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Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion to Preserve Singularities and Delete Isolated Points in Image Smoothing

机译：非线性各向异性扩散的封闭拉普拉斯算子，可保留奇点并删除图像平滑中的孤立点

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摘要

Existing Nonlinear Anisotropic Diffusion (NAD) methods in image smoothing cannot obtain satisfied results near singularities and isolated points because of the discretization errors. In this paper, we propose a new scheme, named Enclosed Laplacian Operator of Nonlinear Anisotropic Diffusion (ELONAD), which allows us to provide a unified framework for points in flat regions, edge points and corners, even can delete isolated points and spurs. ELONAD extends two diffusion directions of classical NAD to eight or more enclosed directions. Thus it not only performs NAD according to modules of enclosed directions which can reduce the influence of traction errors greatly, but also distinguishes isolated points and small spurs from corners which must be preserved. Smoothing results for test patterns and real images using different discretization schemes are also given to test and verify our discussions.
机译：由于离散化误差，图像平滑中的现有非线性各向异性扩散（NAD）方法无法在奇异点和孤立点附近获得满意的结果。在本文中，我们提出了一种新的方案，称为非线性各向异性扩散的封闭拉普拉斯算子（ELONAD），它使我们能够为平坦区域，边缘点和拐角处的点提供统一的框架，甚至可以删除孤立的点和杂散。 ELONAD将经典NAD的两个扩散方向扩展到八个或更多封闭方向。因此，它不仅可以根据封闭方向的模块执行NAD，从而可以大大减少牵引误差的影响，而且可以将孤立的点和小的杂点与必须保留的角落区分开。还给出了使用不同离散方案的测试图案和真实图像的平滑结果，以测试和验证我们的讨论。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第2期|p.1-15|共15页
  • 作者

    Zhiwu Liao; Shaoxiang Hu; Dan Sun; Wufan Chen;

  • 作者单位

    Key Laboratory of Land Resources Evaluation and Monitoring in Southwest (Sichuan Normal University), Ministry of Education, Chengdu 610066, China,School of Computer Science, Sichuan Normal University, Chengdu 610066, China;

    School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China;

    School of Computer Science, Sichuan Normal University, Chengdu 610066, China;

    Institute of Medical Information and Technology, School of Biomedical Engineering, Southern Medical University, Guangzhou 510515, China;

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