基于多项式展开的弥散张量图像配准
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摘要
在本文中,我们基于多项式展开的配准模型,提出了对于两幅磁共振弥散张量图像(DTI)的配准方法；根据临床研究需要,我们在此基础上提出了多幅图象的几何无偏配准方法。
DTI张量成像提供了一种对大脑神经纤维束活体成像的方法,脑功能障碍病人的神经纤维束一般都具有某种程度的变异,对病人和正常人的神经纤维束的变异性分析,对于脑功能障碍病人的病情诊断具有重要的意义。由于成像时间的不同、空间坐标系的不同,或者病人和正常人大脑间的差异,要进行精确的对比分析,一般需要先对病人和正常人的图像序列进行配准。在实际应用中,正常人的图像序列,有时也用正常人的脑图谱代替。为了考察某种疾病病人的共同特征,临床上需要通过分析一组同一种疾病病人的大脑神经纤维束的共同特征来确定该种疾病对于大脑神经纤维束的结构影响。这种情况下,需要同时配准一组具有相同疾病的病人大脑DTI图像序列。
在接下来的工作中,我们主要针对临床上的上述两个需要,提出了一种基于多项式展开的对于两幅或者一组图像的配准方法。首先,我们基于多项式展开的配准模型,提出了两幅DTI图像间的配准方法。由于张量图像所包含的信息量非常大,我们把临床上最关心的张量特征：各向异性和张量方向作为重点考虑对象。第一步基于多项式展开的配准模型完成对张量各向异性特征的配准；第二步,根据各向异性特征配准的结果,对张量场的方向进行逐像素的矫正,以完成张量场的方向匹配。其次,基于两幅图像的配准方法,我们进一步的提出了多幅图像的无偏配准。在以往的多幅图像配准方法中,往往指定其中一幅、或者脑图谱作为目标图像,把其余图像序列配准到目标图像,这就使得配准结果偏向于目标图像。在我们的方法中,我们通过寻找这些图像序列的几何中心位置,把他们都配准到该位置,从而实现了多幅图像的无偏配准。
概括的说,在本文中我们的贡献主要包括以下几点：(1)改进了基于多项式展开的配准模型,提出了更为精确的位移场估计公式,并进一步的提出了对于3D数据的整体仿射配准算法；(2)提出了基于局部邻域的Multi-Affine变形配准算法,实现了对于DTI图像的稳定的高精度配准；(3)基于Multi-Affine的高精度配准,在配准后逐像素的对张量场进行方向矫正,提出了张量方向的整体矫正方法；(4)基于多幅图像的几何中心,提出了多幅图像的快速无偏配准方法,包括仿射配准算法和变形配准算法。
In this dissertation, we proposed affine and deformable registration algorithms for diffusion tensor magnetic resonance images based on polynomial expansion model. Required by clinical research, then we proposed a geometric unbiased pop-ulation registration framework based on the pairwise registration method.
Diffusion tensor imaging is an in-vivo magnetic resonance imaging method based on the diffusion of water molecule, which provides an insight for the white matter fiber of human brain. The comparison analysis of white matter fiber of brain function obstacle patients with healthy subjects is helpful for patients diagnosis. Since the scanning time and spatial coordinate is different, or the difference be-tween different subjects exists, registering the patients'image volume to the healthy subjects'volume is a basic step before analyzing the difference between them ac-curately. In application, researchers sometime use the atlas as the target volume replacing the healthy subjects'volume. For other cases, in order to find the common character of a special brain function obstacle disease, a group brain image volumes with the same disease symptom are required to be registered together.
In the following work, we proposed pair-wise and group-wise registration algo-rithms focusing on the above cases required in clinical diagnosis. First, we proposed an affine and a deformable pair-wise registration algorithms based on quadratic poly-nomial expansion model. As the diffusion tensor images include a lot of information, we complete the registration of diffusion tensor images with two steps focusing on two characters which is the most important in clinical diagnosis. In the first step, we register the shape information of diffusion tensors, and then we reorient the ten-sor's orientation based on the first step's registration. Second, using the method developed for pair-wise registration, we further proposed unbiased population reg-istration for a group of volumes. Different with the former work on this problem using a selected volume as the target, which leads a bias to the selected target in registration, here we search for the geometric center position as the target and reg- ister all the volumes to the center, hereby we complete the registration without any bias.
In a summary, we contribute several points in this thesis:First, we generalized the registration model based on polynomial expansion by proposing a more accurate displacement estimation formula, and then we developed a new affine registration algorithm for 3D medical images based on the proposed method. Second, we pro-posed a deformable registration algorithm named with multi-affine which aimed to register every local regions well. The output with an affine transform pixel by pixel is suitable for diffusion tensor reorientation. Third, we apply a pixel by pixel tensor reorientation strategy into diffusion tensor image registration based on the accurate and steady registration of multi-affine algorithm. Fourth, we further proposed an unbiased population registration for a group of image volumes, which is very useful in neuroscience, clinical research.
