发布时间: 2019-01-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180281 2019 | Volume 24 | Number 1 医学图像处理

1. 河北大学电子信息工程学院, 保定 071000;
2. 河北省数字医疗工程重点实验室, 保定 071000;
3. 河北省机器视觉工程技术研究中心, 保定 071000
 收稿日期: 2018-05-02; 修回日期: 2018-08-13 基金项目: 河北省自然科学基金项目（F2016201187）；河北大学"一省一校"专项经费 第一作者简介: 赵杰, 1969年生, 男, 教授, 主要研究方向为智能数据处理、图像处理与分析、信号检测与模式识别。E-mail:zhaojie_hbu@126.com;徐晓莹, 女, 硕士研究生, 主要研究方向为图像处理与计算机视觉。E-mail:1242211732@qq.com;刘敬, 女, 讲师, 主要研究方向为光学偏振成像、图像处理、功能磁共振rs-fMRI图像处理技术。E-mail:bitliujing@163.com;杜宇航, 男, 硕士研究生, 主要研究方向为图像处理与计算机视觉。E-mail:1583359930@qq.com. 中图法分类号: TP391.41 文献标识码: A 文章编号: 1006-8961(2019)01-0103-12

# 关键词

Multi-channel diffusion tensor imaging registration method based on active demons algorithm by using variable parameters
Zhao Jie, Xu Xiaoying, Liu Jing, Du Yuhang
1. College of Electronic and Information Engineering, Hebei University, Baoding 071000, China;
2. Key Laboratory of Digital Medical Engineering of Hebei Province, Baoding 071000, China;
3. Machine Vision Engineering Technology Research Center of Hebei Province, Baoding 071000, China
Supported by: Natural Science Foundation of Hebei Province, China (F2016201187)

# Abstract

Objective 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 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 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 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.

# Key words

diffusion tensor imaging; diffusion tensor imaging registration; demons algorithm; active demons algorithm; tensor reorientation

# 1.1 弥散张量

 $\mathit{\boldsymbol{D}}=\left[\begin{matrix} {{D}_{xx}}&{{D}_{xy}}&{{D}_{xz}} \\ {{D}_{yx}}&{{D}_{yy}}&{{D}_{yz}} \\ {{D}_{zx}}&{{D}_{zy}}&{{D}_{zz}} \\ \end{matrix} \right]$ (1)

# 1.2 active demons算法

1998年，Thirion等人[15]提出demons非刚性配准算法。假设图像在运动过程中灰度保持不变(能量守恒)，将图像的形变过程看成是一种弥散的过程，将参考图像$\mathit{\boldsymbol{S}}$的灰度轮廓看做是含有“demons”的半透膜，浮动图像$\mathit{\boldsymbol{M}}$上的全部像素点看做可变形的网格，网格上demons的力就会利用图像梯度信息驱动浮动图像$\mathit{\boldsymbol{M}}$朝着参考图像$\mathit{\boldsymbol{S}}$发生形变。且在对形变的优化迭代过程中，为了使形变场连续以及变形后的图像保持良好的拓扑结构，对形变场进行高斯平滑。对于2维图像中任意一点$(x, y)$$S(x, y)$$M(x, y)$分别表示参考图像和浮动图像在点$(x, y)$的灰度值，$\mathit{\boldsymbol{\nabla }}S(x, y)$为参考图像在$(x, y)$处的梯度值，则光流场方程为

 $\mathit{\boldsymbol{u}}\cdot\mathit{\boldsymbol{\nabla}} S\left( {x, y} \right) = M\left( {x, y} \right) - S\left( {x, y} \right)$ (2)

 $\mathit{\boldsymbol{u}} = \frac{{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)\mathit{\boldsymbol{\nabla}} S\left( {x, y} \right)}}{{\left| {\mathit{\boldsymbol{\nabla}} S{{\left( {x, y} \right)}^2}} \right|}}$ (3)

 $\mathit{\boldsymbol{u}} = \frac{{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)\mathit{\boldsymbol{\nabla }}S\left( {x, y} \right)}}{{\left| {\mathit{\boldsymbol{\nabla }}S{{\left( {x, y} \right)}^2}} \right| + {{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)}^2}}}$ (4)

2005年，Wang等人[18]在demons算法的基础上提出了一种将浮动图像和参考图像的梯度信息分别作为光流场正内力和负内力的active demons算法，该算法不仅考虑了参考图像的梯度，而且也考虑了浮动图像的梯度对图像配准的影响，因此能在一定程度上克服demons配准算法的部分缺陷，能够适当提高配准的准确性和一致性，并且收敛速度更快，处理时间较短，特别是在处理参考图像梯度非常小和形变比较大的图像配准问题上，active demons算法的优势更加明显。其形变向量为

 $\begin{array}{l} \mathit{\boldsymbol{u}} = \frac{{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)\mathit{\boldsymbol{\nabla }}S\left( {x, y} \right)}}{{\left| {\mathit{\boldsymbol{\nabla }}S{{\left( {x, y} \right)}^2}} \right| + {\alpha ^2}{{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)}^2}}} + \\ \frac{{\left( {M\left( {x, y} \right)S\left( {x, y} \right)} \right)\mathit{\boldsymbol{\nabla }}M\left( {x, y} \right)}}{{\left| {\mathit{\boldsymbol{\nabla }}M{{\left( {x, y} \right)}^2}} \right| + {\alpha ^2}{{\left( {M\left( {x, y} \right) - S\left( {x, y} \right)} \right)}^2}}} \end{array}$ (5)

# 2.4 变参数active demons算法下的多通道DTI配准结果及分析

Table 2 $p$ and $t$ values of paired sample $t$ test

 MSE OVL $p$值 $t$值 $p$值 $t$值 IAD与demons < 0.001 -6.590 0.009 3.344 IAD与AD 0.042 -2.373 0.032 2.533 AD与demons < 0.001 -6.969 0.011 3.186

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