应用热传导模型的偏微分方程图像修复

将图像修复类比于热传导过程，采用有限差分迭代求解一阶线性偏微分方程组，使图像缺损区周围有效像素所包含的信息逐步向缺损区域传递.相比于其他偏微分方程（PDE）图像修复技术，该方法采用更为简洁的数学表达，能以较低的计算复杂度实现有效的图像结构层修复.通过滤波提取缺损区以外的图像纹理，叠加到被修复区以获得更为自然的视觉效果.实验结果表明，该方法适用于修复图像中的小块缺损和划痕，消除可见水印等叠加成分或从图像中删除某些不需要的局部内容.

PDE-Based Image Inpainting Using a Heat Transfer Model

We use a heat transfer model to treat the image inpainting problem,in which the pixel gray level is analogous to temperature.A finite difference method is developed to solve the partial differential equations(PDE) numerically,and the information contained in the neighborhood is propagated into the missing area in an iterative fashion.Compared to other PDE-based method,this approach is relatively simple,giving satisfactory fill-in effects of the cartoon layer of the damaged image with low computation complexity.Texture information is extracted from the area around the hole,and added to the repaired patches to produce a more natural appearance.Experimental results are presented to show effectiveness of the method.