# Multi-Resolution Image Inpainting

### color percentage threshold dib

**Definition:** Multiple resolution approach can be used in image inpainting (see the article on Digital Inpainting).

We firefly summarize below the mechanism of multi-resolution image painting. The algorithm is further extended and used in a multiple layer approach to repair Chinese paintings .

Let **DIB** be a damaged image block, Let **a** be a threshold of variance, Let **ß 1** , **ß 2** be a threshold of

percentage, **ß 1** < **ß 2**

Algorithm inPaint(block **DIB** )

if **DIB** is a small block then return

divide **DIB** into *n*n* image blocks

for each image block **IB**

let *var* be the color variance of **IB** , let *Mcolor* be the mean color of **IB**

if *var* < **a** then {/** 1 **/

let **PB** be an *x*y* pixel block in **IB** , let *Ncolor* be the mean color of **PB**

for each PB in the image block {/** 2 **/

if the percentage of damaged pixels in **PB** > **ß 2**

inpaint the damaged pixels using *Mcolor*

else if the percentage of damaged pixels in **PB** > **ß 1**

inpaint the damaged pixels using *Ncolor*

else

inpaint the damaged pixels using neighbor pixels

} /** 2 **/

} /** 1 **/

else

call inPaint( **IB** )

Color variance has a strong indication of the degree of details in an **IB** . The threshold **a** sets the criterion of whether a multi-resolution inpainting is required. In our implementation, the value of **a** is a percentage in the range between 0 and 100 (the maximum *var)* of an **IB.** Another criterion is the percentage of potential damaged pixels. We argue that, if the percentage is too high, using surrounding color information to fix a pixel is less realistic as compared to using a global average color. In some severe cases, it is impossible to use neighborhood colors. Note that, both thresholds are adjustable for the sake of analysis. The recursive algorithm iterates through each of the **IBs** in a **DIB.** If the color variance of **IB** is below the threshold **a** , there is not much difference of pixels in **IB.** No subdivision is required (i.e., no need of looking at the next level of details). Thus, the algorithm further divides **IB** into several pixel blocks (i.e., **PB** s). If the percentage of damaged pixels in a **PB** is too high (i.e., greater than **ß 2** ), the mean color of **IB** is used. One example is that the entire **PB** is damaged (thus we need to use the mean color of **IB** ). Alternatif the percentage is still high (i.e., greater than **ß 1** ), the mean color of **PB** is used. Note that, the computation of mean colors does not take damaged pixels into the account. If the percentage is low, neighbor pixels are used for inpainting. Finall color variance of **IB** is not below the threshold **a** , the algorithm is called recursively to handle the next level of details. In the article , a complete analysis is given to show the inpainted results are satisfiable.

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