Lehrstuhl Für Informatik 10 (systemsimulation) a Fast Full Multigrid Solver for Applications in Image Processing a Fast Full Multigrid Solver for Applications in Image Processing
Lehrstuhl Für Informatik 10 (systemsimulation) a Fast Full Multigrid Solver for Applications in Image Processing a Fast Full Multigrid Solver for Applications in Image Processing
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Lehrstuhl Für Informatik 10（系统模拟） 用于图像处理应用的快速完整多重网格求解器 用于图像处理应用的快速完整多重网格求解器
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通讯作者：
U. Rüde
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作者：
M. Stürmer;H. Köstler;U. Rüde
我们提出了一种快速的、以细胞为中心的多重网格求解器，并将其应用于图像去噪和基于非刚性扩散的图像配准。在这两种应用中，3D都需要实时性能，而多重网格法必须与基于快速傅里叶变换的求解器进行比较。对基本变分方法的优化，使图像去噪直接在抛物线型热方程的一个时间步长内得到，对于图像配准，得到了一个非线性的二阶偏微分方程组。采用半隐式时间离散化的不动点迭代法求解该方程，每一时间步同样得到一个椭圆型线性热方程。对于这两种应用，多重网格实现接近于3D医学图像的实时性能，并使用可用的库与基于快速傅立叶变换的解算器进行了比较。
We present a fast, cell-centered multigrid solver and apply it to image denoising and non-rigid diffusion based image registration. In both applications real time performance is required in 3D and the multigrid method has to be compared to solvers based on Fast Fourier Transform. The optimization of the underlying variational approach results for image denoising directly in one time step of a parabolic linear heat equation, for image registration a non-linear 2nd order system of partial differential equations is obtained. This system is solved by a fixpoint iteration using a semi-implicit time discretization, where each time step again results in an elliptic linear heat equation. The multigrid implementation comes close to real time performance for medium size medical images in 3D for both applications and is compared to a solver based on Fast Fourier Transform using available libraries.