the color reconstruct image of an optic nerve head by incorporating the prior knowledge of the optic cup and disk shapes. Finally, smoothing spline curve fitting was resorted to reconstruct the edges of the optic cup and disk obscured by blood vessels, and the measurements of the optic cup and disk were estimated. The tests with the color optic nerve head images of different glaucoma patients showed that this method is able to handle this kind of images, which are of poor quality, very low contrast, obscure due to blood vessels, and distinct inter-differences of individuals and to effectively segment, reconstruct and measure the optic cup and disk in a color of optic nerve head images of glaucoma patients.
5)A novel HMSM-based algorithm was proposed in this paper for InSAR phase unwrapping. To determine the connected components in an InSAR whose quality are distinct, the quality image defined by the variance of the derivative of the phase of an InSAR was first segmented based on the hierarchical Mumford--Shah functional model by an iterative tier-by-tier level set algorithm. Then, SAR interferogram was unwrapped independently in these components by improved Itoh unwrapping algorithm ,first in the best quality component, then the better quality one, and finally the worst quality one, and so on. The phase unwrapping results on real and simulated SAR interferograms show that the algorithm is more effective than some existing algorithms such as the branch-cut algorithm.
引文
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