| 基于偏微分方程的图像修补方法 |
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| 引用本文： | 赵恒军,牛艳霞.基于偏微分方程的图像修补方法[J].河南纺织高等专科学校学报,2010(1):60-62. |
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| 作者姓名： | 赵恒军 牛艳霞 |
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| 作者单位： | [1]河南工程学院数理科学系,河南郑州451191 [2]中原工学院理学院,河南郑州450007 |
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| 基金项目： | 河南工程学院校级科研基金项目（Y09055） |
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| 摘 要： | 根据最小能量化泛函所建立的图像修补模型可以得到其欧拉方程，把该欧拉方程所对应的梯度下降流作用于需要修补的图像，当偏微分方程的解稳定时，此时的解就是修补后的图像．基于该原理建立了一个图像修补方程，并实现了此图像修补算法．从这个修补方法的修补效果可以看到，修补后的图像具有良好的光滑性．
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| 关 键 词： | 图像修补 偏微分方程 变分法 梯度递减 |
Image Inpainting Algorithm Based on Partial Differential Equation |
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| ZHAO Hengjun,NIU Yanxia.Image Inpainting Algorithm Based on Partial Differential Equation[J].Journal of Henan Textile College,2010(1):60-62. |
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| Authors: | ZHAO Hengjun NIU Yanxia |
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| Affiliation: | 1. Department of Mathematics and Physical Science, Henan Institute of Engineering, Zhengzhou 451191, China; 2. Colledge of Science , Zhongyuan University of Technology, Zhengzhou 450007, China) |
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| Abstract: | At first the theory of image inpainting based on PDE is be proposed： the Euler equation from the image inpainting model based on the minimum energy-based faction is constructed, then the gradient descent corresponding to the Euler equation can work for the image being patched. When the final answer of PDE is stable, this final answer will be the patched image. Then one equation of image inpainting using this method is established. Through the patching effects of the different equations of image inpainting, we can see that it make the image smooth very well. |
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| Keywords: | image inpainting partial differential equation calculus of variations gradient descent |
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