本文为加拿大麦克马斯特大学（作者：NAVID SAMAVATI）的硕士论文，共97页。

在过去的二十年中，对医学图像配准的需求越来越大。形变图像配准有着重要的意义，因为大多数的配准应用都是在刚性假设不能产生精确结果的情况下进行的。软组织器官（如肝脏、肾脏和前列腺）在干预过程中可能会改变形状。因此，复杂的配准基本上需要考虑几何变形。

本文主要研究肝脏磁共振（MR）与超声（US）图像之间的可形变肝脏图像配准问题。在我们的方法中，提出了一个追踪系统来获取二维超声图像（IUS），并将其与先前拍摄的MR体进行严格的配准。根据从跟踪系统获得的信息，将二维磁共振图像（IMR）重建为IUS的匹配。在刚性配准问题中，选择互信息作为两种模式之间的相似性度量。然后对配准参数进行搜索优化，为我们提供一个微调的重建IMR。我们提出的策略是从视觉上识别IUS和IMR上相应的解剖标志开始。这些标志是本文提出的两种形变方法的输入。第一种方法是有限元建模（FEM）方法，基于线弹性和静力分析假设生成形变图像。该方法利用标志点的位置来求解线性方程组，从而产生MR图像的最终形变。形变的第二种方法是移动最小二乘法（MLS）。据我们所知，MLS从未用于医学图像配准。这种技术解析地解决了一些最小二乘问题，以找到局部刚性变换。在MR体上应用这些局部刚性变换会在MR图像中创建形变。实验中采用均方根目标配准误差（RMS-TRE）作为性能评价的定量指标。基于有限元方法产生了RMS TRE为7.2mm的最佳结果，而基于MLS的方法产生的RMS TRE为8.9mm。根据已有文献，7.2毫米的精确度对于大多数术中腹部手术是可以接受的，尤其是涉及肝脏的手术。有限元法的缺点是计算复杂度高。我们基于MLS方法的实现比基于FEM的方法至少快20倍。因此，在精度非常关键的应用中，应采用基于有限元的方法。基于MLS的方法更适合于要求更高速度的应用，或者基于有限元方法的并行实现可以解决计算速度问题。  

During the past two decades, there has beenan increasing demand for medical image registration. Deformable imageregistration has a great importance, because the majority of the registrationapplications deal with the conditions in which the rigid assumption would notcreate accurate results. Soft tissue organs (e.g. liver, kidney, and prostate)can change in shape during an intervention. Therefore, a sophisticatedregistration essentially needs to take into account the geometricaldeformations. In this thesis, we study the problem of deformable liver imageregistration between Magnetic Resonance (MR) and Ultrasound (US) images of theliver. In our approach, a tracking system is proposed to acquire and rigidlyregister a 2D US image (IUS) with the previously taken MR volume. According tothe information obtained from the tracking system, a 2D MR image (IMR) isreconstructed as the match of IUS. Mutual information is chosen as thesimilarity measure between the two modalities in our rigid registrationproblem. A search optimization problem on the registration parameters is thenperformed, to provide us with a fine tuned reconstructed IMR. Our proposedstrategy begins with visually identifying corresponding anatomical landmarks onIUS and IMR. These landmarks are the inputs of the two proposed methods ofdeformation in this thesis. The first method, Finite Element Modeling (FEM)approach, produces the deformed images based on the linear elasticity and thestatic analysis assumptions. This method uses the positions of landmarks tosolve a linear system of equations, in order to generate the final deformationsof the MR images. The second method of deformation is the Moving Least Squares(MLS). To the best of our knowledge, MLS has never been used in medical imageregistration. This technique analytically solves a number of least squaresproblems to find the local rigid transformations. Applying these local rigidtransformations on the MR volume creates the deformations throughout the MRimages. In our experiments, Root Mean Square Target Registration Error (RMSTRE) is used as the quantitative measure for the evaluation of performance.FEM-based method produces the best result with an RMS TRE of 7.2mm, whileMLS-based method creates an RMS TRE of 8.9mm. According to the literature, anaccuracy of 7.2mm is acceptable for most intra-operative abdominal procedures, particularlythose involving the liver. The drawback of FEM-based method is its highercomputational complexity. Our implementation of the MLS-based method could beexecuted at least 20 times faster than that of the FEM-based method. Therefore,in applications, where the accuracy is critical, FEM-based method should beused. The MLS-based method is more suitable of the applications demandinghigher speed or a parallel implementation of the FEM-based method can solve thecomputation speed problem.

1.  引言

2. 文献回顾

3. 本文提出的多模态配准方法

4. 实验结果

5. 结论与展望

附录A 互信息

附录B 体模研究

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