Liu Huafeng, Shi Pengcheng
Department of Electrical and Electronic Engineering, Hong Kong University of Science and Technology, Hong Kong.
Inf Process Med Imaging. 2003 Jul;18:560-72. doi: 10.1007/978-3-540-45087-0_47.
For medical image analysis issues where the domain mappings between images involve large geometrical shape changes, such as the cases of nonrigid motion recovery and inter-object image registration, the finite element methods exhibit considerable loss of accuracy when the elements in the mesh become extremely skewed or compressed. Therefore, algorithmically difficult and computationally expensive remeshing procedures must be performed in order to alleviate the problem. We present a general representation and computation framework which is purely based on the sampling nodal points and does not require the construction of mesh structure of the analysis domain. This meshfree strategy can more naturally handle very large object deformation and domain discontinuity problems. Because of its intrinsic h-p adaptivity, the meshfree framework can achieve desired numerical accuracy through adaptive node and polynomial shape function refinement with minimum extra computational expense. We focus on one of the more robust meshfree efforts, the element free Galerkin method, through the moving least square approximation and the Galerkin weak form formulation, and demonstrate its relevancy to medical image analysis problems. Specifically, we show the results of applying this strategy to physically motivated multiframe motion analysis, using synthetic data for accuracy assessment and for comparison to finite element results, and using canine magnetic resonance tagging and phase contrast images for cardiac kinematics recovery.
对于医学图像分析中图像间域映射涉及大几何形状变化的问题，如非刚性运动恢复和物体间图像配准的情况，当网格中的单元变得极度扭曲或压缩时，有限元方法会出现相当大的精度损失。因此，必须执行算法上困难且计算成本高昂的重新网格化过程来缓解该问题。我们提出了一种通用的表示和计算框架，它完全基于采样节点，不需要构建分析域的网格结构。这种无网格策略可以更自然地处理非常大的物体变形和域不连续问题。由于其固有的h-p适应性，无网格框架可以通过自适应节点和多项式形状函数细化以最小的额外计算成本实现所需的数值精度。我们通过移动最小二乘近似和伽辽金弱形式公式，专注于一种更稳健的无网格方法——无单元伽辽金方法，并展示其与医学图像分析问题的相关性。具体而言，我们展示了将此策略应用于物理驱动的多帧运动分析的结果，使用合成数据进行精度评估并与有限元结果进行比较，以及使用犬磁共振标记和相位对比图像进行心脏运动学恢复。
