Maths ... it gives you wings!

Maths ... it gives you wings!

Our image of the week shows Joana Grah, the levitating PhD student.

Image by Carola-Bibiane Schönlieb, Joana Grah and Kostas Papafitsoros.

It's not supernatural powers that help Joana fly, but the equation on the blackboard. This partial differential equation can be used to fill in specific parts of an image based on what's around it. The process is called inpainting. For this image the equation was solved numerically to remove the stool Joana was sitting on. Image inpainting has wide ranging practical applications: from the restoration of satellite images, enhancement of medical images, the renovation of digital photographs and artwork, to special effects in images and videos.

This image was created by Carola-Bibiane Schönlieb, head of the Cambridge Image Analysis group at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Joana Grah and Kostas Papafitsoros. It won the EPSRC science photo competition in 2013. You can read more about Schönlieb's work on inpainting in this Plus article.

See here to see previous images of the week.

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