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收稿：2018-05-02，
修回：2018-8-13，
纸质出版：2019-01-16
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目的
2
弥散张量图像（DTI）配准不仅要保证配准前后图像解剖结构的一致性，还要保持张量方向的一致性。demons算法下的多通道DTI配准方法可充分利用张量的信息，改善配准质量，但大形变区域配准效果不理想，收敛速度慢。active demons算法能够加快收敛速度，但图像的拓扑结构容易改变。由此提出一种变参数active demons算法下的多通道DTI配准方法。
方法
2
综合active demons算法中平衡系数能加快收敛速度、均化系数能提高DTI配准精度的优点，手动选择一个均化系数，并在算法收敛过程中随着高斯核的减小动态调整平衡系数。在配准开始时采用较小的平衡系数获得较快的收敛速度，随着收敛的加深逐渐增大平衡系数获得较小的配准误差。
结果
2
active demons方法能改善DTI大形变区域的配准问题，但均化系数太小会改变图像拓扑结构。固定均化系数，引入单一的平衡系数能加快收敛速度，但会导致拓扑结构改变。变参数active demons方法有效提高了配准的收敛速度，明显改善大形变区域的配准效果，同时能保持图像拓扑结构不变。变参数active demons配准后的10组数据均获得最小均方差（MSE）和最大特征值特征向量对重叠率（OVL），配准精度最高。在0.05的配对样本
$$t$$
检验水平下，变参数active demons和active demons方法配准后的MSE、OVL的差异均有统计学意义；变参数active demons和demons方法配准后的MSE、OVL的差异均有统计学意义（
$$p$$
<
0.05）。
结论
2
变参数active demons算法下的多通道DTI配准方法明显提高了配准精度和速度，改善了demons方法不能有效配准大形变区域的问题，同时能够保持配准前后图像的拓扑结构，尤其适合个体间形变较大的DTI配准。
Objective
2
Diffusion tensor imaging (DTI) is widely recognized as the most attractive non-invasive magnetic resonance imaging method. DTI is sensitive to subtle differences in the orientation of white matter fiber and diffuse anisotropy. Hence
it is a powerful method studying brain diseases and group research
such as Alzheimer's disease
Parkinson's disease
and multiple sclerosis. DTI registration is a prerequisite for these studies
and its effect will directly affect the reliability and completeness of the follow-up medical research and clinical diagnosis. DT images contain many information about the direction of brain white matter fibers. DTI registration not only requires the consistency of the anatomy between the reference and the moving image after registration but also demands consistency between the diffusion tensor direction and the anatomic structure. The DTI registration based on demons algorithm
which uses the six independent components of the tensor as inputs
can fully use the direction information of the diffusion tensor data and improve the quality of registration. However
this algorithm does not perform well in the large deformation area
and its convergence speed is slow. The active demons algorithm can accelerate the convergence to some extent
but the internal structure of the moving image is prone to being teared
deformed
and folded due to the presence of false demons force
which can alter the topological structure of the moving image. To solve these problems
this paper proposes a multi-channel DTI registration method based on active demons algorithm by using variable parameters.
Method
2
The active demons algorithm is introduced into the multi-channel DTI registration. By analyzing the influence of the homogeneous and the balance coefficient in the active demons algorithm on the DTI registration and combining the advantages of the balance coefficient of improving the convergence speed and that of homogeneous coefficient of enhancing the accuracy of the multi-channel DTI registration
an appropriate homogeneous coefficient is first manually selected in a reasonable range. Then
the size of the balance coefficient value is dynamically adjusted with the decreasing Gaussian kernel during the convergence of this proposed algorithm. A smaller balance coefficient is used in the initial stage of DTI registration for a faster convergence speed
and then the balance coefficient is gradually increased for a smaller registration error. To verify whether the proposed multi-channel DTI registration method based on active demons algorithm using variable parameters statistically improves the effect of registration compared with the demons and active demons methods
10 pairs of DTI data volumes of patients with Alzheimer's disease are used for registration. The mean square error (MSE) and overlap of eigenvalue-eigenvector pairs (OVL) obtained from the three DTI registration methods are used for the paired
$$t$$
test.
Result
2
When the demons algorithm is used for the multi-channel DTI registration
a good registration effect is achieved in small deformation areas. However
the registration effect in larger deformation areas is not ideal and the convergence rate is slow. The homogenization coefficient in the active demons method for DTI registration resolved the registration problem in large deformation areas
but the image topology will change if the homogenization coefficient is too small. Although a faster convergence can be achieved by fixing the homogenization coefficient and introducing a single balance coefficient
the topological structure of the image changes simultaneously. Compared with the DTI registration method based on demons and active demons algorithm by using multiple channels
the convergence speed of the proposed approach is increased
the registration effect in large deformation areas is significantly improved
and the topology consistency of the image is preserved before and after registration. Moreover
the minimum MSE and maximum OVL values are obtained after registration using the proposed method for 10 sets of DTI data. At the given level of significance of 0.05
a significant difference can be found in the MSE values and OVL values between the active demons algorithm using variable parameters and active demons algorithm and between the active demons algorithm using variable parameters and demons algorithm (
$$p$$
<
0.05).
Conclusion
2
The application of variable parameters in the proposed DTI registration method not only effectively improves the registration accuracy and registration speed but also enhance the registration of large deformation areas of DT image by the demons algorithm. It maintains the topological structure of DT images before and after registration simultaneously
which is one of the major drawbacks in multi-channel DTI registration method based on active demons algorithm. The experimental results indicate that a multi-channel DTI registration method based on active demons algorithm using variable parameters is suitable for the registration of DT images with large deformation areas between individuals.
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