Multi-Resolution Image Inpainting

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.