医学图像倾斜校正方法与应用研究
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摘要
由于医学图像有效地反映了人体生物组织大量信息,因此在临床医学上得到广泛应用。临床医生能够充分利用这些图像信息,为临床诊断、制定有效的治疗方案提供更加全面准确的资料；另一方面也可以辅助医生对病变体及其它感兴趣的区域进行定性甚至定量的分析,可以大大提高医疗诊断的准确性和可靠性,进一步丰富医生的诊断经验。医学图像处理作为医学图像研究中非常关键的一环,它对完善医学诊断与治疗的手段和方法、提高计算机辅助诊断的精度与效率有重大的实用价值。
论文针对采集到的医学图像存在倾斜现象,讨论了医学图像倾斜校正方法；针对医学图像配准速度慢、易陷入局部最优等问题,论文把倾斜校正方法应用于互信息和迭代最近点医学图像配准,并提出了改进的迭代最近点医学图像配准方法；在分析模糊集的基础上,进一步提出了基于倾斜校正和模糊理论的医学图像配准方法,这些方法不仅丰富与完善了医学图像处理的相关理论与方法,也解决了医学图像处理上的一些难题,有重大的理论意义和实用价值。概括地说,论文的研究工作包括如下内容：
(1)医学图像倾斜校正方法研究。在医学图像成像过程中,由于某些原因,采集到的医学图像中经常存在倾斜现象,这给医学图像匹配和融合带来极大困难。针对这种情况,为了解决倾斜问题,论文在建立医学图像倾斜模型基础上,把医学图像倾斜校正分为五个过程,但总体上讲,关键在于获取图像质心坐标和图像倾斜角。根据获取图像倾斜角的方法,论文介绍和提出了七种倾斜校正方法：(a)基于图像几何矩的医学图像倾斜校正算法(Algorithm for Medical Image Tilt Correction Based on Image Moments, ACIM);(b)基于图像惯量矩阵的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Inertia Matrix, MCIM); (c)基于奇异值分解的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Singular Value Decomposition, MSVD);(d)基于主分量分析的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Principal Component Analysis, MPCA);(e)基于K-Means聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on K-Means Clustering, MKMC); (f)基于模糊均值聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Fuzzy C-Means Clustering, MFCM); (g)基于自组织特征映射(Self-Organizing Feature Map, SOFM)神经网络聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on SOFM, MSOFM)。ACIM利用了医学图像几何矩的特点,使二阶中心矩变得最小时的旋转角α即为图像倾斜角；MCIM利用了医学图像惯量矩阵来获取倾斜角α;MSVD利用了SVD技术,对医学图像坐标进行奇异值分解,得到特征向量(注：论文中特征向量均为单位特征向量),获取倾斜角；MPCA是在分析PCA的基础上,通过对医学图像坐标进行K-L变换,得到特征向量,进而获取倾斜角；在分析了K-means聚类和模糊C-均值聚类算法之后,论文讨论了MKMC和MFCM,先把医学图像坐标聚成两类,拟合成一条直线,通过计算该直线斜率得到倾斜角；MSOFM与MKMC和MFCM类似,利用SOFM神经网络,把医学图像坐标聚成两类,拟合成一条直线,通过计算该直线斜率得到倾斜角。实验结果表明,这些方法对倾斜图像均有效,ACIM和MCIM校正效果最好,MSVD、MPCA、MKMC、MFCM次之,由于MSOFM聚类时间较长,时间效率最差。
(2)倾斜校正方法在医学图像配准中应用研究。论文分析了基于互信息配准和基于迭代最近点配准两种方法的优、缺点,并把医学图像配准分为两个过程：粗配准和细配准。在粗配准中,通过ACIM、MCIM、MSVD、MPCA、MKMC和MFCM等获取配准图像的质心坐标和旋转角,并作为细配准中多参数寻优方法的初值。另外,论文提出了改进的迭代最近点配准算法,即用粗配准获取迭代最近点配准算法的初始旋转参数和平移参数,然后使用B样条梯度算子生成特征点,得到参考点集和浮动点集。实验结果表明,使用了倾斜校正方法的互信息配准和改进的迭代最近点配准能有效减少运算量,配准速度快,精度较高,而且克服了容易陷入局部最优的问题。
(3)倾斜校正方法和模糊理论在医学图像配准中应用研究。在研究模糊集理论基础上,提出了两幅图像之间模糊距离的概念,并进一步提出了模糊信噪比的概念。以Z函数作为模糊集的隶属度函数,以参考图像和浮动图像之间的模糊信噪比作为相似性测度,通过倾斜校正方法获取配准参数初值,使用单纯形法作为多参数寻优方法寻找最优几何变换参数,进行细配准。实验结果表明,模糊信噪比和互信息一样,均能作为两幅图像的相似性测度,两者具有接近的配准精度,但前者时间效率更高,运算量更少。论文进一步推导出峰值信噪比是模糊信噪比的特例,并把峰值信噪比用作配准函数,实验表明峰值信噪比也具有较好的配准性能。在研究了线性插值、二次样条插值(a=1)、三次样条插值(a=-0.5)、二次B样条插值和三次B样条插值等插值方法之后,从插值方法、数据缺失和噪声干扰等三个方面分析和研究了模糊信噪比、峰值信噪比和互信息等三个相似性测度的鲁棒性。实验结果表明,在基于倾斜校正和模糊理论的医学图像配准时使用不同的插值方法,峰值信噪比和模糊信噪比保持了较好的有效性；在数据缺失不严重时,三个相似性测度保持了较好的有效性,但是当数据缺失较严重时,三个相似性测度均失效；当图像中存在椒盐噪声干扰时,模糊信噪比保持了较好的有效性,互信息次之,而峰值信噪比完全失效；当图像中存在高斯噪声干扰时,三个相似性测度完全失效。
Since the medical image represents a great amount of the useful information on tissues and organs inside human body, it is widely used in clinical medicine. The clinicians can make full use of the information extracted from the medical images to provide more comprehensive and accurate data for the clinical diagnosis and the decision on the effective treatment scheme. Also, based on the information provided, the doctors can qualitatively and even quantitatively analyze the contour and focus of a disease and other regions of interesting, which will significantly improve the accuracy and reliability of medical diagnosis, and further accumulates the clinical diagnostic experience for the clinicians. Medical image processing, as a very crucial part of medical image research, plays a significant role on perfecting the scheme and method for medical diagnosis and treatment, and advancing the accuracy and efficiency of computer-aided diagnosis.
