医学图像配准算法研究
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摘要
图像配准是指对不同时间、不同视场、不同成像模式的两幅或多幅图像进行空间几何变换,以使代表相同解剖结构的像素或体素在几何上能够匹配对应起来。医学图像可以提供有病变组织或器官的大小,形状,空间关系等详细信息,比如计算机断层扫描成像(Computed Tomography,CT)图像可以显示骨骼结构和组织密度分布情况;磁共振图像(Magnetic Resonance Image,MRI)和超声图像(Ultrasound Image,US)提供的则是软组织的信息;正电子发射断层成像(Positron Emission Tomography,PET),单光子发射计算机断层成像(Single PhotonEmission Computed Tomography,SPECT)能反映人体的功能和代谢信息。多模态医学图像配准是目前临床诊断中的一个重要的基础性问题。在临床应用中,单一模态的图像往往不能提供医生所需要的足够的信息,通常需要将不同模态的图像融合在一起,得到更丰富的信息以便了解病变组织或器官的综合情况,从而做出准确的诊断或制订出合适的治疗方案,而配准则是进行融合的前提。此外配准还广泛应用于实际医学图像和图谱的比较、外科手术导航、心脏运动估计等许多方面。
本文主要作了以下四个方面的工作:
1基于共生互信息量的医学图像配准
互信息法的最大缺陷是忽略了图像的空间信息,原始香农熵没有包括前一信号的相关性,实际中使用的定义是一个独立的连续信号。这种独立性假设一般在医学图像中不成立。由熵的定义可知熵的大小并不依赖于灰度本身,而只依赖于这些灰度出现的概率。基于传统互信息量的图像配准算法只考虑单个相对应点间的关系,忽略了图像的空间与方向信息,在一些情况下容易出现误配。Markov随机场理论(Markov Random Field,MRF)能够很好地描述相邻的图像像素或者相关特征间的相互关系,因而在图像分析领域得到了广泛地应用。在MRF理论中,图像的像素点的位置关系可以通过邻域系统来体现。我们考虑对应点及其邻域内不同方向上的像素点,将图像的空间与方向信息引入到配准中,提出了一种新的相似性测度——共生互信息量(Concurrent Mutual Information,CMI),并在此基础上构造了一种新的配准算法——最大共生互信息量法。实验结果表明在图像空间分辨率较低,有噪声影响和图像部分缺损的情况下,该算法具有计算速度快,精度高,鲁棒性强的特点。作为一种一般性的配准方法,共生互信息量同互信息一样,不仅可以用于图像的刚性和弹性配准,还可以应用到图像配准以外的更广阔的领域,如经济学、运筹学、模式识别等。
2基于主相位一致性的医学图像配准
相位一致性就是指图像的各个位置上各个频率成分的相位相似度的一种度量方式,即假定图像中傅里叶相位最大的点为特征点。它不是基于亮度梯度的,所以其值对图像亮度和对比度变化具有不变性。传统的边缘检测算子,如Marr算子、Sobel算子、Canny算子,其原理都是基于灰度图像像素值梯度的变化程度。检测结果严重依赖于图像亮度和对比度的变化程度,在光照条件不理想、噪声污染或者亮度变化不剧烈的时候检测效果往往不理想。基于相位一致性的边缘检测可以很好地解决这个问题,即使是在对比非常弱的地方,也能够检测到边缘的存在,也就是说,相位一致性原理能够检测到“实质上”的边缘的存在,而不受到明暗对比的影响。这就从另外一个角度说明了相位谱能够从底层描述图像纹理结构,而与光照条件、噪声或者是图像亮度分布是否均匀等无关。本文提出了一种新的图像特征——主相位一致性(Principal Phase Congruency,PPC),并在此基础上构造了一种新的基于主相位一致性的配准算法。首先计算不同尺度、方向上的相位一致性,然后利用主成分分析将它们进行融合,从而得到信息更加丰富的主相位一致性;将待配准图像的主相位一致性看作模糊集合,引入模糊数学中的贴近度(Close-degree)概念,计算它们的模糊相似性。我们对模拟和真实数据(CT,MR,PET)进行了实验,结果表明在图像空间分辨率较低,有噪声影响等情况下,该算法具有精度高,鲁棒性强的特点,特别适合于医学图像的配准。
3基于当量子午面的三维医学图像快速配准算法
基于像素或体素相似性的配准方法可以避免由特征分割和提取等预处理所造成的精度损失,配准过程可以由计算机自动实现,所以吸引了大量的研究兴趣。根据文献报道,基于最大互信息量法(Mutual Information,MI)的图像配准结果是目前刚性图像配准中最为精确的。但是,由于互信息量的计算涉及大量的浮点运算,所以配准过程比较费时。另外,以互信息量定义的目标函数在某些情况下存在局部极值,不利于快速的最优化搜索,甚至可能因为终止到局部极值而得到错误的结果。
对于三维医学图像而言,由于是无标记配准,所以无法利用标记点实现快速配准。而如果利用整个三维数据的信息,计算复杂度太大,无法满足临床要求。我们试图找到三维空间中的一个“特殊”平面,将三维数据的配准简化为二维数据的配准,在保证精度的前提下,提高配准的速度。子午面是地理学中的一个重要概念,它是过地球南北两极所确定的轴线(地轴)的平面。推而广之,对于任意曲线,绕曲线端点所确定的轴线旋转360度都可以形成一个三维体,而过轴线的平面即为该三维体的子午面。对于医学图像,由成像设备产生的断层序列图像也可以重建为三维体,但该三维体一般是非常不规则的,故不能求取一般意义上的子午面。为此我们提出了当量子午面(Equivalent Meridian Plane,EMP)的概念:对于断层序列图像重建出的三维体,分别求出其第一主轴和与之正交的第二主轴,而由第一主轴和第二主轴所确定的平面称之为当量子午面。
