大尺度图像编辑的泊松方程并行多重网格求解算法

Parallel Multigrid Approach for Solving Poisson PDE in Gigapixel Image Editing

随着获取设备的发展,大尺度、高分辨率数字图像已逐步进入人们的生活,大尺度图像的梯度域编辑显得更为重要,求解大规模未知数的泊松方程是大尺度图像梯度域编辑的关键。传统多重网格算法的迭代、约束和插值操作单独进行,内存和外存间通讯量大,算法效率低,为此提出了一种面向大尺度图像梯度域编辑的并行多重网格求解泊松方程的算法。该算法利用多重网格的迭代、约束和插值过程的内存数据访问局部性和更新相关性,构造滑动工作窗口,使迭代、约束和插值操作并行运行,提高了多重网格算法求解泊松方程的计算效率。全景图拼接实验表明,所提算法的运行效率高于超松弛迭代、高斯塞德尔迭代和传统多重网格算法。

With the development of image acquisition technology,gigapixel images are being produced and emerged into the modern society, and how to efficiently compile these gigapixel images within gradient domain is the research focus of image processing and computer graphics. To solve the Poisson PDE with large-scale unknowns is crucial to gigapixel image editing in gradient domain. Traditional multigrid approach separately performs iteration, restriction and prolonga- tion, bears heavy communication load between RAM and external memory. In the paper, a parallel multigrid approach for solving poisson PDE was proposed, which exploits the locality and relevance of memory accessing and updating a- mong the different stages to parallelly perform the iteration, restriction and prolongation in the sweeping window. Ex- periments of image stitching show that the presented method has the higher efficiency than the algorithms of successive over-relaxation,gauss-seider iteration and traditional multigrid.