Since medical images frequently have some visible and serious tilt, which acts as costly barrier for the subsequent image registration and fusion, it is very necessary to correct the tilt. In this paper, seven correction methods are used to deal with the medical image tilt. Since the traditional medical image registrations have a heavily computational load and often trap into the local optima, the mutual information and improved iterative closest point medical image registrations based on the tilt correction are proposed. On the foundation of the analysis for fuzzy theory, the fuzzy theory medical image registration based on the tilt correction is presented in detail. These methods mentioned above not only enrich and advance the related theories and methods of medical image processing, but also resolve some problems of medical image processing. Therefore, they have great theoretical significance and practical value. In summary, the main research work and innovation are as follows:
(1) The medical image tilt correction methods are introduced. In the process of medical imaging, often because of the pertinent imaging device with a low stability, the patients with voluntary movement or with emotional tension, and so on, the medical images frequently have some undesirable tilt, which has costly negative effect on the following image alignment and fusion. In order to solve the tilt problem, the tilt models of medical images are first designed, and then the correction tilt process is divided into five main stages. Among these stages, the key tasks focus on finding the centroid and obtaining the tilt angle of a medical image. According to the various methods for acquiring the tilt angle, seven tilt correction methods are introduced and pioneered, which are an algorithm for medical image tilt correction based on image moments (ACIM), a method for medical image tilt correction based on inertia matrix (MCIM), a method for medical image tilt correction based on singular value decomposition (MSVD), a method for medical image tilt correction based on principal component analysis (MPCA), a method for medical image tilt correction based on K-means clustering (MKMC), a method for medical image tilt correction based on fuzzy C-means clustering (MFCM), and a method for medical image tilt correction based on self-organizing feature map (MSOFM). ACIM obtains the tilt angle a by minimizing the second order central moment based on rotational invariance of a medical image; MCIM calculates the tilt angle a by the image inertia moment; MSVD and MPCA compute the eigenvectors of the coordinates of a medical image by singular value decomposition and principal component analysis respectively to get the tilt angleα; As for MKMC, MFCM and MSOFM, they first cluster the coordinates of a medical image into two classes by using the K-means clustering, fuzzy C-means clustering and self-organizing feature map respectively, and then fit the two classes to a straight line, finally obtain the tilt angle a by computing the slope of the straight line. The experimental results reveal that, all the proposed methods are effective for correcting the tilt medical images. Among these methods, the correction effects of ACIM and MCIM occupy first place, MSVD, MPCA, MKMC and MFCM comes second. Since MSOFM has the longest clustering time, it is the worst correction method.