我们构造了一种新的基于当量子午面和互信息量的三维医学图像快速配准算法—EMP-MI算法。传统的基于互信息量的方法需要考虑整个三维数据的信息,计算复杂度大,无法满足临床需要。而本算法将三维数据的配准减化为二维数据的配准,在保证精度的前提下,减少了配准所需时间。本算法创新点在于利用主成分分析计算出图像的当量子午面并将图像转化到标准坐标系下,从而将质心和当量子午面粗配准,精细配准时只需要对浮动图像进行微小的调整计算当量子午面的互信息量,这就大大提高了配准速度,减少了陷入局部极值的可能。实验结果表明此方法能准确,快速地处理图像刚性配准问题,特别适用于三维医学图像的配准。
4不同时态胸腹部图像的刚-弹性混合配准
除了多模态的图像配准,还有一个重要的临床应用领域就是单一设备间图像的配准。它主要用来分析同一设备不同时期成像的差异,在手术的介入治疗中用以判断病情的变化。因为不同病灶在身体不同部位的不同生长时期具有不同的生长规律,对它的这些生长规律进行研究,将为疾病的诊断和治疗提供重要的先验信息。
我们构造了一种针对同一病人不同时间扫描的胸腹部CT图像的刚-弹性混合配准算法。首先分别分割出两组CT图像中的骨骼结构,并抽取骨骼边缘上的点作为标志点,利用软对应匹配(Soft Correspondence Matching)算法计算出每一个骨骼与其对应骨骼的刚性变换矩阵;然后通过薄板样条插值得到整幅图像的变形场,完成骨骼的精确配准;最后为了对软组织进行配准,我们以B样条为变形函数,在保证骨骼等刚性结构不变的同时,不断迭代直到归一化互信息量(Normalized Mutual Information,NMI)值达到最大。通过对多组临床数据的实验表明该方法能够满足临床医生的要求。
Using images to guide therapeutic, such as surgical, radio-surgical, and radiotherapeutic, planning is a rapidly growing field. Precise registration would provide useful clinical information. It can increase treatment efficiency and minimize neurological damage. Given two image sets acquired from the same patient but at different times or with different devices, image registration is the process of finding the geometric transformation that aligns one image to another. The geometric alignment or registration of multimodality images is an essential and fundamental task to clinical diagnosis. X-ray computed tomography (CT) data depict high contrast structure of bony tissue, magnetic resonance imaging (MRI) and , Ultrasound Image (US) provide excellent contrast of soft tissue, and nuclear imaging techniques such as positron emission tomography (PET) and single photon emission computed tomography (SPECT) provide functional data. Analysis of the data is enhanced by the complementary information present in a multimodality study, and techniques exist that use anatomical datasets to further process functional images. In order to analyze or utilize data from two different modalities, accurate registration is necessary. Image registration is mainly applied to the areas of video compression and coding, motion analysis, objection tracking etc.
