In practical applications, images are often corroded by noise. These noises are dust or water droplets on the lens, or scratches from old photos, or the image is artificially painted or part of the image Itself has been damaged.

在实际应用中，图像经常被噪声腐蚀。 这些噪音是镜头上的灰尘或水滴，或者是旧照片的划痕，或者是人为绘制的图像，或者图像的一部分已损坏。

Generally speaking, there are two main image restoration methods in the literature:

一般而言，文献中有两种主要的图像恢复方法：

• The purpose of the PDE-based method is to extend the line or edge in the known area to the area specified by the user. These areas pay full attention to the structure propagation, but are not suitable for handling large areas due to the blur effect in their cases.
  基于PDE的方法的目的是将已知区域中的线或边扩展到用户指定的区域。 这些区域充分注意结构的传播，但是由于其情况下的模糊效果，因此不适合处理大区域。
• The example-based method uses a texture synthesis method to synthesize pixels in a user-specified area.
  基于示例的方法使用纹理合成方法来合成用户指定区域中的像素。

This article mainly studies small-scale damaged image inpainting technology and large-scale damaged image completion technology and related applications.

本文主要研究小型破损图像修复技术和大型破损图像完成技术及其相关应用。

基于补丁的方法 (Patch-based Method)

Let I be an input image defined on Ω, and O be the occluded region in Ω. We note D = Ω∖O the unoccluded region. The image I is known on D but unknown on O.

设I是在Ω上定义的输入图像，O是在Ω上的遮挡区域。 我们注意到D =Ω∖ O未被遮挡的区域。 我在D上已知的图像，但在O上未知。

We consider here odd sizes of patches :

我们在这里考虑补丁的奇数大小：

We first define a neighbourhood associated with this size of patch Ψ :

我们首先定义与补丁Ψ的大小相关的邻域：

We define the patch Ψ_p, a patch centred on pixel p as a vector of the pixel values in the patch neighbourhood around p:

我们定义补丁Ψ_p(一个以像素p为中心的补丁)作为p周围补丁附近的像素值的矢量：

This definition is basically a square centred around the pixel p

该定义基本上是围绕像素p的正方形

We note D˜ the set of unoccluded pixels in Ω whose (2a+1)×(2a+1) neighborhoods are also unoccluded.

我们注意到d〜在Ω其(2A + 1)设定的未被遮挡像素×(2A + 1)邻域也未被遮挡。

Wexler et al. [1] presented a general algorithm for video inpainting that was the predecessor of the bidirectional similarity approach and requires no object detection or segmentation.

Wexler等。 [1]提出了一种通用的视频修复算法，该算法是双向相似性方法的前身，并且不需要对象检测或分割。

The method basically maximizes a coherence term of the form.

该方法基本上使形式的连贯项最大化。

where ϕ is a correspondence map between pixels in Ω that must satisfy x+ϕ(x)∈D˜ fo