(2) Medical image registration based on the tilt correction is studied. In this paper, after the advantages and disadvantages of the traditional mutual information and iterative closet point medical image registrations are analyzed and expounded, and then the medical image registration is divided into two steps:the coarse and precise registrations. In the process of the coarse registration, the centroids and the tilt angles of reference and floating images are obtained by applying ACIM, MCIM, MSVD, MPCA, MKMC and MFCM respectively, and are viewed as the initial values for the precise registration. In addition, an improved iterative closest point algorithm is proposed. The use of the coarse registration first obtains the initial rotation and translation parameters for the iterative closest point algorithm, and then the B-spline gradient operator is applied to yield the feature points for the reference and floating point sets. The experiments reveal that the mutual information and iterative closet point registrations based on the tilt correction can effectively reduce the computational load, advance registration efficiency, decrease the possibility of failing to register images, and avoid getting into the local optima.
(3) Medical image registration based on the tilt correction and fuzzy theory is proposed. Two new concepts of fuzzy distance and fuzzy signal-to-noise ratio (FSNR) between two images are put forward after delineating the fuzzy theory. Taking the Z-function as the membership function of a fuzzy set, the FSNR as a new similarity measure between the reference and floating images, the tilt correction method mentioned above as the tool for acquiring the initial registration parameters, and combining with the simplex method, applies to explore the optimal transformation parameters, finally precise registration is realized. This proposed method can cater to both mono-modality and multi-modality image registrations. The experimental results show that this proposed method has a simple implementation, a low computational load, a fast registration and good registration accuracy. Furthermore, compared with the mutual information medical image registration, the proposed method has a higher processing efficiency and a lower computational load. However, they have approximate registration accuracy. Further, the peak signal-to-noise ratio (PSNR) is derived from the definition of the FSNR, and is selected as a similar measure in this paper. The experiments show that the PSNR has an acceptable registration performance as well. The linear, quadratic spline (a=1), cubic spline (a=-0.5), quadratic B-spline, and cubic B-spline interpolations are first depicted and discussed, and then the robustnesses of the FSNR, PSNR and mutual information are analyzed and elaborated from three aspects:interpolation method, data deficiency and noise interference. The experimental results illustrate that when various interpolation methods are used for the medical image registration based on the tilt correction and fuzzy theory, the FSNR and PSNR are effective and practical. In the case of the images with less data deficiency, the three similarity measures are effective; but with serious data deficiency, the three similarity measures badly run. Also, when the images are corrupted by the salt & pepper noise, the FSNR is the most effective, the mutual information takes second, and the PSNR completely fails. More unfortunately, the three similarity measures are totally ineffective in the case of the images corrupted by Gaussian noise.