We mainly focus our research on four image registration topics, as follows:
1 Medical Image Registration Using Concurrence Mutual Information
Mutual information (MI) is calculated on a pixel by pixel basis. It takes into account only the relationship between corresponding individual pixels rather than those of each pixel's respective neighborhood, which ignores the spatial information. In this article we propose a new measure—Concurrence Mutual Information(CMI). It is an extension of the mutual information framework which incorporates spatial information about image structure into the registration process, and has the potential to improve the accuracy and robustness of image registration. The results indicate that CMI is a more robust similarity measure for image registration than MI. Furthermore CMI can be used in other fields, such as economics, operational research and pattern recognition, just like MI.
2 Medical Image Registration Based on Principal Phase Congruency
A novel image attribute, principal phase congruency (PPC), is defined and used to register medical images. Phase congruency is computed on different scales and orientations. PPC can be developed from a fusion of the phase congruency by using principal component analysis. A fuzzy similarity measure is introduced as the registration function. We evaluate the effectiveness of the proposed approach by applying it to the simulated and real brain image data (CT, MR and PET). Experimental results indicate that the algorithm is less sensitive to low sampling resolution and noise, does not contain incorrect local maxima that are sometimes found in the traditional algorithm.
3 Fast 3-D Medical Image Registration Based on Equivalent Meridian Plane
As is well known, a meridian plane is arbitrary plane perpendicular to the celestial equator, which passes through the earth's axis of rotation. For three-dimensional medical image, it is necessary to propose a new Equivalent Meridian Plane (EMP) concept since estimating the meridian plane is not always feasible in practice.
For a three-dimensional irregular volume, a set of orthogonal principal axes can be always found, by which a family of orthogonal planes can be determined. One of these planes, containing the first and the second principal axis, is defined as EMP.
For the rigid registration of multi-modality medical images, mutual information (MI) technique is unsuitable to clinical diagnose because of high computational cost and low robustness. A new concept of equivalent meridian plane (EMP) is proposed, and the EMP and other two normal feature planes are determined using principal component analysis (PCA); the rough registrations of those 2D planes are carried out at six freedom degree; finally, the refine registrations can be completed using MI in a small neighboring region. This method is called as EMP based MI registration technique. The accuracy and robustness of EMP-MI approach can be verified by applying it to the simulated and real brain image data (CT, MR, PET, and SPECT). The experimental results indicate that the proposed algorithm reduces computational time distinctly and is a global optimal strategy.
4 Hybrids Rigid and Non-rigid Registration Algorithm for Alignment of Serial Thoracic and Abdominal Images
Registration of the same subject with the same modality at different time is useful for physicians, either to follow the development of a disease, or for interventions (dynamic acquisition during the operation or its validation).
