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差分格式对偏微分方程滤波模型的影响

Impact on Partial Differential Equations Filtering Models of Difference Scheme

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摘要

电子散斑干涉技术(ESPI)中,基于偏微分方程(PDE)的滤波模型是一种重要的滤波方法。偏微分方程滤波模型中的微分算符通常利用差分近似表示。给出了中心差分、九点差分、高阶差分三种不同的差分格式。以典型有效的方向二阶偏微分方程滤波模型为例,分别利用三种不同的差分格式近似滤波模型中的微分算符,通过模拟条纹图、相位图以及实验条纹图进行了分析研究,结果表明,对于密度变化特别大的条纹图,采用高阶差分格式能够更好地平衡高密度区域和稀疏密度区域的滤波效果,九点差分和中心差分格式需要使用均值滤波做进一步的处理,中心差分格式处理速度最快,高阶差分格式次之,九点差分格式则最慢。

Abstract

The partial differential equations (PDE) filtering model is an important filtering method in electronic speckle pattern interferometry (ESPI) technology. The differential operator is often approximated by difference scheme in PDE models. Three kinds of difference scheme such as central difference, nine point difference and higher difference are introduced. The representative orientation second order PDE filtering model is selected and analyzed, approximating differential operator in PDE model with three different difference schemes using simulated fringe image, simulated phase image and experiment fringe image. The result indicates the high density region and sparse density region can be balanced preferably with higher difference for large density change image. Nine point difference and central difference schemes should be deposed with average filtering. The processing rate with central difference scheme is the fastest, the higher difference takes the second place, and the nine point difference is the slowest.

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中图分类号:O436.1

DOI:10.3788/lop52.091004

所属栏目:图像处理

基金项目:国家自然科学基金(61177007)、辽宁省教育厅科学研究一般项目(L2015411)

收稿日期:2015-01-25

修改稿日期:2015-02-27

网络出版日期:2015-08-12

作者单位    点击查看

王琳霖:沈阳航空航天大学工程训练中心, 辽宁 沈阳 110136
唐晨:天津大学理学院应用物理系, 天津 300072
王亚杰:沈阳航空航天大学工程训练中心, 辽宁 沈阳 110136

联系人作者:王琳霖(wlin_23@163.com)

备注:王琳霖(1981—),女,博士,工程师,主要从事现代光学测试技术与光信息处理、图像处理等方面的研究。

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引用该论文

Wang Linlin,Tang Chen,Wang Yajie. Impact on Partial Differential Equations Filtering Models of Difference Scheme[J]. Laser & Optoelectronics Progress, 2015, 52(9): 091004

王琳霖,唐晨,王亚杰. 差分格式对偏微分方程滤波模型的影响[J]. 激光与光电子学进展, 2015, 52(9): 091004

被引情况

【1】叶小威,沈锋. 航天器轨道动力学模型及瞄准提前量误差分析. 中国激光, 2017, 44(6): 604003--1

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