论文针对采集到的医学图像存在倾斜现象,讨论了医学图像倾斜校正方法；针对医学图像配准速度慢、易陷入局部最优等问题,论文把倾斜校正方法应用于互信息和迭代最近点医学图像配准,并提出了改进的迭代最近点医学图像配准方法；在分析模糊集的基础上,进一步提出了基于倾斜校正和模糊理论的医学图像配准方法,这些方法不仅丰富与完善了医学图像处理的相关理论与方法,也解决了医学图像处理上的一些难题,有重大的理论意义和实用价值。概括地说,论文的研究工作包括如下内容：
(1)医学图像倾斜校正方法研究。在医学图像成像过程中,由于某些原因,采集到的医学图像中经常存在倾斜现象,这给医学图像匹配和融合带来极大困难。针对这种情况,为了解决倾斜问题,论文在建立医学图像倾斜模型基础上,把医学图像倾斜校正分为五个过程,但总体上讲,关键在于获取图像质心坐标和图像倾斜角。根据获取图像倾斜角的方法,论文介绍和提出了七种倾斜校正方法：(a)基于图像几何矩的医学图像倾斜校正算法(Algorithm for Medical Image Tilt Correction Based on Image Moments, ACIM);(b)基于图像惯量矩阵的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Inertia Matrix, MCIM); (c)基于奇异值分解的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Singular Value Decomposition, MSVD);(d)基于主分量分析的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Principal Component Analysis, MPCA);(e)基于K-Means聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on K-Means Clustering, MKMC); (f)基于模糊均值聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on Fuzzy C-Means Clustering, MFCM); (g)基于自组织特征映射(Self-Organizing Feature Map, SOFM)神经网络聚类的医学图像倾斜校正方法(Method for Medical Image Tilt Correction Based on SOFM, MSOFM)。ACIM利用了医学图像几何矩的特点,使二阶中心矩变得最小时的旋转角α即为图像倾斜角；MCIM利用了医学图像惯量矩阵来获取倾斜角α;MSVD利用了SVD技术,对医学图像坐标进行奇异值分解,得到特征向量(注：论文中特征向量均为单位特征向量),获取倾斜角；MPCA是在分析PCA的基础上,通过对医学图像坐标进行K-L变换,得到特征向量,进而获取倾斜角；在分析了K-means聚类和模糊C-均值聚类算法之后,论文讨论了MKMC和MFCM,先把医学图像坐标聚成两类,拟合成一条直线,通过计算该直线斜率得到倾斜角；MSOFM与MKMC和MFCM类似,利用SOFM神经网络,把医学图像坐标聚成两类,拟合成一条直线,通过计算该直线斜率得到倾斜角。实验结果表明,这些方法对倾斜图像均有效,ACIM和MCIM校正效果最好,MSVD、MPCA、MKMC、MFCM次之,由于MSOFM聚类时间较长,时间效率最差。
(2)倾斜校正方法在医学图像配准中应用研究。论文分析了基于互信息配准和基于迭代最近点配准两种方法的优、缺点,并把医学图像配准分为两个过程：粗配准和细配准。在粗配准中,通过ACIM、MCIM、MSVD、MPCA、MKMC和MFCM等获取配准图像的质心坐标和旋转角,并作为细配准中多参数寻优方法的初值。另外,论文提出了改进的迭代最近点配准算法,即用粗配准获取迭代最近点配准算法的初始旋转参数和平移参数,然后使用B样条梯度算子生成特征点,得到参考点集和浮动点集。实验结果表明,使用了倾斜校正方法的互信息配准和改进的迭代最近点配准能有效减少运算量,配准速度快,精度较高,而且克服了容易陷入局部最优的问题。
(3)倾斜校正方法和模糊理论在医学图像配准中应用研究。在研究模糊集理论基础上,提出了两幅图像之间模糊距离的概念,并进一步提出了模糊信噪比的概念。以Z函数作为模糊集的隶属度函数,以参考图像和浮动图像之间的模糊信噪比作为相似性测度,通过倾斜校正方法获取配准参数初值,使用单纯形法作为多参数寻优方法寻找最优几何变换参数,进行细配准。实验结果表明,模糊信噪比和互信息一样,均能作为两幅图像的相似性测度,两者具有接近的配准精度,但前者时间效率更高,运算量更少。论文进一步推导出峰值信噪比是模糊信噪比的特例,并把峰值信噪比用作配准函数,实验表明峰值信噪比也具有较好的配准性能。在研究了线性插值、二次样条插值(a=1)、三次样条插值(a=-0.5)、二次B样条插值和三次B样条插值等插值方法之后,从插值方法、数据缺失和噪声干扰等三个方面分析和研究了模糊信噪比、峰值信噪比和互信息等三个相似性测度的鲁棒性。实验结果表明,在基于倾斜校正和模糊理论的医学图像配准时使用不同的插值方法,峰值信噪比和模糊信噪比保持了较好的有效性；在数据缺失不严重时,三个相似性测度保持了较好的有效性,但是当数据缺失较严重时,三个相似性测度均失效；当图像中存在椒盐噪声干扰时,模糊信噪比保持了较好的有效性,互信息次之,而峰值信噪比完全失效；当图像中存在高斯噪声干扰时,三个相似性测度完全失效。
Since the medical image represents a great amount of the useful information on tissues and organs inside human body, it is widely used in clinical medicine. The clinicians can make full use of the information extracted from the medical images to provide more comprehensive and accurate data for the clinical diagnosis and the decision on the effective treatment scheme. Also, based on the information provided, the doctors can qualitatively and even quantitatively analyze the contour and focus of a disease and other regions of interesting, which will significantly improve the accuracy and reliability of medical diagnosis, and further accumulates the clinical diagnostic experience for the clinicians. Medical image processing, as a very crucial part of medical image research, plays a significant role on perfecting the scheme and method for medical diagnosis and treatment, and advancing the accuracy and efficiency of computer-aided diagnosis.