A hybrid rigid and non-rigid registration algorithm has been presented to register thoracic and abdominal CT images of the same subject scanned at different times. The bony structures are first segmented from two different time CT images, respectively. Then, the segmented bony structures in the two respective images are registered based on their boundary points using a soft correspondence matching algorithm with a rigid transformation constraint on each bony structure. With estimated correspondences in bony structures, the dense deformations in the entire images are interpolated by a Thin Plate Spline (TPS) interpolation technique. To improve the alignment of soft tissues in the images as well, a normalized mutual information based B-Spline registration algorithm is used to iteratively refine the registration of soft tissues, and at the same time keeps the rigid transformation for each bony structure. This registration refinement procedure is repeated until the algorithm converges. The proposed hybrid registration algorithm has been applied to the clinical data with encouraging results as evaluated by two clinical radiologists.
本文主要作了以下四个方面的工作:
1基于共生互信息量的医学图像配准
互信息法的最大缺陷是忽略了图像的空间信息,原始香农熵没有包括前一信号的相关性,实际中使用的定义是一个独立的连续信号。这种独立性假设一般在医学图像中不成立。由熵的定义可知熵的大小并不依赖于灰度本身,而只依赖于这些灰度出现的概率。基于传统互信息量的图像配准算法只考虑单个相对应点间的关系,忽略了图像的空间与方向信息,在一些情况下容易出现误配。Markov随机场理论(Markov Random Field,MRF)能够很好地描述相邻的图像像素或者相关特征间的相互关系,因而在图像分析领域得到了广泛地应用。在MRF理论中,图像的像素点的位置关系可以通过邻域系统来体现。我们考虑对应点及其邻域内不同方向上的像素点,将图像的空间与方向信息引入到配准中,提出了一种新的相似性测度——共生互信息量(Concurrent Mutual Information,CMI),并在此基础上构造了一种新的配准算法——最大共生互信息量法。实验结果表明在图像空间分辨率较低,有噪声影响和图像部分缺损的情况下,该算法具有计算速度快,精度高,鲁棒性强的特点。作为一种一般性的配准方法,共生互信息量同互信息一样,不仅可以用于图像的刚性和弹性配准,还可以应用到图像配准以外的更广阔的领域,如经济学、运筹学、模式识别等。
2基于主相位一致性的医学图像配准
相位一致性就是指图像的各个位置上各个频率成分的相位相似度的一种度量方式,即假定图像中傅里叶相位最大的点为特征点。它不是基于亮度梯度的,所以其值对图像亮度和对比度变化具有不变性。传统的边缘检测算子,如Marr算子、Sobel算子、Canny算子,其原理都是基于灰度图像像素值梯度的变化程度。检测结果严重依赖于图像亮度和对比度的变化程度,在光照条件不理想、噪声污染或者亮度变化不剧烈的时候检测效果往往不理想。基于相位一致性的边缘检测可以很好地解决这个问题,即使是在对比非常弱的地方,也能够检测到边缘的存在,也就是说,相位一致性原理能够检测到“实质上”的边缘的存在,而不受到明暗对比的影响。这就从另外一个角度说明了相位谱能够从底层描述图像纹理结构,而与光照条件、噪声或者是图像亮度分布是否均匀等无关。本文提出了一种新的图像特征——主相位一致性(Principal Phase Congruency,PPC),并在此基础上构造了一种新的基于主相位一致性的配准算法。首先计算不同尺度、方向上的相位一致性,然后利用主成分分析将它们进行融合,从而得到信息更加丰富的主相位一致性;将待配准图像的主相位一致性看作模糊集合,引入模糊数学中的贴近度(Close-degree)概念,计算它们的模糊相似性。我们对模拟和真实数据(CT,MR,PET)进行了实验,结果表明在图像空间分辨率较低,有噪声影响等情况下,该算法具有精度高,鲁棒性强的特点,特别适合于医学图像的配准。
3基于当量子午面的三维医学图像快速配准算法
基于像素或体素相似性的配准方法可以避免由特征分割和提取等预处理所造成的精度损失,配准过程可以由计算机自动实现,所以吸引了大量的研究兴趣。根据文献报道,基于最大互信息量法(Mutual Information,MI)的图像配准结果是目前刚性图像配准中最为精确的。但是,由于互信息量的计算涉及大量的浮点运算,所以配准过程比较费时。另外,以互信息量定义的目标函数在某些情况下存在局部极值,不利于快速的最优化搜索,甚至可能因为终止到局部极值而得到错误的结果。
