Painting by numbers – restoring frescoes

You may have seen in the news this week that an elderly amateur attempted the restoration of a religious fresco. The result is pictured below.


Ecce homo from Borja

Ecce homo from Borja



I took the picture from the BBC article that you can read here.

By coincidence this week I saw an article by Carola-Bibiane Schönlieb on the mathematical technique of inpainting. This allows restoration of damaged pictures by using some mathematical process to fill in the damaged part. A particular common method is to use diffusion equations – the idea is that we use something like the heat equation. Imagine the ink on the border of the damaged region as being like heat and the heat travels into the region through conduction.

Compare the two images below take from a preprint by Schönlieb and others. The top one is a vandalized picture and the bottom is the version restored through a diffusion equation method. Most people probably wouldn’t realize that the picture had been repaired unless they’d been told.

Heat flow restoration

Heat flow restoration

Schönlieb and others have worked on restoring the following Austrian fresco

Austrian fresco

Austrian fresco


Here’s a picture of the proposed restoration (unfortunately only in black and white):
Proposed fresco restoration

Proposed fresco restoration


The pictures come from a paper which contains the details.

The article I saw this week is more accessible and can be read in the Matlab Mathworks Newsletter

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