Since medical images frequently have some visible and serious tilt, which acts as costly barrier for the subsequent image registration and fusion, it is very necessary to correct the tilt. In this paper, seven correction methods are used to deal with the medical image tilt. Since the traditional medical image registrations have a heavily computational load and often trap into the local optima, the mutual information and improved iterative closest point medical image registrations based on the tilt correction are proposed. On the foundation of the analysis for fuzzy theory, the fuzzy theory medical image registration based on the tilt correction is presented in detail. These methods mentioned above not only enrich and advance the related theories and methods of medical image processing, but also resolve some problems of medical image processing. Therefore, they have great theoretical significance and practical value. In summary, the main research work and innovation are as follows:
(1) The medical image tilt correction methods are introduced. In the process of medical imaging, often because of the pertinent imaging device with a low stability, the patients with voluntary movement or with emotional tension, and so on, the medical images frequently have some undesirable tilt, which has costly negative effect on the following image alignment and fusion. In order to solve the tilt problem, the tilt models of medical images are first designed, and then the correction tilt process is divided into five main stages. Among these stages, the key tasks focus on finding the centroid and obtaining the tilt angle of a medical image. According to the various methods for acquiring the tilt angle, seven tilt correction methods are introduced and pioneered, which are an algorithm for medical image tilt correction based on image moments (ACIM), a method for medical image tilt correction based on inertia matrix (MCIM), a method for medical image tilt correction based on singular value decomposition (MSVD), a method for medical image tilt correction based on principal component analysis (MPCA), a method for medical image tilt correction based on K-means clustering (MKMC), a method for medical image tilt correction based on fuzzy C-means clustering (MFCM), and a method for medical image tilt correction based on self-organizing feature map (MSOFM). ACIM obtains the tilt angle a by minimizing the second order central moment based on rotational invariance of a medical image; MCIM calculates the tilt angle a by the image inertia moment; MSVD and MPCA compute the eigenvectors of the coordinates of a medical image by singular value decomposition and principal component analysis respectively to get the tilt angleα; As for MKMC, MFCM and MSOFM, they first cluster the coordinates of a medical image into two classes by using the K-means clustering, fuzzy C-means clustering and self-organizing feature map respectively, and then fit the two classes to a straight line, finally obtain the tilt angle a by computing the slope of the straight line. The experimental results reveal that, all the proposed methods are effective for correcting the tilt medical images. Among these methods, the correction effects of ACIM and MCIM occupy first place, MSVD, MPCA, MKMC and MFCM comes second. Since MSOFM has the longest clustering time, it is the worst correction method.
(2) Medical image registration based on the tilt correction is studied. In this paper, after the advantages and disadvantages of the traditional mutual information and iterative closet point medical image registrations are analyzed and expounded, and then the medical image registration is divided into two steps:the coarse and precise registrations. In the process of the coarse registration, the centroids and the tilt angles of reference and floating images are obtained by applying ACIM, MCIM, MSVD, MPCA, MKMC and MFCM respectively, and are viewed as the initial values for the precise registration. In addition, an improved iterative closest point algorithm is proposed. The use of the coarse registration first obtains the initial rotation and translation parameters for the iterative closest point algorithm, and then the B-spline gradient operator is applied to yield the feature points for the reference and floating point sets. The experiments reveal that the mutual information and iterative closet point registrations based on the tilt correction can effectively reduce the computational load, advance registration efficiency, decrease the possibility of failing to register images, and avoid getting into the local optima.
(3) Medical image registration based on the tilt correction and fuzzy theory is proposed. Two new concepts of fuzzy distance and fuzzy signal-to-noise ratio (FSNR) between two images are put forward after delineating the fuzzy theory. Taking the Z-function as the membership function of a fuzzy set, the FSNR as a new similarity measure between the reference and floating images, the tilt correction method mentioned above as the tool for acquiring the initial registration parameters, and combining with the simplex method, applies to explore the optimal transformation parameters, finally precise registration is realized. This proposed method can cater to both mono-modality and multi-modality image registrations. The experimental results show that this proposed method has a simple implementation, a low computational load, a fast registration and good registration accuracy. Furthermore, compared with the mutual information medical image registration, the proposed method has a higher processing efficiency and a lower computational load. However, they have approximate registration accuracy. Further, the peak signal-to-noise ratio (PSNR) is derived from the definition of the FSNR, and is selected as a similar measure in this paper. The experiments show that the PSNR has an acceptable registration performance as well. The linear, quadratic spline (a=1), cubic spline (a=-0.5), quadratic B-spline, and cubic B-spline interpolations are first depicted and discussed, and then the robustnesses of the FSNR, PSNR and mutual information are analyzed and elaborated from three aspects:interpolation method, data deficiency and noise interference. The experimental results illustrate that when various interpolation methods are used for the medical image registration based on the tilt correction and fuzzy theory, the FSNR and PSNR are effective and practical. In the case of the images with less data deficiency, the three similarity measures are effective; but with serious data deficiency, the three similarity measures badly run. Also, when the images are corrupted by the salt & pepper noise, the FSNR is the most effective, the mutual information takes second, and the PSNR completely fails. More unfortunately, the three similarity measures are totally ineffective in the case of the images corrupted by Gaussian noise.
引文
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