对于三维医学图像而言,由于是无标记配准,所以无法利用标记点实现快速配准。而如果利用整个三维数据的信息,计算复杂度太大,无法满足临床要求。我们试图找到三维空间中的一个“特殊”平面,将三维数据的配准简化为二维数据的配准,在保证精度的前提下,提高配准的速度。子午面是地理学中的一个重要概念,它是过地球南北两极所确定的轴线(地轴)的平面。推而广之,对于任意曲线,绕曲线端点所确定的轴线旋转360度都可以形成一个三维体,而过轴线的平面即为该三维体的子午面。对于医学图像,由成像设备产生的断层序列图像也可以重建为三维体,但该三维体一般是非常不规则的,故不能求取一般意义上的子午面。为此我们提出了当量子午面(Equivalent Meridian Plane,EMP)的概念:对于断层序列图像重建出的三维体,分别求出其第一主轴和与之正交的第二主轴,而由第一主轴和第二主轴所确定的平面称之为当量子午面。
我们构造了一种新的基于当量子午面和互信息量的三维医学图像快速配准算法—EMP-MI算法。传统的基于互信息量的方法需要考虑整个三维数据的信息,计算复杂度大,无法满足临床需要。而本算法将三维数据的配准减化为二维数据的配准,在保证精度的前提下,减少了配准所需时间。本算法创新点在于利用主成分分析计算出图像的当量子午面并将图像转化到标准坐标系下,从而将质心和当量子午面粗配准,精细配准时只需要对浮动图像进行微小的调整计算当量子午面的互信息量,这就大大提高了配准速度,减少了陷入局部极值的可能。实验结果表明此方法能准确,快速地处理图像刚性配准问题,特别适用于三维医学图像的配准。
4不同时态胸腹部图像的刚-弹性混合配准
除了多模态的图像配准,还有一个重要的临床应用领域就是单一设备间图像的配准。它主要用来分析同一设备不同时期成像的差异,在手术的介入治疗中用以判断病情的变化。因为不同病灶在身体不同部位的不同生长时期具有不同的生长规律,对它的这些生长规律进行研究,将为疾病的诊断和治疗提供重要的先验信息。
我们构造了一种针对同一病人不同时间扫描的胸腹部CT图像的刚-弹性混合配准算法。首先分别分割出两组CT图像中的骨骼结构,并抽取骨骼边缘上的点作为标志点,利用软对应匹配(Soft Correspondence Matching)算法计算出每一个骨骼与其对应骨骼的刚性变换矩阵;然后通过薄板样条插值得到整幅图像的变形场,完成骨骼的精确配准;最后为了对软组织进行配准,我们以B样条为变形函数,在保证骨骼等刚性结构不变的同时,不断迭代直到归一化互信息量(Normalized Mutual Information,NMI)值达到最大。通过对多组临床数据的实验表明该方法能够满足临床医生的要求。
Using images to guide therapeutic, such as surgical, radio-surgical, and radiotherapeutic, planning is a rapidly growing field. Precise registration would provide useful clinical information. It can increase treatment efficiency and minimize neurological damage. Given two image sets acquired from the same patient but at different times or with different devices, image registration is the process of finding the geometric transformation that aligns one image to another. The geometric alignment or registration of multimodality images is an essential and fundamental task to clinical diagnosis. X-ray computed tomography (CT) data depict high contrast structure of bony tissue, magnetic resonance imaging (MRI) and , Ultrasound Image (US) provide excellent contrast of soft tissue, and nuclear imaging techniques such as positron emission tomography (PET) and single photon emission computed tomography (SPECT) provide functional data. Analysis of the data is enhanced by the complementary information present in a multimodality study, and techniques exist that use anatomical datasets to further process functional images. In order to analyze or utilize data from two different modalities, accurate registration is necessary. Image registration is mainly applied to the areas of video compression and coding, motion analysis, objection tracking etc.