DTI张量成像提供了一种对大脑神经纤维束活体成像的方法,脑功能障碍病人的神经纤维束一般都具有某种程度的变异,对病人和正常人的神经纤维束的变异性分析,对于脑功能障碍病人的病情诊断具有重要的意义。由于成像时间的不同、空间坐标系的不同,或者病人和正常人大脑间的差异,要进行精确的对比分析,一般需要先对病人和正常人的图像序列进行配准。在实际应用中,正常人的图像序列,有时也用正常人的脑图谱代替。为了考察某种疾病病人的共同特征,临床上需要通过分析一组同一种疾病病人的大脑神经纤维束的共同特征来确定该种疾病对于大脑神经纤维束的结构影响。这种情况下,需要同时配准一组具有相同疾病的病人大脑DTI图像序列。
在接下来的工作中,我们主要针对临床上的上述两个需要,提出了一种基于多项式展开的对于两幅或者一组图像的配准方法。首先,我们基于多项式展开的配准模型,提出了两幅DTI图像间的配准方法。由于张量图像所包含的信息量非常大,我们把临床上最关心的张量特征：各向异性和张量方向作为重点考虑对象。第一步基于多项式展开的配准模型完成对张量各向异性特征的配准；第二步,根据各向异性特征配准的结果,对张量场的方向进行逐像素的矫正,以完成张量场的方向匹配。其次,基于两幅图像的配准方法,我们进一步的提出了多幅图像的无偏配准。在以往的多幅图像配准方法中,往往指定其中一幅、或者脑图谱作为目标图像,把其余图像序列配准到目标图像,这就使得配准结果偏向于目标图像。在我们的方法中,我们通过寻找这些图像序列的几何中心位置,把他们都配准到该位置,从而实现了多幅图像的无偏配准。
概括的说,在本文中我们的贡献主要包括以下几点：(1)改进了基于多项式展开的配准模型,提出了更为精确的位移场估计公式,并进一步的提出了对于3D数据的整体仿射配准算法；(2)提出了基于局部邻域的Multi-Affine变形配准算法,实现了对于DTI图像的稳定的高精度配准；(3)基于Multi-Affine的高精度配准,在配准后逐像素的对张量场进行方向矫正,提出了张量方向的整体矫正方法；(4)基于多幅图像的几何中心,提出了多幅图像的快速无偏配准方法,包括仿射配准算法和变形配准算法。
In this dissertation, we proposed affine and deformable registration algorithms for diffusion tensor magnetic resonance images based on polynomial expansion model. Required by clinical research, then we proposed a geometric unbiased pop-ulation registration framework based on the pairwise registration method.
Diffusion tensor imaging is an in-vivo magnetic resonance imaging method based on the diffusion of water molecule, which provides an insight for the white matter fiber of human brain. The comparison analysis of white matter fiber of brain function obstacle patients with healthy subjects is helpful for patients diagnosis. Since the scanning time and spatial coordinate is different, or the difference be-tween different subjects exists, registering the patients'image volume to the healthy subjects'volume is a basic step before analyzing the difference between them ac-curately. In application, researchers sometime use the atlas as the target volume replacing the healthy subjects'volume. For other cases, in order to find the common character of a special brain function obstacle disease, a group brain image volumes with the same disease symptom are required to be registered together.
In the following work, we proposed pair-wise and group-wise registration algo-rithms focusing on the above cases required in clinical diagnosis. First, we proposed an affine and a deformable pair-wise registration algorithms based on quadratic poly-nomial expansion model. As the diffusion tensor images include a lot of information, we complete the registration of diffusion tensor images with two steps focusing on two characters which is the most important in clinical diagnosis. In the first step, we register the shape information of diffusion tensors, and then we reorient the ten-sor's orientation based on the first step's registration. Second, using the method developed for pair-wise registration, we further proposed unbiased population reg-istration for a group of volumes. Different with the former work on this problem using a selected volume as the target, which leads a bias to the selected target in registration, here we search for the geometric center position as the target and reg- ister all the volumes to the center, hereby we complete the registration without any bias.
In a summary, we contribute several points in this thesis:First, we generalized the registration model based on polynomial expansion by proposing a more accurate displacement estimation formula, and then we developed a new affine registration algorithm for 3D medical images based on the proposed method. Second, we pro-posed a deformable registration algorithm named with multi-affine which aimed to register every local regions well. The output with an affine transform pixel by pixel is suitable for diffusion tensor reorientation. Third, we apply a pixel by pixel tensor reorientation strategy into diffusion tensor image registration based on the accurate and steady registration of multi-affine algorithm. Fourth, we further proposed an unbiased population registration for a group of image volumes, which is very useful in neuroscience, clinical research.
引文
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