Shape from Shading Based on Lax-Friedrichs Fast Sweeping and Regularization Techniques With Applications to Document Image Restoration
Shape from Shading Based on Lax-Friedrichs Fast Sweeping and Regularization Techniques With Applications to Document Image Restoration
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基于Lax-Friedrichs快速扫描和正则化技术的阴影形状及其在文档图像恢复中的应用
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
C. Tan
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文献类型：
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作者：
Li Zhang;A. Yip;C. Tan
在本文中，我们描述了一种 2 遍迭代方案来求解与远距离和近点光源下的阴影形状 (SFS) 问题相关的一般偏微分方程 (PDE)。我们特别讨论了它在恢复日常快照中经常出现的扭曲文档图像方面的应用。所提出的方法包括两个步骤。首先，将图像辐照度方程表述为静态 Hamilton-Jacobi (HJ) 方程，并使用 Lax-Friedrichs Hamiltonian 的快速扫描策略进行求解。然而，当应用于真实文档图像时，由于近似阴影图像中的噪声，可能会出现突然的错误。为了降低噪声敏感性，采用最小化方法来平滑初始结果中的陡峭脊并产生更好的重建。与地面真实数据相比，合成表面的实验显示出有希望的结果。此外，还开发了一个通用框架，表明SFS方法可以帮助消除扭曲文档图像中的几何和光度畸变，以获得更好的视觉外观和更高的识别率。
In this paper, we describe a 2-pass iterative scheme to solve the general partial differential equation (PDE) related to the Shape-from-Shading (SFS) problem under both distant and close point light sources. In particular, we discuss its applications in restoring warped document images that often appear in the daily snapshots. The proposed method consists of two steps. First the image irradiance equation is formulated as a static Hamilton-Jacobi (HJ) equation and solved using a fast sweeping strategy with Lax-Friedrichs Hamiltonian. However, abrupt errors may arise when applying to real document images due to noises in the approximated shading image. To reduce the noise sensitivity, a minimization method thus follows to smooth out the abrupt ridges in the initial result and produce a better reconstruction. Experiments on synthetic surfaces show promising results comparing to the ground truth data. Moreover, a general framework is developed, which demonstrates that the SFS method can help to remove both geometric and photometric distortions in warped document images for better visual appearance and higher recognition rate.