We mainly focus our research on four image registration topics, as follows:
1 Medical Image Registration Using Concurrence Mutual Information
Mutual information (MI) is calculated on a pixel by pixel basis. It takes into account only the relationship between corresponding individual pixels rather than those of each pixel's respective neighborhood, which ignores the spatial information. In this article we propose a new measure—Concurrence Mutual Information(CMI). It is an extension of the mutual information framework which incorporates spatial information about image structure into the registration process, and has the potential to improve the accuracy and robustness of image registration. The results indicate that CMI is a more robust similarity measure for image registration than MI. Furthermore CMI can be used in other fields, such as economics, operational research and pattern recognition, just like MI.
2 Medical Image Registration Based on Principal Phase Congruency
A novel image attribute, principal phase congruency (PPC), is defined and used to register medical images. Phase congruency is computed on different scales and orientations. PPC can be developed from a fusion of the phase congruency by using principal component analysis. A fuzzy similarity measure is introduced as the registration function. We evaluate the effectiveness of the proposed approach by applying it to the simulated and real brain image data (CT, MR and PET). Experimental results indicate that the algorithm is less sensitive to low sampling resolution and noise, does not contain incorrect local maxima that are sometimes found in the traditional algorithm.
3 Fast 3-D Medical Image Registration Based on Equivalent Meridian Plane
As is well known, a meridian plane is arbitrary plane perpendicular to the celestial equator, which passes through the earth's axis of rotation. For three-dimensional medical image, it is necessary to propose a new Equivalent Meridian Plane (EMP) concept since estimating the meridian plane is not always feasible in practice.
For a three-dimensional irregular volume, a set of orthogonal principal axes can be always found, by which a family of orthogonal planes can be determined. One of these planes, containing the first and the second principal axis, is defined as EMP.
For the rigid registration of multi-modality medical images, mutual information (MI) technique is unsuitable to clinical diagnose because of high computational cost and low robustness. A new concept of equivalent meridian plane (EMP) is proposed, and the EMP and other two normal feature planes are determined using principal component analysis (PCA); the rough registrations of those 2D planes are carried out at six freedom degree; finally, the refine registrations can be completed using MI in a small neighboring region. This method is called as EMP based MI registration technique. The accuracy and robustness of EMP-MI approach can be verified by applying it to the simulated and real brain image data (CT, MR, PET, and SPECT). The experimental results indicate that the proposed algorithm reduces computational time distinctly and is a global optimal strategy.
4 Hybrids Rigid and Non-rigid Registration Algorithm for Alignment of Serial Thoracic and Abdominal Images
Registration of the same subject with the same modality at different time is useful for physicians, either to follow the development of a disease, or for interventions (dynamic acquisition during the operation or its validation).
A hybrid rigid and non-rigid registration algorithm has been presented to register thoracic and abdominal CT images of the same subject scanned at different times. The bony structures are first segmented from two different time CT images, respectively. Then, the segmented bony structures in the two respective images are registered based on their boundary points using a soft correspondence matching algorithm with a rigid transformation constraint on each bony structure. With estimated correspondences in bony structures, the dense deformations in the entire images are interpolated by a Thin Plate Spline (TPS) interpolation technique. To improve the alignment of soft tissues in the images as well, a normalized mutual information based B-Spline registration algorithm is used to iteratively refine the registration of soft tissues, and at the same time keeps the rigid transformation for each bony structure. This registration refinement procedure is repeated until the algorithm converges. The proposed hybrid registration algorithm has been applied to the clinical data with encouraging results as evaluated by two clinical radiologists.
引文
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