图像处理中拉普拉斯矩阵的稀疏化处理  

Fast Method for Extracting the Main Structure of Textile Patterns

作　　者：田俊杰 赵祖烨[1] 张军飞 TIAN Jun-jie;ZHAO Zu-ye;ZHANG Jun-fei(State Key Laboratory of Materials Processing and Die ＆ Mould Technology,Huazhong University of Science and Technology,Wuhan 430074,China;ZWCAD Software Co.,Ltd.,Guangzhou 510000,China)

机构地区：[1]华中科技大学材料成型与模具技术国家重点实验室,湖北武汉430074 [2]广州中望龙腾软件股份有限公司,广东广州510000

出　　处：《机电工程技术》2018年第9期9-11,共3页Mechanical & Electrical Engineering Technology

基　　金：国家863计划(编号:2015AA042505);广东省重大科技专项(编号:2014B010130001)

摘　　要：图像处理领域中有许多解决方案都使用离散泊松方程来求解,这涉及到大型拉普拉斯矩阵的求逆,直接求解时间消耗较大。提出一种分层稀疏化算法,通过剔除拉普拉斯矩阵邻接三角形中的最小边,补偿其他两条相邻边,并在子系统上不断迭代这个过程,通过减小拉普拉斯矩阵的条件数来减少时间消耗。以图像处理中保边滤波算法过程中的拉普拉斯矩阵求逆为例进行稀疏化算法研究,通过比较稀疏化处理前后在拉普拉斯矩阵迭代求逆过程中的条件数,验证了该算法的有效性。通过收集500张图案,建立不同大小图案的样本库,利用样本库统计稀疏化处理前后拉普拉斯矩阵求逆所需时间。统计数据证明该算法可将大型拉普拉斯矩阵的求逆的时间消耗减少60%,且随矩阵规模变大,加速效果增强。Many solutions in the field of image processing are solved using the discrete Poisson equation, which involves the inversion of large Laplacian matrices, it consumes a lot of time to solve directly. A hierarchical thinning algorithm was proposed. By eliminating the weakest edge of Laplacian adjoining triangles, compensating the other two adjacent edges and iterating the process on the subsystems, the number of conditions of the Laplacian matrix was reduced to reduce the time consumption. Taking the Laplacian matrix inversion in preserving edge filtering algorithm in image processing as an example, the thinning algorithm was studied. By comparing the number of conditions in iterative inversion of Laplacian matrix before and after thinning, the effectiveness of the algorithm was verified.. 1000 samples were collected, and a sample library of different size patterns was established. The sample library was used to calculate the time required for Laplace matrix inversion before and after sparse processing. The statistics show that this algorithm can reduce the time consumption of large Laplacian inversions by 60%, and the acceleration effect increases with the increase of matrix size.

关 键 词：图像处理 离散泊松方程 拉普拉斯矩阵 分层迭代 稀疏化 

分 类 号：TP751[自动化与计算机技术—检测技术与自动化装置]