Acton S T
Sch. of Electr. and Comput. Eng., Oklahoma State Univ., Stillwater, OK 74078-0321, USA.
IEEE Trans Image Process. 1998;7(3):280-91. doi: 10.1109/83.661178.
A multigrid anisotropic diffusion algorithm for image processing is presented. The multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time-critical processes. Through a multigrid V-cycle, the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse-to-fine error correction scheme. When a coarse grid with a trivial solution is reached, the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution. The main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low-frequency error. The theory of multigrid anisotropic diffusion is developed. Then, the intergrid transfer functions, relaxation techniques, diffusion coefficients, and boundary conditions are discussed. The analysis includes the examination of the storage requirements, the computational cost, and the solution quality. Finally, experimental results are reported that demonstrate the effectiveness of the multigrid approach.
提出了一种用于图像处理的多重网格各向异性扩散算法。多重网格实现提供了一种高效的分层松弛方法，便于将各向异性扩散应用于对时间要求严格的过程。通过多重网格V循环，各向异性扩散方程被依次转移到更粗的网格，并用于从粗到细的误差校正方案。当达到具有平凡解的粗网格时，残余误差的粗网格估计可以传播到原始网格并用于细化解。多重网格方法的主要优点是区域内快速平滑以及由于消除低频误差而减少伪影。发展了多重网格各向异性扩散理论。然后，讨论了网格间传递函数、松弛技术、扩散系数和边界条件。分析包括对存储需求、计算成本和求解质量的考察。最后，报告了实验结果，证明了多重网格方法的有效性。
