Mesmerising Mathematics

The Centre for Mathematical Studies in Cambridge is running a photo competition this year in an effort to build a library of photos to use for publicity. It is open to current and former employees, students and visitors of the CMS. I teamed up with Joana Grah and Veronica Corona and we submitted images to two out of the three categories: ‘Mathematics at Cambridge’ and ‘Life at CMS’.

Ellese Cotterill in her office at the Centre for Mathematical Studies in Cambridge
Veronica Corona and Joana Grah. This was the image we submitted to the “Life at CMS” category.
Veronica Corona outside the CMS
This is a version of the photo of Veronica Corona and Joana Grah that we submitted. In the original version we also marked parts of the textures with grey circles. For the submitted version, click here (full res).

We revisit the artistic Droste effect, that is an infinite reproduction of a photo within itself, in a mathematical sense. The recursive image follows the mathematical total variation flow. Starting from the original photo we evolve, or in optimisation terms we regularised the texture while preserving edges. The result is that the photo progressively becomes more piecewise constant in a cartoon-like effect, until we end up with a constant image.

The algorithm taken from http://guygilboa.eew.technion.ac.il/code/spectral-total-variation-color/ is based on the paper “A total variation spectral framework for scale and texture analysis” by Guy Gilboa (see reference).
By pointing at the grass and leaf textures, we want to stress that the decomposition yields a spectral component corresponding to texture, revealed just underneath the fingertips.
 
Reference: G. Gilboa, “A total variation spectral framework for scale and texture analysis.” SIAM Journal on Imaging Sciences 7.4 (2014): 1937-1961. (link)
Veronica Corona

It is not a proper photoshoot unless you take some fun photos as well.

Veronica Corona and Joana Grah.
Veronica Corona and Joana Grah. #womance

Click here to see more blog posts with photos from the CMS.

Many thanks to Joana and Veronica for a great collaboration. It was great to be back for a bit at CMS and see some of the old crew. Also thanks to Ellese! See you guys next visit!

— Johannes

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